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"cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "# Data Analysis and Machine Learning\n", - "\n", - " \n", - "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", - "\n", - "Date: **Jan 27, 2018**\n", - "\n", - "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "# What is Machine Learning?\n", - "\n", - "Machine learning is the science of giving computers the ability to\n", - "learn without being explicitly programmed. The idea is that there\n", - "exist generic algorithms which can be used to find patterns in a broad\n", - "class of data sets without having to write code specifically for each\n", - "problem. The algorithm will build its own logic based on the data.\n", - "\n", - "Machine learning is a subfield of computer science, and is closely\n", - "related to computational statistics. It evolved from the study of\n", - "pattern recognition in artificial intelligence (AI) research, and has\n", - "made contributions to AI tasks like computer vision, natural language\n", - "processing and speech recognition. It has also, especially in later\n", - "years, found applications in a wide variety of other areas, including\n", - "bioinformatics, economy, physics, finance and marketing.\n", - "\n", - "\n", - "## Types of Machine Learning\n", - "\n", - "\n", - "The approaches to machine learning are many, but are often split into two main categories. \n", - "In *supervised learning* we know the answer to a problem,\n", - "and let the computer deduce the logic behind it. On the other hand, *unsupervised learning*\n", - "is a method for finding patterns and relationship in data sets without any prior knowledge of the system.\n", - "Some authours also operate with a third category, namely *reinforcement learning*. This is a paradigm \n", - "of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, \n", - "solely from rewards and punishment.\n", - "\n", - "Another way to categorize machine learning tasks is to consider the desired output of a system.\n", - "Some of the most common tasks are:\n", - "\n", - " * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.\n", - "\n", - " * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.\n", - "\n", - " * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.\n", - "\n", - "## Different algorithms\n", - "In this course we will build our machine learning approach on a statistical foundation, with elements \n", - "from data analysis, stochastic processes etc before we proceed with the following machine learning algorithms\n", - "\n", - "1. Linear regression and its variants\n", - "\n", - "2. Decision tree algorithms, from simpler to more complex ones\n", - "\n", - "3. Nearest neighbors models\n", - "\n", - "4. Bayesian statistics \n", - "\n", - "5. Support vector machines and finally various variants of\n", - "\n", - "6. Artifical neural networks\n", - "\n", - "Before we proceed however, there are several practicalities with data analysis and software tools we would \n", - "like to present. These tools will help us in our understanding of various machine learning algorithms. \n", - "\n", - "Our emphasis here is on understanding the mathematical aspects of different algorithms, however, where possible \n", - "we will emphasize the importance of using available software. \n", - "\n", - "\n", - "\n", - "## Software and needed installations\n", - "We will make intensive use of python as programming language and the myriad of available libraries. \n", - "Furthermore, you will find IPython/Jupyter notebooks invaluable in your work. \n", - "You can run **R** codes in the Jupyter/IPython notebooks, with the immediate benefit of visualizing your data.\n", - "\n", - "\n", - "If you have Python installed (we recommend Python3) and you feel pretty familiar with installing different packages, \n", - "we recommend that you install the following Python packages via **pip** as\n", - "1. pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow\n", - "\n", - "For Python3, replace **pip** with **pip3**.\n", - "\n", - "For OSX users we recommend also, after having installed Xcode, to install **brew**. Brew allows \n", - "for a seamless installation of additional software via for example\n", - "1. brew install python3\n", - "\n", - "For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution\n", - "you can use **pip** as well and simply install Python as \n", - "1. sudo apt-get install python3 (or python for pyhton2.7)\n", - "\n", - "etc etc. \n", - "\n", - "\n", - "## Python installers\n", - "If you don't want to perform these operations separately, we recommend two widely used distrubutions which set up \n", - "all relevant dependencies for Python, namely\n", - "1. [Anaconda](https://docs.anaconda.com/) Anaconda is an open source distribution of the Python and R programming languages for large-scale data processing, predictive analytics, and scientific computing, that aims to simplify package management and deployment. Package versions are managed by the package management system **conda**\n", - "\n", - "2. [Enthought canopy](https://www.enthought.com/product/canopy/) is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.\n", - "\n", - "## Installing R, C++, cython or Julia\n", - "\n", - "You will also find it convenient to utilize R. \n", - "Jupyter/Ipython notebook allows you run **R** code interactively in your browser. The software library **R** is \n", - "tuned to statistically analysis and allows for an easy usage of the tools we will discuss in these texts.\n", - "\n", - "To install **R** with Jupyter notebook [following the link here](https://mpacer.org/maths/r-kernel-for-ipython-notebook)\n", - "\n", - "\n", - "\n", - "\n", - "## Installing R, C++, cython or Julia\n", - "\n", - "\n", - "For the C++ affecianodas, Jupyter/IPython notebook allows you also to install C++ and run codes written in this language \n", - "interactively in the browser. Since we will emphasize writing many of the algorithms yourself, you can thus opt for\n", - "either Python or C++ as programming languages. \n", - "\n", - "To add more entropy, **cython** can also be used when running your notebooks. It means that Python with the Jupyter/IPython notebook \n", - "setup allows you to integrate widely popular softwares and tools for scientific computing. With its versatility, \n", - "including symbolic operations, Python offers a unique computational environment. Your Jupyter/IPython notebook \n", - "can easily be converted into a nicely rendered **PDF** file or a Latex file for further processing. For example, convert to latex as" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "jupyter nbconvert filename.ipynb --to latex" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If you use the light mark-up language **doconce** you can convert a standard ascii text file into various HTML \n", - "formats, ipython notebooks, latex files, pdf files etc. \n", - "\n", - "\n", - "\n", - "\n", - "## Introduction to Jupyter notebook and available tools" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy import sparse\n", - "import pandas as pd\n", - "from IPython.display import display\n", - "eye = np.eye(4)\n", - "print(eye)\n", - "sparse_mtx = sparse.csr_matrix(eye)\n", - "print(sparse_mtx)\n", - "x = np.linspace(-10,10,100)\n", - "y = np.sin(x)\n", - "plt.plot(x,y,marker='x')\n", - "plt.show()\n", - "data = {'Name': [\"John\", \"Anna\", \"Peter\", \"Linda\"], 'Location': [\"Nairobi\", \"Napoli\", \"London\", \"Buenos Aires\"], 'Age':[51, 21, 34, 45]}\n", - "data_pandas = pd.DataFrame(data)\n", - "display(data_pandas)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Representing data, more examples" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy import sparse\n", - "import pandas as pd\n", - "from IPython.display import display\n", - "import mglearn\n", - "import sklearn\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.tree import DecisionTreeRegressor\n", - "x, y = mglearn.datasets.make_wave(n_samples=100)\n", - "line = np.linspace(-3,3,1000,endpoint=False).reshape(-1,1)\n", - "reg = DecisionTreeRegressor(min_samples_split=3).fit(x,y)\n", - "plt.plot(line, reg.predict(line), label=\"decision tree\")\n", - "regline = LinearRegression().fit(x,y)\n", - "plt.plot(line, regline.predict(line), label= \"Linear Rgression\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Predator-Prey model from ecology\n", - "\n", - "\n", - "The population dynamics of a simple predator-prey system is a\n", - "classical example shown in many biology textbooks when ecological\n", - "systems are discussed. The system contains all elements of the\n", - "scientific method:\n", - "\n", - " * The set up of a specific hypothesis combined with\n", - "\n", - " * the experimental methods needed (one can study existing data or perform experiments)\n", - "\n", - " * analyzing and interpreting the data and performing further experiments if needed\n", - "\n", - " * trying to extract general behaviors and extract eventual laws or patterns\n", - "\n", - " * develop mathematical relations for the uncovered regularities/laws and test these by per forming new experiments\n", - "\n", - "## Case study from Hudson bay\n", - "\n", - "\n", - "Lots of data about populations of hares and lynx collected from furs in Hudson Bay, Canada, are available. It is known that the populations oscillate. Why?\n", - "Here we start by\n", - "\n", - "1. plotting the data\n", - "\n", - "2. derive a simple model for the population dynamics\n", - "\n", - "3. (fitting parameters in the model to the data)\n", - "\n", - "4. using the model predict the evolution other predator-pray systems\n", - "\n", - "## Hudson bay data\n", - "\n", - "\n", - "\n", - "\n", - "Most mammalian predators rely on a variety of prey, which complicates mathematical modeling; however, a few predators have become highly specialized and seek almost exclusively a single prey species. An example of this simplified predator-prey interaction is seen in Canadian northern forests, where the populations of the lynx and the snowshoe hare are intertwined in a life and death struggle.\n", - "\n", - "One reason that this particular system has been so extensively studied is that the Hudson Bay company kept careful records of all furs from the early 1800s into the 1900s. The records for the furs collected by the Hudson Bay company showed distinct oscillations (approximately 12 year periods), suggesting that these species caused almost periodic fluctuations of each other's populations. The table here shows data from 1900 to 1920.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "
Year Hares (x1000) Lynx (x1000)
1900 30.0 4.0
1901 47.2 6.1
1902 70.2 9.8
1903 77.4 35.2
1904 36.3 59.4
1905 20.6 41.7
1906 18.1 19.0
1907 21.4 13.0
1908 22.0 8.3
1909 25.4 9.1
1910 27.1 7.4
1911 40.3 8.0
1912 57 12.3
1913 76.6 19.5
1914 52.3 45.7
1915 19.5 51.1
1916 11.2 29.7
1917 7.6 15.8
1918 14.6 9.7
1919 16.2 10.1
1920 24.7 8.6
\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Plotting the data" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "from matplotlib import pyplot as plt\n", - "\n", - "# Load in data file\n", - "data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1)\n", - "# Make arrays containing x-axis and hares and lynx populations\n", - "year = data[:,0]\n", - "hares = data[:,1]\n", - "lynx = data[:,2]\n", - "\n", - "plt.plot(year, hares ,'b-+', year, lynx, 'r-o')\n", - "plt.axis([1900,1920,0, 100.0])\n", - "plt.xlabel(r'Year')\n", - "plt.ylabel(r'Numbers of hares and lynx ')\n", - "plt.legend(('Hares','Lynx'), loc='upper right')\n", - "plt.title(r'Population of hares and lynx from 1900-1920 (x1000)}')\n", - "plt.savefig('Hudson_Bay_data.pdf')\n", - "plt.savefig('Hudson_Bay_data.png')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hares and lynx in Hudson bay from 1900 to 1920\n", - "\n", - "\n", - "\n", - "\n", - "

\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Why now create a computer model for the hare and lynx populations?\n", - "\n", - "We see from the plot that there are indeed fluctuations.\n", - "We would like to create a mathematical model that explains these\n", - "population fluctuations. Ecologists have predicted that in a simple\n", - "predator-prey system that a rise in prey population is followed (with\n", - "a lag) by a rise in the predator population. When the predator\n", - "population is sufficiently high, then the prey population begins\n", - "dropping. After the prey population falls, then the predator\n", - "population falls, which allows the prey population to recover and\n", - "complete one cycle of this interaction. Thus, we see that\n", - "qualitatively oscillations occur. Can a mathematical model predict\n", - "this? What causes cycles to slow or speed up? What affects the\n", - "amplitude of the oscillation or do you expect to see the oscillations\n", - "damp to a stable equilibrium? The models tend to ignore factors like\n", - "climate and other complicating factors. How significant are these?\n", - "\n", - " * We see oscillations in the data\n", - "\n", - " * What causes cycles to slow or speed up?\n", - "\n", - " * What affects the amplitude of the oscillation or do you expect to see the oscillations damp to a stable equilibrium?\n", - "\n", - " * With a model we can better *understand the data*\n", - "\n", - " * More important: we can understand the ecology dynamics of\n", - " predator-pray populations\n", - "\n", - "## The traditional (top-down) approach\n", - "\n", - "\n", - "The classical way (in all books) is to present the Lotka-Volterra equations:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "\\frac{dH}{dt} &= H(a - b L)\\\\\n", - "\\frac{dL}{dt} &= - L(d - c H)\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here,\n", - "\n", - " * $H$ is the number of preys\n", - "\n", - " * $L$ the number of predators\n", - "\n", - " * $a$, $b$, $d$, $c$ are parameters\n", - "\n", - "Most books quickly establish the model and then use considerable space on\n", - "discussing the qualitative properties of this *nonlinear system of\n", - "ODEs* (which cannot be solved)\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Basic mathematics notation\n", - "\n", - " * Time points: $t_0,t_1,\\ldots,t_m$\n", - "\n", - " * Uniform distribution of time points: $t_n=n\\Delta t$\n", - "\n", - " * $H^n$: population of hares at time $t_n$\n", - "\n", - " * $L^n$: population of lynx at time $t_n$\n", - "\n", - " * We want to model the changes in populations, $\\Delta H=H^{n+1}-H^n$\n", - " and $\\Delta L=L^{n+1}-L^n$ during a general time interval $[t_{n+1},t_n]$\n", - " of length $\\Delta t=t_{n+1}-t_n$\n", - "\n", - "## Basic dynamics of the population of hares\n", - "\n", - "\n", - "The population of hares evolves due to births and deaths exactly as a bacteria population:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\Delta H = a \\Delta t H^n\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "However, hares have an additional loss in the population because\n", - "they are eaten by lynx.\n", - "All the hares and lynx can form\n", - "$H\\cdot L$ pairs in total. When such pairs meet during a time\n", - "interval $\\Delta t$, there is some\n", - "small probablity that the lynx will eat the hare.\n", - "So in fraction $b\\Delta t HL$, the lynx eat hares. This\n", - "loss of hares must be accounted for. Subtracted in the equation for hares:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\Delta H = a\\Delta t H^n - b \\Delta t H^nL^n\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Basic dynamics of the population of lynx\n", - "\n", - "\n", - "We assume that the primary growth for the lynx population depends on sufficient food for raising lynx kittens, which implies an adequate source of nutrients from predation on hares. Thus, the growth of the lynx population does not only depend of how many lynx there are, but on how many hares they can eat.\n", - "In a time interval $\\Delta t HL$ hares and lynx can meet, and in a\n", - "fraction $b\\Delta t HL$ the lynx eats the hare. All of this does not\n", - "contribute to the growth of lynx, again just a fraction of\n", - "$b\\Delta t HL$ that we write as\n", - "$d\\Delta t HL$. In addition, lynx die just as in the population\n", - "dynamics with one isolated animal population, leading to a loss\n", - "$-c\\Delta t L$.\n", - "\n", - "\n", - "\n", - "The accounting of lynx then looks like" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\Delta L = d\\Delta t H^nL^n - c\\Delta t L^n\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Evolution equations\n", - "\n", - "\n", - "By writing up the definition of $\\Delta H$ and $\\Delta L$, and putting\n", - "all assumed known terms $H^n$ and $L^n$ on the right-hand side, we have" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "H^{n+1} = H^n + a\\Delta t H^n - b\\Delta t H^n L^n\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "L^{n+1} = L^n + d\\Delta t H^nL^n - c\\Delta t L^n\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note:\n", - "\n", - " * These equations are ready to be implemented!\n", - "\n", - " * But to start, we need $H^0$ and $L^0$ \n", - " (which we can get from the data)\n", - "\n", - " * We also need values for $a$, $b$, $d$, $c$\n", - "\n", - "## Adapt the model to the Hudson Bay case\n", - "\n", - "\n", - " * As always, models tend to be general - as here, applicable\n", - " to \"all\" predator-pray systems\n", - "\n", - " * The critical issue is whether the *interaction* between hares and lynx\n", - " is sufficiently well modeled by $\\hbox{const}HL$\n", - "\n", - " * The parameters $a$, $b$, $d$, and $c$ must be\n", - " estimated from data\n", - "\n", - " * Measure time in years\n", - "\n", - " * $t_0=1900$, $t_m=1920$\n", - "\n", - "## The program" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "def solver(m, H0, L0, dt, a, b, c, d, t0):\n", - " \"\"\"Solve the difference equations for H and L over m years\n", - " with time step dt (measured in years.\"\"\"\n", - "\n", - " num_intervals = int(m/float(dt))\n", - " t = np.linspace(t0, t0 + m, num_intervals+1)\n", - " H = np.zeros(t.size)\n", - " L = np.zeros(t.size)\n", - "\n", - " print('Init:', H0, L0, dt)\n", - " H[0] = H0\n", - " L[0] = L0\n", - "\n", - " for n in range(0, len(t)-1):\n", - " H[n+1] = H[n] + a*dt*H[n] - b*dt*H[n]*L[n]\n", - " L[n+1] = L[n] + d*dt*H[n]*L[n] - c*dt*L[n]\n", - " return H, L, t\n", - "\n", - "# Load in data file\n", - "data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1)\n", - "# Make arrays containing x-axis and hares and lynx populations\n", - "t_e = data[:,0]\n", - "H_e = data[:,1]\n", - "L_e = data[:,2]\n", - "\n", - "# Simulate using the model\n", - "H, L, t = solver(m=20, H0=34.91, L0=3.857, dt=0.1,\n", - " a=0.4807, b=0.02482, c=0.9272, d=0.02756,\n", - " t0=1900)\n", - "\n", - "# Visualize simulations and data\n", - "plt.plot(t_e, H_e, 'b-+', t_e, L_e, 'r-o', t, H, 'm--', t, L, 'k--')\n", - "plt.xlabel('Year')\n", - "plt.ylabel('Numbers of hares and lynx')\n", - "plt.axis([1900, 1920, 0, 140])\n", - "plt.title(r'Population of hares and lynx 1900-1920 (x1000)')\n", - "plt.legend(('H_e', 'L_e', 'H', 'L'), loc='upper left')\n", - "plt.savefig('Hudson_Bay_sim.pdf')\n", - "plt.savefig('Hudson_Bay_sim.png')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The plot\n", - "\n", - "\n", - "\n", - "\n", - "

\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "If we perform a least-square fitting, we can find optimal values for the parameters $a$, $b$, $d$, $c$. The optimal parameters are $a=0.4807$, $b=0.02482$, $d=0.9272$ and $c=0.02756$. These parameters result in a slightly modified initial conditions, namely $H(0) = 34.91$ and $L(0)=3.857$. With these parameters we are now ready to solve the equations and plot these data together with the experimental values.\n", - "\n", - "\n", - "\n", - "## Linear regression in Python" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from IPython.display import display\n", - "import sklearn\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.tree import DecisionTreeRegressor\n", - "\n", - "\n", - "data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1)\n", - "x = data[:,0]\n", - "y = data[:,1]\n", - "line = np.linspace(1900,1920,1000,endpoint=False).reshape(-1,1)\n", - "reg = DecisionTreeRegressor(min_samples_split=3).fit(x.reshape(-1,1),y.reshape(-1,1))\n", - "plt.plot(line, reg.predict(line), label=\"decision tree\")\n", - "regline = LinearRegression().fit(x.reshape(-1,1),y.reshape(-1,1))\n", - "plt.plot(line, regline.predict(line), label= \"Linear Regression\")\n", - "plt.plot(x, y, label= \"Linear Regression\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Linear Least squares in R" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " HudsonBay = read.csv(\"src/Hudson_Bay.csv\",header=T)\n", - " fix(HudsonBay)\n", - " dim(HudsonBay)\n", - " names(HudsonBay)\n", - " plot(HudsonBay$Year, HudsonBay$Hares..x1000.)\n", - " attach(HudsonBay)\n", - " plot(Year, Hares..x1000.)\n", - " plot(Year, Hares..x1000., col=\"red\", varwidth=T, xlab=\"Years\", ylab=\"Haresx 1000\")\n", - " summary(HudsonBay)\n", - " summary(Hares..x1000.)\n", - " library(MASS)\n", - " library(ISLR)\n", - " scatter.smooth(x=Year, y = Hares..x1000.)\n", - " linearMod = lm(Hares..x1000. ~ Year)\n", - " print(linearMod)\n", - " summary(linearMod)\n", - " plot(linearMod)\n", - " confint(linearMod)\n", - " predict(linearMod,data.frame(Year=c(1910,1914,1920)),interval=\"confidence\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Non-Linear Least squares in R" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " set.seed(1485)\n", - " len = 24\n", - " x = runif(len)\n", - " y = x^3+rnorm(len, 0,0.06)\n", - " ds = data.frame(x = x, y = y)\n", - " str(ds)\n", - " plot( y ~ x, main =\"Known cubic with noise\")\n", - " s = seq(0,1,length =100)\n", - " lines(s, s^3, lty =2, col =\"green\")\n", - " m = nls(y ~ I(x^power), data = ds, start = list(power=1), trace = T)\n", - " class(m)\n", - " summary(m)\n", - " power = round(summary(m)$coefficients[1], 3)\n", - " power.se = round(summary(m)$coefficients[2], 3)\n", - " plot(y ~ x, main = \"Fitted power model\", sub = \"Blue: fit; green: known\")\n", - " s = seq(0, 1, length = 100)\n", - " lines(s, s^3, lty = 2, col = \"green\")\n", - " lines(s, predict(m, list(x = s)), lty = 1, col = \"blue\")\n", - " text(0, 0.5, paste(\"y =x^ (\", power, \" +/- \", power.se, \")\", sep = \"\"), pos = 4)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Important Matrix and vector handling packages\n", - "\n", - "The Numerical Recipes codes have been rewritten in Fortran 90/95 and\n", - "C/C++ by us. The original source codes are taken from the widely used\n", - "software package LAPACK, which follows two other popular packages\n", - "developed in the 1970s, namely EISPACK and LINPACK.\n", - "\n", - " * LINPACK: package for linear equations and least square problems.\n", - "\n", - " * LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.\n", - "\n", - " * BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from .\n", - "\n", - "**Add python material on linear algebra and array handling, text on numpy etc**\n", - "\n", - "\n", - "## Basic Matrix Features\n", - "\n", - " Matrix properties reminder" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A} =\n", - " \\begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\\\\n", - " a_{21} & a_{22} & a_{23} & a_{24} \\\\\n", - " a_{31} & a_{32} & a_{33} & a_{34} \\\\\n", - " a_{41} & a_{42} & a_{43} & a_{44}\n", - " \\end{bmatrix}\\qquad\n", - "\\mathbf{I} =\n", - " \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\\n", - " 0 & 1 & 0 & 0 \\\\\n", - " 0 & 0 & 1 & 0 \\\\\n", - " 0 & 0 & 0 & 1\n", - " \\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Basic Matrix Features\n", - "\n", - "The inverse of a matrix is defined by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}^{-1} \\cdot \\mathbf{A} = I\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Basic Matrix Features\n", - "\n", - " Matrix Properties Reminder\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "
Relations Name matrix elements
$A = A^{T}$ symmetric $a_{ij} = a_{ji}$
$A = \\left (A^{T} \\right )^{-1}$ real orthogonal $\\sum_k a_{ik} a_{jk} = \\sum_k a_{ki} a_{kj} = \\delta_{ij}$
$A = A^{ * }$ real matrix $a_{ij} = a_{ij}^{ * }$
$A = A^{\\dagger}$ hermitian $a_{ij} = a_{ji}^{ * }$
$A = \\left (A^{\\dagger} \\right )^{-1}$ unitary $\\sum_k a_{ik} a_{jk}^{ * } = \\sum_k a_{ki}^{ * } a_{kj} = \\delta_{ij}$
\n", - "\n", - "\n", - "\n", - "## Some famous Matrices\n", - "\n", - " * Diagonal if $a_{ij}=0$ for $i\\ne j$\n", - "\n", - " * Upper triangular if $a_{ij}=0$ for $i > j$\n", - "\n", - " * Lower triangular if $a_{ij}=0$ for $i < j$\n", - "\n", - " * Upper Hessenberg if $a_{ij}=0$ for $i > j+1$\n", - "\n", - " * Lower Hessenberg if $a_{ij}=0$ for $i < j+1$\n", - "\n", - " * Tridiagonal if $a_{ij}=0$ for $|i -j| > 1$\n", - "\n", - " * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i > j+p$\n", - "\n", - " * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i < j+p$\n", - "\n", - " * Banded, block upper triangular, block lower triangular....\n", - "\n", - "## Basic Matrix Features\n", - "\n", - " Some Equivalent Statements\n", - "For an $N\\times N$ matrix $\\mathbf{A}$ the following properties are all equivalent\n", - "\n", - " * If the inverse of $\\mathbf{A}$ exists, $\\mathbf{A}$ is nonsingular.\n", - "\n", - " * The equation $\\mathbf{Ax}=0$ implies $\\mathbf{x}=0$.\n", - "\n", - " * The rows of $\\mathbf{A}$ form a basis of $R^N$.\n", - "\n", - " * The columns of $\\mathbf{A}$ form a basis of $R^N$.\n", - "\n", - " * $\\mathbf{A}$ is a product of elementary matrices.\n", - "\n", - " * $0$ is not eigenvalue of $\\mathbf{A}$.\n", - "\n", - "## Matrix Handling in C/C++, Static and Dynamical allocation\n", - "\n", - " Static\n", - "We have an $N\\times N$ matrix A with $N=100$\n", - "In C/C++ this would be defined as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " int N = 100;\n", - " double A[100][100];\n", - " // initialize all elements to zero\n", - " for(i=0 ; i < N ; i++) {\n", - " for(j=0 ; j < N ; j++) {\n", - " A[i][j] = 0.0;\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note the way the matrix is organized, row-major order.\n", - "\n", - "\n", - "\n", - "## Matrix Handling in C/C++\n", - "\n", - " Row Major Order, Addition\n", - "We have $N\\times N$ matrices A, B and C and we wish to\n", - "evaluate $A=B+C$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}= \\mathbf{B}\\pm\\mathbf{C} \\Longrightarrow a_{ij} = b_{ij}\\pm c_{ij},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In C/C++ this would be coded like" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " for(i=0 ; i < N ; i++) {\n", - " for(j=0 ; j < N ; j++) {\n", - " a[i][j] = b[i][j]+c[i][j]\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Matrix Handling in C/C++\n", - "\n", - " Row Major Order, Multiplication\n", - "We have $N\\times N$ matrices A, B and C and we wish to\n", - "evaluate $A=BC$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}=\\mathbf{BC} \\Longrightarrow a_{ij} = \\sum_{k=1}^{n} b_{ik}c_{kj},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In C/C++ this would be coded like" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " for(i=0 ; i < N ; i++) {\n", - " for(j=0 ; j < N ; j++) {\n", - " for(k=0 ; k < N ; k++) {\n", - " a[i][j]+=b[i][k]*c[k][j];\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Dynamic memory allocation in C/C++\n", - "\n", - "At least three possibilities in this course\n", - "\n", - " * Do it yourself\n", - "\n", - " * Use the functions provided in the library package lib.cpp\n", - "\n", - " * Use Armadillo (a C++ linear algebra library, discussion both here and at lab). \n", - "\n", - "## Matrix Handling in C/C++, Dynamic Allocation\n", - "\n", - " Do it yourself" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " int N;\n", - " double ** A;\n", - " A = new double*[N]\n", - " for ( i = 0; i < N; i++)\n", - " A[i] = new double[N];\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Always free space when you don't need an array anymore." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " for ( i = 0; i < N; i++)\n", - " delete[] A[i];\n", - " delete[] A;\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, recommended!!\n", - "\n", - " * Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. The syntax is deliberately similar to Matlab.\n", - "\n", - " * Integer, floating point and complex numbers are supported, as well as a subset of trigonometric and statistics functions. Various matrix decompositions are provided through optional integration with LAPACK, or one of its high performance drop-in replacements (such as the multi-threaded MKL or ACML libraries).\n", - "\n", - " * A delayed evaluation approach is employed (at compile-time) to combine several operations into one and reduce (or eliminate) the need for temporaries. This is accomplished through recursive templates and template meta-programming.\n", - "\n", - " * Useful for conversion of research code into production environments, or if C++ has been decided as the language of choice, due to speed and/or integration capabilities.\n", - "\n", - " * The library is open-source software, and is distributed under a license that is useful in both open-source and commercial/proprietary contexts.\n", - "\n", - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " #include \n", - " #include \n", - " \n", - " using namespace std;\n", - " using namespace arma;\n", - " \n", - " int main(int argc, char** argv)\n", - " {\n", - " mat A = randu(5,5);\n", - " mat B = randu(5,5);\n", - " \n", - " cout << A*B << endl;\n", - " \n", - " return 0;\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, how to compile and install\n", - "\n", - "For people using Ubuntu, Debian, Linux Mint, simply go to the synaptic package manager and install\n", - "armadillo from there.\n", - "You may have to install Lapack as well.\n", - "For Mac and Windows users, follow the instructions from the webpage\n", - ".\n", - "To compile, use for example (linux/ubuntu)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " c++ -O2 -o program.x program.cpp -larmadillo -llapack -lblas\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the `-l` option indicates the library you wish to link to.\n", - "\n", - "For OS X users you may have to declare the paths to the include files and the libraries as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " c++ -O2 -o program.x program.cpp -L/usr/local/lib -I/usr/local/include -larmadillo -llapack -lblas\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " #include \n", - " #include \"armadillo\"\n", - " using namespace arma;\n", - " using namespace std;\n", - " \n", - " int main(int argc, char** argv)\n", - " {\n", - " // directly specify the matrix size (elements are uninitialised)\n", - " mat A(2,3);\n", - " // .n_rows = number of rows (read only)\n", - " // .n_cols = number of columns (read only)\n", - " cout << \"A.n_rows = \" << A.n_rows << endl;\n", - " cout << \"A.n_cols = \" << A.n_cols << endl;\n", - " // directly access an element (indexing starts at 0)\n", - " A(1,2) = 456.0;\n", - " A.print(\"A:\");\n", - " // scalars are treated as a 1x1 matrix,\n", - " // hence the code below will set A to have a size of 1x1\n", - " A = 5.0;\n", - " A.print(\"A:\");\n", - " // if you want a matrix with all elements set to a particular value\n", - " // the .fill() member function can be used\n", - " A.set_size(3,3);\n", - " A.fill(5.0); A.print(\"A:\");\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " mat B;\n", - " \n", - " // endr indicates \"end of row\"\n", - " B << 0.555950 << 0.274690 << 0.540605 << 0.798938 << endr\n", - " << 0.108929 << 0.830123 << 0.891726 << 0.895283 << endr\n", - " << 0.948014 << 0.973234 << 0.216504 << 0.883152 << endr\n", - " << 0.023787 << 0.675382 << 0.231751 << 0.450332 << endr;\n", - " \n", - " // print to the cout stream\n", - " // with an optional string before the contents of the matrix\n", - " B.print(\"B:\");\n", - " \n", - " // the << operator can also be used to print the matrix\n", - " // to an arbitrary stream (cout in this case)\n", - " cout << \"B:\" << endl << B << endl;\n", - " // save to disk\n", - " B.save(\"B.txt\", raw_ascii);\n", - " // load from disk\n", - " mat C;\n", - " C.load(\"B.txt\");\n", - " C += 2.0 * B;\n", - " C.print(\"C:\");\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " // submatrix types:\n", - " //\n", - " // .submat(first_row, first_column, last_row, last_column)\n", - " // .row(row_number)\n", - " // .col(column_number)\n", - " // .cols(first_column, last_column)\n", - " // .rows(first_row, last_row)\n", - " \n", - " cout << \"C.submat(0,0,3,1) =\" << endl;\n", - " cout << C.submat(0,0,3,1) << endl;\n", - " \n", - " // generate the identity matrix\n", - " mat D = eye(4,4);\n", - " \n", - " D.submat(0,0,3,1) = C.cols(1,2);\n", - " D.print(\"D:\");\n", - " \n", - " // transpose\n", - " cout << \"trans(B) =\" << endl;\n", - " cout << trans(B) << endl;\n", - " \n", - " // maximum from each column (traverse along rows)\n", - " cout << \"max(B) =\" << endl;\n", - " cout << max(B) << endl;\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " // maximum from each row (traverse along columns)\n", - " cout << \"max(B,1) =\" << endl;\n", - " cout << max(B,1) << endl;\n", - " // maximum value in B\n", - " cout << \"max(max(B)) = \" << max(max(B)) << endl;\n", - " // sum of each column (traverse along rows)\n", - " cout << \"sum(B) =\" << endl;\n", - " cout << sum(B) << endl;\n", - " // sum of each row (traverse along columns)\n", - " cout << \"sum(B,1) =\" << endl;\n", - " cout << sum(B,1) << endl;\n", - " // sum of all elements\n", - " cout << \"sum(sum(B)) = \" << sum(sum(B)) << endl;\n", - " cout << \"accu(B) = \" << accu(B) << endl;\n", - " // trace = sum along diagonal\n", - " cout << \"trace(B) = \" << trace(B) << endl;\n", - " // random matrix -- values are uniformly distributed in the [0,1] interval\n", - " mat E = randu(4,4);\n", - " E.print(\"E:\");\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " // row vectors are treated like a matrix with one row\n", - " rowvec r;\n", - " r << 0.59499 << 0.88807 << 0.88532 << 0.19968;\n", - " r.print(\"r:\");\n", - " \n", - " // column vectors are treated like a matrix with one column\n", - " colvec q;\n", - " q << 0.81114 << 0.06256 << 0.95989 << 0.73628;\n", - " q.print(\"q:\");\n", - " \n", - " // dot or inner product\n", - " cout << \"as_scalar(r*q) = \" << as_scalar(r*q) << endl;\n", - " \n", - " // outer product\n", - " cout << \"q*r =\" << endl;\n", - " cout << q*r << endl;\n", - " \n", - " \n", - " // sum of three matrices (no temporary matrices are created)\n", - " mat F = B + C + D;\n", - " F.print(\"F:\");\n", - " \n", - " return 0;\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " #include \n", - " #include \"armadillo\"\n", - " using namespace arma;\n", - " using namespace std;\n", - " \n", - " int main(int argc, char** argv)\n", - " {\n", - " cout << \"Armadillo version: \" << arma_version::as_string() << endl;\n", - " \n", - " mat A;\n", - " \n", - " A << 0.165300 << 0.454037 << 0.995795 << 0.124098 << 0.047084 << endr\n", - " << 0.688782 << 0.036549 << 0.552848 << 0.937664 << 0.866401 << endr\n", - " << 0.348740 << 0.479388 << 0.506228 << 0.145673 << 0.491547 << endr\n", - " << 0.148678 << 0.682258 << 0.571154 << 0.874724 << 0.444632 << endr\n", - " << 0.245726 << 0.595218 << 0.409327 << 0.367827 << 0.385736 << endr;\n", - " \n", - " A.print(\"A =\");\n", - " \n", - " // determinant\n", - " cout << \"det(A) = \" << det(A) << endl;\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Armadillo, simple examples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " // inverse\n", - " cout << \"inv(A) = \" << endl << inv(A) << endl;\n", - " double k = 1.23;\n", - " \n", - " mat B = randu(5,5);\n", - " mat C = randu(5,5);\n", - " \n", - " rowvec r = randu(5);\n", - " colvec q = randu(5);\n", - " \n", - " \n", - " // examples of some expressions\n", - " // for which optimised implementations exist\n", - " // optimised implementation of a trinary expression\n", - " // that results in a scalar\n", - " cout << \"as_scalar( r*inv(diagmat(B))*q ) = \";\n", - " cout << as_scalar( r*inv(diagmat(B))*q ) << endl;\n", - " \n", - " // example of an expression which is optimised\n", - " // as a call to the dgemm() function in BLAS:\n", - " cout << \"k*trans(B)*C = \" << endl << k*trans(B)*C;\n", - " \n", - " return 0;\n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Gaussian Elimination\n", - "\n", - "We start with the linear set of equations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}\\mathbf{x} = \\mathbf{w}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We assume also that the matrix $\\mathbf{A}$ is non-singular and that the\n", - "matrix elements along the diagonal satisfy $a_{ii} \\ne 0$. Simple $4\\times 4 $ example" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{bmatrix}\n", - " a_{11}& a_{12} &a_{13}& a_{14}\\\\\n", - " a_{21}& a_{22} &a_{23}& a_{24}\\\\\n", - " a_{31}& a_{32} &a_{33}& a_{34}\\\\\n", - " a_{41}& a_{42} &a_{43}& a_{44}\\\\\n", - " \\end{bmatrix} \\begin{bmatrix}\n", - " x_1\\\\\n", - " x_2\\\\\n", - " x_3 \\\\\n", - " x_4 \\\\\n", - " \\end{bmatrix}\n", - " =\\begin{bmatrix}\n", - " w_1\\\\\n", - " w_2\\\\\n", - " w_3 \\\\\n", - " w_4\\\\\n", - " \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Gaussian Elimination\n", - "or" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{11}x_1 +a_{12}x_2 +a_{13}x_3 + a_{14}x_4=w_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{21}x_1 + a_{22}x_2 + a_{23}x_3 + a_{24}x_4=w_2 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{31}x_1 + a_{32}x_2 + a_{33}x_3 + a_{34}x_4=w_3 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{41}x_1 + a_{42}x_2 + a_{43}x_3 + a_{44}x_4=w_4. \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Gaussian Elimination\n", - "\n", - "The basic idea of Gaussian elimination is to use the first equation to eliminate the first unknown $x_1$\n", - "from the remaining $n-1$ equations. Then we use the new second equation to eliminate the second unknown\n", - "$x_2$ from the remaining $n-2$ equations. With $n-1$ such eliminations\n", - "we obtain a so-called upper triangular set of equations of the form" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "b_{11}x_1 +b_{12}x_2 +b_{13}x_3 + b_{14}x_4=y_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "b_{22}x_2 + b_{23}x_3 + b_{24}x_4=y_2 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "b_{33}x_3 + b_{34}x_4=y_3 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "b_{44}x_4=y_4. \\nonumber\n", - "\\label{eq:gaussbacksub} \\tag{1}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can solve this system of equations recursively starting from $x_n$ (in our case $x_4$) and proceed with\n", - "what is called a backward substitution. \n", - "\n", - "\n", - "## Gaussian Elimination\n", - "This process can be expressed mathematically as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " x_m = \\frac{1}{b_{mm}}\\left(y_m-\\sum_{k=m+1}^nb_{mk}x_k\\right)\\quad m=n-1,n-2,\\dots,1.\n", - "\\label{_auto1} \\tag{2}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To arrive at such an upper triangular system of equations, we start by eliminating\n", - "the unknown $x_1$ for $j=2,n$. We achieve this by multiplying the first equation by $a_{j1}/a_{11}$ and then subtract\n", - "the result from the $j$th equation. We assume obviously that $a_{11}\\ne 0$ and that\n", - "$\\mathbf{A}$ is not singular.\n", - "\n", - "\n", - "## Gaussian Elimination\n", - "\n", - "Our actual $4\\times 4$ example reads after the first operation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{bmatrix}\n", - " a_{11}& a_{12} &a_{13}& a_{14}\\\\\n", - " 0& (a_{22}-\\frac{a_{21}a_{12}}{a_{11}}) &(a_{23}-\\frac{a_{21}a_{13}}{a_{11}}) & (a_{24}-\\frac{a_{21}a_{14}}{a_{11}})\\\\\n", - "0& (a_{32}-\\frac{a_{31}a_{12}}{a_{11}})& (a_{33}-\\frac{a_{31}a_{13}}{a_{11}})& (a_{34}-\\frac{a_{31}a_{14}}{a_{11}})\\\\\n", - "0&(a_{42}-\\frac{a_{41}a_{12}}{a_{11}}) &(a_{43}-\\frac{a_{41}a_{13}}{a_{11}}) & (a_{44}-\\frac{a_{41}a_{14}}{a_{11}}) \\\\\n", - " \\end{bmatrix} \\begin{bmatrix}\n", - " x_1\\\\\n", - " x_2\\\\\n", - " x_3 \\\\\n", - " x_4 \\\\\n", - " \\end{bmatrix} \n", - " =\\begin{bmatrix}\n", - " y_1\\\\\n", - " w_2^{(2)}\\\\\n", - " w_3^{(2)} \\\\\n", - " w_4^{(2)}\\\\\n", - " \\end{bmatrix},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "b_{11}x_1 +b_{12}x_2 +b_{13}x_3 + b_{14}x_4=y_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a^{(2)}_{22}x_2 + a^{(2)}_{23}x_3 + a^{(2)}_{24}x_4=w^{(2)}_2 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a^{(2)}_{32}x_2 + a^{(2)}_{33}x_3 + a^{(2)}_{34}x_4=w^{(2)}_3 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a^{(2)}_{42}x_2 + a^{(2)}_{43}x_3 + a^{(2)}_{44}x_4=w^{(2)}_4, \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation} \n", - "\\label{_auto2} \\tag{3}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Gaussian Elimination\n", - "\n", - "The new coefficients are" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " b_{1k} = a_{1k}^{(1)} \\quad k=1,\\dots,n,\n", - "\\label{_auto3} \\tag{4}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where each $a_{1k}^{(1)}$ is equal to the original $a_{1k}$ element. The other coefficients are" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "a_{jk}^{(2)} = a_{jk}^{(1)}-\\frac{a_{j1}^{(1)}a_{1k}^{(1)}}{a_{11}^{(1)}} \\quad j,k=2,\\dots,n,\n", - "\\label{_auto4} \\tag{5}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with a new right-hand side given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "y_{1}=w_1^{(1)}, \\quad w_j^{(2)} =w_j^{(1)}-\\frac{a_{j1}^{(1)}w_1^{(1)}}{a_{11}^{(1)}} \\quad j=2,\\dots,n.\n", - "\\label{_auto5} \\tag{6}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have also set $w_1^{(1)}=w_1$, the original vector element.\n", - "We see that the system of unknowns $x_1,\\dots,x_n$ is transformed into an $(n-1)\\times (n-1)$ problem.\n", - "\n", - "\n", - "## Gaussian Elimination\n", - "\n", - "This step is called forward substitution.\n", - "Proceeding with these substitutions, we obtain the\n", - "general expressions for the new coefficients" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " a_{jk}^{(m+1)} = a_{jk}^{(m)}-\\frac{a_{jm}^{(m)}a_{mk}^{(m)}}{a_{mm}^{(m)}} \\quad j,k=m+1,\\dots,n,\n", - "\\label{_auto6} \\tag{7}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with $m=1,\\dots,n-1$ and a\n", - "right-hand side given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " w_j^{(m+1)} =w_j^{(m)}-\\frac{a_{jm}^{(m)}w_m^{(m)}}{a_{mm}^{(m)}}\\quad j=m+1,\\dots,n.\n", - "\\label{_auto7} \\tag{8}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This set of $n-1$ elimations leads us to an equations which is solved by back substitution.\n", - "If the arithmetics is exact and the matrix $\\mathbf{A}$ is not singular, then the computed answer will be exact.\n", - "\n", - "Even though the matrix elements along the diagonal are not zero,\n", - "numerically small numbers may appear and subsequent divisions may lead to large numbers, which, if added\n", - "to a small number may yield losses of precision. Suppose for example that our first division in $(a_{22}-a_{21}a_{12}/a_{11})$\n", - "results in $-10^{-7}$ and that $a_{22}$ is one.\n", - "one. We are then\n", - "adding $10^7+1$. With single precision this results in $10^7$.\n", - "\n", - "\n", - "\n", - "\n", - "## Linear Algebra Methods\n", - "\n", - " * Gaussian elimination, $O(2/3n^3)$ flops, general matrix\n", - "\n", - " * LU decomposition, upper triangular and lower tridiagonal matrices, $O(2/3n^3)$ flops, general matrix. Get easily the inverse, determinant and can solve linear equations with back-substitution only, $O(n^2)$ flops\n", - "\n", - " * Cholesky decomposition. Real symmetric or hermitian positive definite matrix, $O(1/3n^3)$ flops.\n", - "\n", - " * Tridiagonal linear systems, important for differential equations. Normally positive definite and non-singular. $O(8n)$ flops for symmetric. Special case of banded matrices.\n", - "\n", - " * Singular value decomposition\n", - "\n", - " * the QR method will be discussed in chapter 7 in connection with eigenvalue systems. $O(4/3n^3)$ flops.\n", - "\n", - "## LU Decomposition\n", - "\n", - "The LU decomposition method means that we can rewrite\n", - "this matrix as the product of two matrices $\\mathbf{L}$ and $\\mathbf{U}$\n", - "where" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{bmatrix}\n", - " a_{11} & a_{12} & a_{13} & a_{14} \\\\\n", - " a_{21} & a_{22} & a_{23} & a_{24} \\\\\n", - " a_{31} & a_{32} & a_{33} & a_{34} \\\\\n", - " a_{41} & a_{42} & a_{43} & a_{44}\n", - " \\end{bmatrix}\n", - " = \\begin{bmatrix}\n", - " 1 & 0 & 0 & 0 \\\\\n", - " l_{21} & 1 & 0 & 0 \\\\\n", - " l_{31} & l_{32} & 1 & 0 \\\\\n", - " l_{41} & l_{42} & l_{43} & 1\n", - " \\end{bmatrix}\n", - " \\begin{bmatrix}\n", - " u_{11} & u_{12} & u_{13} & u_{14} \\\\\n", - " 0 & u_{22} & u_{23} & u_{24} \\\\\n", - " 0 & 0 & u_{33} & u_{34} \\\\\n", - " 0 & 0 & 0 & u_{44}\n", - " \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LU Decomposition\n", - "\n", - "LU decomposition forms the backbone of other algorithms in linear algebra, such as the\n", - "solution of linear equations given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{11}x_1 +a_{12}x_2 +a_{13}x_3 + a_{14}x_4=w_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{21}x_1 + a_{22}x_2 + a_{23}x_3 + a_{24}x_4=w_2 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{31}x_1 + a_{32}x_2 + a_{33}x_3 + a_{34}x_4=w_3 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{41}x_1 + a_{42}x_2 + a_{43}x_3 + a_{44}x_4=w_4. \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above set of equations is conveniently solved by using LU decomposition as an intermediate step.\n", - "\n", - "The matrix $\\mathbf{A}\\in \\mathbb{R}^{n\\times n}$ has an LU factorization if the determinant\n", - "is different from zero. If the LU factorization exists and $\\mathbf{A}$ is non-singular, then the LU factorization\n", - "is unique and the determinant is given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "det\\{\\mathbf{A}\\}=det\\{\\mathbf{LU}\\}= det\\{\\mathbf{L}\\}det\\{\\mathbf{U}\\}=u_{11}u_{22}\\dots u_{nn}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LU Decomposition, why?\n", - "\n", - "There are at least three main advantages with LU decomposition compared with standard Gaussian elimination:\n", - "\n", - " * It is straightforward to compute the determinant of a matrix\n", - "\n", - " * If we have to solve sets of linear equations with the same matrix but with different vectors $\\mathbf{y}$, the number of FLOPS is of the order $n^3$.\n", - "\n", - " * The inverse is such an operation \n", - "\n", - "## LU Decomposition, linear equations\n", - "\n", - "With the LU decomposition it is rather\n", - "simple to solve a system of linear equations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{11}x_1 +a_{12}x_2 +a_{13}x_3 + a_{14}x_4=w_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{21}x_1 + a_{22}x_2 + a_{23}x_3 + a_{24}x_4=w_2 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{31}x_1 + a_{32}x_2 + a_{33}x_3 + a_{34}x_4=w_3 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "a_{41}x_1 + a_{42}x_2 + a_{43}x_3 + a_{44}x_4=w_4. \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This can be written in matrix form as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{Ax}=\\mathbf{w}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\mathbf{A}$ and $\\mathbf{w}$ are known and we have to solve for\n", - "$\\mathbf{x}$. Using the LU dcomposition we write" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A} \\mathbf{x} \\equiv \\mathbf{L} \\mathbf{U} \\mathbf{x} =\\mathbf{w}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LU Decomposition, linear equations\n", - "\n", - "The previous equation can be calculated in two steps" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{L} \\mathbf{y} = \\mathbf{w};\\qquad \\mathbf{Ux}=\\mathbf{y}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To show that this is correct we use to the LU decomposition\n", - "to rewrite our system of linear equations as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{LUx}=\\mathbf{w},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and since the determinat of $\\mathbf{L}$ is equal to 1 (by construction\n", - "since the diagonals of $\\mathbf{L}$ equal 1) we can use the inverse of\n", - "$\\mathbf{L}$ to obtain" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{Ux}=\\mathbf{L^{-1}w}=\\mathbf{y},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which yields the intermediate step" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{L^{-1}w}=\\mathbf{y}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and as soon as we have $\\mathbf{y}$ we can obtain $\\mathbf{x}$\n", - "through $\\mathbf{Ux}=\\mathbf{y}$.\n", - "\n", - "\n", - "## LU Decomposition, why?\n", - "\n", - "For our four-dimentional example this takes the form" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "y_1=w_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "l_{21}y_1 + y_2=w_2\\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "l_{31}y_1 + l_{32}y_2 + y_3 =w_3\\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "l_{41}y_1 + l_{42}y_2 + l_{43}y_3 + y_4=w_4. \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "u_{11}x_1 +u_{12}x_2 +u_{13}x_3 + u_{14}x_4=y_1 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "u_{22}x_2 + u_{23}x_3 + u_{24}x_4=y_2\\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "u_{33}x_3 + u_{34}x_4=y_3\\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "u_{44}x_4=y_4 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This example shows the basis for the algorithm\n", - "needed to solve the set of $n$ linear equations.\n", - "\n", - "\n", - "## LU Decomposition, linear equations\n", - "\n", - "The algorithm goes as follows\n", - "\n", - " * Set up the matrix $\\bf A$ and the vector $\\bf w$ with their correct dimensions. This determines the dimensionality of the unknown vector $\\bf x$.\n", - "\n", - " * Then LU decompose the matrix $\\bf A$ through a call to the function `ludcmp(double a, int n, int indx, double &d)`. This functions returns the LU decomposed matrix $\\bf A$, its determinant and the vector indx which keeps track of the number of interchanges of rows. If the determinant is zero, the solution is malconditioned.\n", - "\n", - " * Thereafter you call the function `lubksb(double a, int n, int indx, double w)` which uses the LU decomposed matrix $\\bf A$ and the vector $\\bf w$ and returns $\\bf x$ in the same place as $\\bf w$. Upon exit the original content in $\\bf w$ is destroyed. If you wish to keep this information, you should make a backup of it in your calling function.\n", - "\n", - "## LU Decomposition, the inverse of a matrix\n", - "\n", - "If the inverse exists then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}^{-1}\\mathbf{A}=\\mathbf{I},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "the identity matrix. With an LU decomposed matrix we can rewrite the last equation as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{LU}\\mathbf{A}^{-1}=\\mathbf{I}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LU Decomposition, the inverse of a matrix\n", - "\n", - "If we assume that the first column (that is column 1) of the inverse matrix\n", - "can be written as a vector with unknown entries" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}_1^{-1}= \\begin{bmatrix}\n", - " a_{11}^{-1} \\\\\n", - " a_{21}^{-1} \\\\\n", - " \\dots \\\\\n", - " a_{n1}^{-1} \\\\\n", - " \\end{bmatrix},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "then we have a linear set of equations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{LU}\\begin{bmatrix}\n", - " a_{11}^{-1} \\\\\n", - " a_{21}^{-1} \\\\\n", - " \\dots \\\\\n", - " a_{n1}^{-1} \\\\\n", - " \\end{bmatrix} =\\begin{bmatrix}\n", - " 1 \\\\\n", - " 0 \\\\\n", - " \\dots \\\\\n", - " 0 \\\\\n", - " \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## LU Decomposition, the inverse\n", - "\n", - "In a similar way we can compute the unknow entries of the second column," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{LU}\\begin{bmatrix}\n", - " a_{12}^{-1} \\\\\n", - " a_{22}^{-1} \\\\\n", - " \\dots \\\\\n", - " a_{n2}^{-1} \\\\\n", - " \\end{bmatrix}=\\begin{bmatrix}\n", - " 0 \\\\\n", - " 1 \\\\\n", - " \\dots \\\\\n", - " 0 \\\\\n", - " \\end{bmatrix},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and continue till we have solved all $n$ sets of linear equations.\n", - "\n", - "\n", - "\n", - "## [Using Armadillo to perform an LU decomposition](https://github.com/CompPhysics/ComputationalPhysicsMSU/blob/master/doc/Programs/CppQtCodesLectures/MatrixTest/main.cpp)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " #include \n", - " #include \"armadillo\"\n", - " using namespace arma;\n", - " using namespace std;\n", - " \n", - " int main()\n", - " {\n", - " mat A = randu(5,5);\n", - " vec b = randu(5);\n", - " \n", - " A.print(\"A =\");\n", - " b.print(\"b=\");\n", - " // solve Ax = b\n", - " vec x = solve(A,b);\n", - " // print x\n", - " x.print(\"x=\");\n", - " // find LU decomp of A, if needed, P is the permutation matrix\n", - " mat L, U;\n", - " lu(L,U,A);\n", - " // print l\n", - " L.print(\" L= \");\n", - " // print U\n", - " U.print(\" U= \");\n", - " //Check that A = LU\n", - " (A-L*U).print(\"Test of LU decomposition\");\n", - " return 0;\n", - " }\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Iterative methods, Chapter 6\n", - "\n", - " * Direct solvers such as Gauss elimination and LU decomposition discussed in connection with project 1.\n", - "\n", - " * Iterative solvers such as Basic iterative solvers, Jacobi, Gauss-Seidel, Successive over-relaxation. These methods are easy to parallelize, as we will se later. Much used in solutions of partial differential equations.\n", - "\n", - " * Other iterative methods such as Krylov subspace methods with Generalized minimum residual (GMRES) and Conjugate gradient etc will not be discussed.\n", - "\n", - "## Iterative methods, Jacobi's method\n", - "\n", - "It is a simple method for solving" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}\\mathbf{x}=\\mathbf{b},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\mathbf{A}$ is a matrix and $\\mathbf{x}$ and $\\mathbf{b}$ are vectors. The vector $\\mathbf{x}$ is \n", - "the unknown.\n", - "\n", - "It is an iterative scheme where we start with a guess for the unknown, and \n", - "after $k+1$ iterations we have" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{x}^{(k+1)}= \\mathbf{D}^{-1}(\\mathbf{b}-(\\mathbf{L}+\\mathbf{U})\\mathbf{x}^{(k)}),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with $\\mathbf{A}=\\mathbf{D}+\\mathbf{U}+\\mathbf{L}$ and\n", - "$\\mathbf{D}$ being a diagonal matrix, $\\mathbf{U}$ an upper triangular matrix and $\\mathbf{L}$ a lower triangular\n", - "matrix.\n", - "\n", - "If the matrix $\\mathbf{A}$ is positive definite or diagonally dominant, one can show that this method will always converge to the exact solution. \n", - "\n", - "\n", - "\n", - "\n", - "## Iterative methods, Jacobi's method\n", - "\n", - "We can demonstrate Jacobi's method by this $4\\times 4$ matrix problem. We assume a guess\n", - "for the vector elements $x_i^{(0)}$, a guess which represents our first iteration. The new\n", - "values are obtained by substitution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_1^{(1)} =(b_1-a_{12}x_2^{(0)} -a_{13}x_3^{(0)} - a_{14}x_4^{(0)})/a_{11} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_2^{(1)} =(b_2-a_{21}x_1^{(0)} - a_{23}x_3^{(0)} - a_{24}x_4^{(0)})/a_{22} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_3^{(1)} =(b_3- a_{31}x_1^{(0)} -a_{32}x_2^{(0)} -a_{34}x_4^{(0)})/a_{33} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_4^{(1)}=(b_4-a_{41}x_1^{(0)} -a_{42}x_2^{(0)} - a_{43}x_3^{(0)})/a_{44}, \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which after $k+1$ iterations reads" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_1^{(k+1)} =(b_1-a_{12}x_2^{(k)} -a_{13}x_3^{(k)} - a_{14}x_4^{(k)})/a_{11} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_2^{(k+1)} =(b_2-a_{21}x_1^{(k)} - a_{23}x_3^{(k)} - a_{24}x_4^{(k)})/a_{22} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_3^{(k+1)} =(b_3- a_{31}x_1^{(k)} -a_{32}x_2^{(k)} -a_{34}x_4^{(k)})/a_{33} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_4^{(k+1)}=(b_4-a_{41}x_1^{(k)} -a_{42}x_2^{(k)} - a_{43}x_3^{(k)})/a_{44}, \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Iterative methods, Jacobi's method\n", - "\n", - "We can generalize the above equations to" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_i^{(k+1)}=(b_i-\\sum_{j=1, j\\ne i}^{n}a_{ij}x_j^{(k)})/a_{ii}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or in an even more compact form as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{x}^{(k+1)}= \\mathbf{D}^{-1}(\\mathbf{b}-(\\mathbf{L}+\\mathbf{U})\\mathbf{x}^{(k)}),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with $\\mathbf{A}=\\mathbf{D}+\\mathbf{U}+\\mathbf{L}$ and\n", - "$\\mathbf{D}$ being a diagonal matrix, $\\mathbf{U}$ an upper triangular matrix and $\\mathbf{L}$ a lower triangular\n", - "matrix.\n", - "\n", - "\n", - "\n", - "## Iterative methods, Gauss-Seidel's method\n", - "\n", - "Our $4\\times 4$ matrix problem" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_1^{(k+1)} =(b_1-a_{12}x_2^{(k)} -a_{13}x_3^{(k)} - a_{14}x_4^{(k)})/a_{11} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_2^{(k+1)} =(b_2-a_{21}x_1^{(k)} - a_{23}x_3^{(k)} - a_{24}x_4^{(k)})/a_{22} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_3^{(k+1)} =(b_3- a_{31}x_1^{(k)} -a_{32}x_2^{(k)} -a_{34}x_4^{(k)})/a_{33} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_4^{(k+1)}=(b_4-a_{41}x_1^{(k)} -a_{42}x_2^{(k)} - a_{43}x_3^{(k)})/a_{44}, \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "can be rewritten as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_1^{(k+1)} =(b_1-a_{12}x_2^{(k)} -a_{13}x_3^{(k)} - a_{14}x_4^{(k)})/a_{11} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_2^{(k+1)} =(b_2-a_{21}x_1^{(k+1)} - a_{23}x_3^{(k)} - a_{24}x_4^{(k)})/a_{22} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_3^{(k+1)} =(b_3- a_{31}x_1^{(k+1)} -a_{32}x_2^{(k+1)} -a_{34}x_4^{(k)})/a_{33} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_4^{(k+1)}=(b_4-a_{41}x_1^{(k+1)} -a_{42}x_2^{(k+1)} - a_{43}x_3^{(k+1)})/a_{44}, \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which allows us to utilize the preceding solution (forward substitution). This improves normally the convergence\n", - "behavior and leads to the Gauss-Seidel method!\n", - "\n", - "\n", - "\n", - "## Iterative methods, Gauss-Seidel's method\n", - "\n", - "We can generalize" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_1^{(k+1)} =(b_1-a_{12}x_2^{(k)} -a_{13}x_3^{(k)} - a_{14}x_4^{(k)})/a_{11} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_2^{(k+1)} =(b_2-a_{21}x_1^{(k+1)} - a_{23}x_3^{(k)} - a_{24}x_4^{(k)})/a_{22} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_3^{(k+1)} =(b_3- a_{31}x_1^{(k+1)} -a_{32}x_2^{(k+1)} -a_{34}x_4^{(k)})/a_{33} \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_4^{(k+1)}=(b_4-a_{41}x_1^{(k+1)} -a_{42}x_2^{(k+1)} - a_{43}x_3^{(k+1)})/a_{44}, \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "to the following form" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x^{(k+1)}_i = \\frac{1}{a_{ii}} \\left(b_i - \\sum_{j > i}a_{ij}x^{(k)}_j - \\sum_{j < i}a_{ij}x^{(k+1)}_j \\right),\\quad i=1,2,\\ldots,n.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The procedure is generally continued until the changes made by an iteration are below some tolerance.\n", - "\n", - "The convergence properties of the Jacobi method and the \n", - "Gauss-Seidel method are dependent on the matrix $\\mathbf{A}$. These methods converge when\n", - "the matrix is symmetric positive-definite, or is strictly or irreducibly diagonally dominant.\n", - "Both methods sometimes converge even if these conditions are not satisfied.\n", - "\n", - "\n", - "\n", - "## Iterative methods, Successive over-relaxation\n", - "\n", - "Given a square system of n linear equations with unknown $\\mathbf x$:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}\\mathbf x = \\mathbf b\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}=\\begin{bmatrix} a_{11} & a_{12} & \\cdots & a_{1n} \\\\ a_{21} & a_{22} & \\cdots & a_{2n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\a_{n1} & a_{n2} & \\cdots & a_{nn} \\end{bmatrix}, \\qquad \\mathbf{x} = \\begin{bmatrix} x_{1} \\\\ x_2 \\\\ \\vdots \\\\ x_n \\end{bmatrix} , \\qquad \\mathbf{b} = \\begin{bmatrix} b_{1} \\\\ b_2 \\\\ \\vdots \\\\ b_n \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Iterative methods, Successive over-relaxation\n", - "\n", - "Then A can be decomposed into a diagonal component D, and strictly lower and upper triangular components L and U:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A} =\\mathbf{D} + \\mathbf{L} + \\mathbf{U},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "D = \\begin{bmatrix} a_{11} & 0 & \\cdots & 0 \\\\ 0 & a_{22} & \\cdots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\0 & 0 & \\cdots & a_{nn} \\end{bmatrix}, \\quad L = \\begin{bmatrix} 0 & 0 & \\cdots & 0 \\\\ a_{21} & 0 & \\cdots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\a_{n1} & a_{n2} & \\cdots & 0 \\end{bmatrix}, \\quad U = \\begin{bmatrix} 0 & a_{12} & \\cdots & a_{1n} \\\\ 0 & 0 & \\cdots & a_{2n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\0 & 0 & \\cdots & 0 \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The system of linear equations may be rewritten as:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "(D+\\omega L) \\mathbf{x} = \\omega \\mathbf{b} - [\\omega U + (\\omega-1) D ] \\mathbf{x}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "for a constant $\\omega > 1$.\n", - "\n", - "\n", - "\n", - "\n", - "## Iterative methods, Successive over-relaxation\n", - "\n", - "The method of successive over-relaxation is an iterative technique that solves the left hand side of this expression for $x$, using previous value for $x$ on the right hand side. Analytically, this may be written as:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{x}^{(k+1)} = (D+\\omega L)^{-1} \\big(\\omega \\mathbf{b} - [\\omega U + (\\omega-1) D ] \\mathbf{x}^{(k)}\\big).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "However, by taking advantage of the triangular form of $(D+\\omega L)$, the elements of $x^{(k+1)}$ can be computed sequentially using forward substitution:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x^{(k+1)}_i = (1-\\omega)x^{(k)}_i + \\frac{\\omega}{a_{ii}} \\left(b_i - \\sum_{j > i} a_{ij}x^{(k)}_j - \\sum_{j < i} a_{ij}x^{(k+1)}_j \\right),\\quad i=1,2,\\ldots,n.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The choice of relaxation factor is not necessarily easy, and depends upon the properties of the coefficient matrix. For symmetric, positive-definite matrices it can be proven that $0 < \\omega < 2$ will lead to convergence, but we are generally interested in faster convergence rather than just convergence.\n", - "\n", - "\n", - "\n", - "# Cubic Splines\n", - "\n", - "Cubic spline interpolation is among one of the most used \n", - "methods for interpolating between data points where the arguments\n", - "are organized as ascending series. In the library program we supply\n", - "such a function, based on the so-called cubic spline method to be \n", - "described below. \n", - "\n", - "A spline function consists of polynomial pieces defined on\n", - "subintervals. The different subintervals are connected via\n", - "various continuity relations.\n", - "\n", - "Assume we have at our disposal $n+1$ points $x_0, x_1, \\dots x_n$ \n", - "arranged so that $x_0 < x_1 < x_2 < \\dots x_{n-1} < x_n$ (such points are called\n", - "knots). A spline function $s$ of degree $k$ with $n+1$ knots is defined\n", - "as follows\n", - " * On every subinterval $[x_{i-1},x_i)$ *s* is a polynomial of degree $\\le k$.\n", - "\n", - " * $s$ has $k-1$ continuous derivatives in the whole interval $[x_0,x_n]$.\n", - "\n", - "## Splines\n", - "\n", - "As an example, consider a spline function of degree $k=1$ defined as follows" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s(x)=\\begin{bmatrix} s_0(x)=a_0x+b_0 & x\\in [x_0, x_1) \\\\ \n", - " s_1(x)=a_1x+b_1 & x\\in [x_1, x_2) \\\\ \n", - " \\dots & \\dots \\\\\n", - " s_{n-1}(x)=a_{n-1}x+b_{n-1} & x\\in \n", - " [x_{n-1}, x_n] \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this case the polynomial consists of series of straight lines \n", - "connected to each other at every endpoint. The number of continuous\n", - "derivatives is then $k-1=0$, as expected when we deal with straight lines.\n", - "Such a polynomial is quite easy to construct given\n", - "$n+1$ points $x_0, x_1, \\dots x_n$ and their corresponding \n", - "function values. \n", - "\n", - "\n", - "\n", - "\n", - "## Splines\n", - "\n", - "The most commonly used spline function is the one with $k=3$, the so-called\n", - "cubic spline function. \n", - "Assume that we have in adddition to the $n+1$ knots a series of\n", - "functions values $y_0=f(x_0), y_1=f(x_1), \\dots y_n=f(x_n)$.\n", - "By definition, the polynomials $s_{i-1}$ and $s_i$ \n", - "are thence supposed to interpolate the same point $i$, that is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s_{i-1}(x_i)= y_i = s_i(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with $1 \\le i \\le n-1$. In total we have $n$ polynomials of the \n", - "type" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s_i(x)=a_{i0}+a_{i1}x+a_{i2}x^2+a_{i2}x^3,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "yielding $4n$ coefficients to determine.\n", - "\n", - "\n", - "\n", - "\n", - "## Splines\n", - "\n", - "Every subinterval provides in addition the $2n$ conditions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "y_i = s(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s(x_{i+1})= y_{i+1},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "to be fulfilled. If we also assume that $s'$ and $s''$ are continuous,\n", - "then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s'_{i-1}(x_i)= s'_i(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "yields $n-1$ conditions. Similarly," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s''_{i-1}(x_i)= s''_i(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "results in additional $n-1$ conditions. In total we have $4n$ coefficients\n", - "and $4n-2$ equations to determine them, leaving us with $2$ degrees of \n", - "freedom to be determined. \n", - "\n", - "\n", - "\n", - "## Splines\n", - "\n", - "Using the last equation we define two values for the second derivative, namely" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s''_{i}(x_i)= f_i,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s''_{i}(x_{i+1})= f_{i+1},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and setting up a straight line between $f_i$ and $f_{i+1}$ we have" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s_i''(x) = \\frac{f_i}{x_{i+1}-x_i}(x_{i+1}-x)+\n", - " \\frac{f_{i+1}}{x_{i+1}-x_i}(x-x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and integrating twice one obtains" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s_i(x) = \\frac{f_i}{6(x_{i+1}-x_i)}(x_{i+1}-x)^3+\n", - " \\frac{f_{i+1}}{6(x_{i+1}-x_i)}(x-x_i)^3\n", - " +c(x-x_i)+d(x_{i+1}-x).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Splines\n", - "\n", - "Using the conditions $s_i(x_i)=y_i$ and $s_i(x_{i+1})=y_{i+1}$ \n", - "we can in turn determine the constants $c$ and $d$ resulting in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s_i(x) =\\frac{f_i}{6(x_{i+1}-x_i)}(x_{i+1}-x)^3+\n", - " \\frac{f_{i+1}}{6(x_{i+1}-x_i)}(x-x_i)^3 \\nonumber\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation} \n", - " +(\\frac{y_{i+1}}{x_{i+1}-x_i}-\\frac{f_{i+1}(x_{i+1}-x_i)}{6})\n", - " (x-x_i)+\n", - " (\\frac{y_{i}}{x_{i+1}-x_i}-\\frac{f_{i}(x_{i+1}-x_i)}{6})\n", - " (x_{i+1}-x).\n", - "\\label{_auto8} \\tag{9}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Splines\n", - "\n", - "How to determine the values of the second\n", - "derivatives $f_{i}$ and $f_{i+1}$? We use the continuity assumption \n", - "of the first derivatives" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "s'_{i-1}(x_i)= s'_i(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and set $x=x_i$. Defining $h_i=x_{i+1}-x_i$ we obtain finally\n", - "the following expression" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "h_{i-1}f_{i-1}+2(h_{i}+h_{i-1})f_i+h_if_{i+1}=\n", - " \\frac{6}{h_i}(y_{i+1}-y_i)-\\frac{6}{h_{i-1}}(y_{i}-y_{i-1}),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and introducing the shorthands $u_i=2(h_{i}+h_{i-1})$, \n", - "$v_i=\\frac{6}{h_i}(y_{i+1}-y_i)-\\frac{6}{h_{i-1}}(y_{i}-y_{i-1})$,\n", - "we can reformulate the problem as a set of linear equations to be \n", - "solved through e.g., Gaussian elemination\n", - "\n", - "\n", - "\n", - "\n", - "## Splines\n", - "\n", - "Gaussian elimination" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{bmatrix} u_1 & h_1 &0 &\\dots & & & & \\\\\n", - " h_1 & u_2 & h_2 &0 &\\dots & & & \\\\\n", - " 0 & h_2 & u_3 & h_3 &0 &\\dots & & \\\\\n", - " \\dots& & \\dots &\\dots &\\dots &\\dots &\\dots & \\\\\n", - " &\\dots & & &0 &h_{n-3} &u_{n-2} &h_{n-2} \\\\\n", - " & && & &0 &h_{n-2} &u_{n-1} \\end{bmatrix}\n", - " \\begin{bmatrix} f_1 \\\\ \n", - " f_2 \\\\\n", - " f_3\\\\\n", - " \\dots \\\\\n", - " f_{n-2} \\\\ \n", - " f_{n-1} \\end{bmatrix} =\n", - " \\begin{bmatrix} v_1 \\\\ \n", - " v_2 \\\\\n", - " v_3\\\\\n", - " \\dots \\\\\n", - " v_{n-2}\\\\\n", - " v_{n-1} \\end{bmatrix}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that this is a set of tridiagonal equations and can be solved \n", - "through only $O(n)$ operations.\n", - "\n", - "\n", - "\n", - "## Splines\n", - "\n", - "The functions supplied in the program library are *spline* and *splint*.\n", - "In order to use cubic spline interpolation you need first to call" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " spline(double x[], double y[], int n, double yp1, double yp2, double y2[])\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This function takes as\n", - "input $x[0,..,n - 1]$ and $y[0,..,n - 1]$ containing a tabulation\n", - "$y_i = f(x_i)$ with $x_0 < x_1 < .. < x_{n - 1}$ \n", - "together with the \n", - "first derivatives of $f(x)$ at $x_0$ and $x_{n-1}$, respectively. Then the\n", - "function returns $y2[0,..,n-1]$ which contains the second derivatives of\n", - "$f(x_i)$ at each point $x_i$. $n$ is the number of points.\n", - "This function provides the cubic spline interpolation for all subintervals\n", - "and is called only once.\n", - "\n", - "\n", - "\n", - "\n", - "## Splines\n", - "\n", - "Thereafter, if you wish to make various interpolations, you need to call the function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " splint(double x[], double y[], double y2a[], int n, double x, double *y)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which takes as input\n", - "the tabulated values $x[0,..,n - 1]$ and $y[0,..,n - 1]$ and the output \n", - "y2a[0,..,n - 1] from *spline*. It returns the value $y$ corresponding\n", - "to the point $x$.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Conjugate gradient (CG) method\n", - "\n", - "The success of the CG method for finding solutions of non-linear problems is based\n", - "on the theory of conjugate gradients for linear systems of equations. It belongs\n", - "to the class of iterative methods for solving problems from linear algebra of the type" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{A}\\hat{x} = \\hat{b}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the iterative process we end up with a problem like" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{r}= \\hat{b}-\\hat{A}\\hat{x},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\hat{r}$ is the so-called residual or error in the iterative process.\n", - "\n", - "When we have found the exact solution, $\\hat{r}=0$.\n", - "\n", - "\n", - "\n", - "\n", - "## Conjugate gradient method\n", - "\n", - "\n", - "The residual is zero when we reach the minimum of the quadratic equation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "P(\\hat{x})=\\frac{1}{2}\\hat{x}^T\\hat{A}\\hat{x} - \\hat{x}^T\\hat{b},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with the constraint that the matrix $\\hat{A}$ is positive definite and symmetric.\n", - "If we search for a minimum of the quantum mechanical variance, then the matrix \n", - "$\\hat{A}$, which is called the Hessian, is given by the second-derivative of the function we want to minimize. This quantity is always positive definite. In our case this corresponds normally to the second derivative of the energy. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Conjugate gradient method, Newton's method first\n", - "\n", - "We seek the minimum of the energy or the variance as function of various variational parameters. \n", - "In our case we have thus a function $f$ whose minimum we are seeking.\n", - "In Newton's method we set $\\nabla f = 0$ and we can thus compute the next iteration point" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{x}-\\hat{x}_i=\\hat{A}^{-1}\\nabla f(\\hat{x}_i).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Subtracting this equation from that of $\\hat{x}_{i+1}$ we have" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{x}_{i+1}-\\hat{x}_i=\\hat{A}^{-1}(\\nabla f(\\hat{x}_{i+1})-\\nabla f(\\hat{x}_i)).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simple example and demonstration\n", - "\n", - "The function $f$ can be either the energy or the variance. If we choose the energy then we have" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{\\alpha}_{i+1}-\\hat{\\alpha}_i=\\hat{A}^{-1}(\\nabla E(\\hat{\\alpha}_{i+1})-\\nabla E(\\hat{\\alpha}_i)).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the simple harmonic oscillator model, the gradient and the Hessian $\\hat{A}$ are" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{d\\langle E_L[\\alpha]\\rangle}{d\\alpha} = \\alpha-\\frac{1}{4\\alpha^3}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and a second derivative which is always positive (meaning that we find a minimum)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{A}= \\frac{d^2\\langle E_L[\\alpha]\\rangle}{d\\alpha^2} = 1+\\frac{3}{4\\alpha^4}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simple example and demonstration\n", - "\n", - "We get then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\alpha_{i+1}=\\frac{4}{3}\\alpha_i-\\frac{\\alpha_i^4}{3\\alpha_{i+1}^3},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which can be rewritten as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\alpha_{i+1}^4-\\frac{4}{3}\\alpha_i\\alpha_{i+1}^4+\\frac{1}{3}\\alpha_i^4.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conjugate gradient method\n", - "\n", - "In the CG method we define so-called conjugate directions and two vectors \n", - "$\\hat{s}$ and $\\hat{t}$\n", - "are said to be\n", - "conjugate if" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{s}^T\\hat{A}\\hat{t}= 0.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The philosophy of the CG method is to perform searches in various conjugate directions\n", - "of our vectors $\\hat{x}_i$ obeying the above criterion, namely" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{x}_i^T\\hat{A}\\hat{x}_j= 0.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Two vectors are conjugate if they are orthogonal with respect to \n", - "this inner product. Being conjugate is a symmetric relation: if $\\hat{s}$ is conjugate to $\\hat{t}$, then $\\hat{t}$ is conjugate to $\\hat{s}$.\n", - "\n", - "\n", - "\n", - "## Conjugate gradient method\n", - "\n", - "An example is given by the eigenvectors of the matrix" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{v}_i^T\\hat{A}\\hat{v}_j= \\lambda\\hat{v}_i^T\\hat{v}_j,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which is zero unless $i=j$. \n", - "\n", - "\n", - "\n", - "\n", - "## Conjugate gradient method\n", - "\n", - "Assume now that we have a symmetric positive-definite matrix $\\hat{A}$ of size\n", - "$n\\times n$. At each iteration $i+1$ we obtain the conjugate direction of a vector" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{x}_{i+1}=\\hat{x}_{i}+\\alpha_i\\hat{p}_{i}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We assume that $\\hat{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", - "Then the $\\hat{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", - "$ \\hat{A}\\hat{x} = \\hat{b}$ in this basis, namely" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{x} = \\sum^{n}_{i=1} \\alpha_i \\hat{p}_i.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conjugate gradient method\n", - "\n", - "The coefficients are given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Multiplying with $\\hat{p}_k^T$ from the left gives" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{p}_k^T \\hat{A}\\hat{x} = \\sum^{n}_{i=1} \\alpha_i\\hat{p}_k^T \\hat{A}\\hat{p}_i= \\hat{p}_k^T \\hat{b},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and we can define the coefficients $\\alpha_k$ as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\alpha_k = \\frac{\\hat{p}_k^T \\hat{b}}{\\hat{p}_k^T \\hat{A} \\hat{p}_k}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conjugate gradient method and iterations\n", - "\n", - "\n", - "If we choose the conjugate vectors $\\hat{p}_k$ carefully, \n", - "then we may not need all of them to obtain a good approximation to the solution \n", - "$\\hat{x}$. \n", - "We want to regard the conjugate gradient method as an iterative method. \n", - "This will us to solve systems where $n$ is so large that the direct \n", - "method would take too much time.\n", - "\n", - "We denote the initial guess for $\\hat{x}$ as $\\hat{x}_0$. \n", - "We can assume without loss of generality that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{x}_0=0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or consider the system" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{A}\\hat{z} = \\hat{b}-\\hat{A}\\hat{x}_0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "instead.\n", - "\n", - "\n", - "\n", - "\n", - "## Conjugate gradient method\n", - "\n", - "One can show that the solution $\\hat{x}$ is also the unique minimizer of the quadratic form" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "f(\\hat{x}) = \\frac{1}{2}\\hat{x}^T\\hat{A}\\hat{x} - \\hat{x}^T \\hat{x} , \\quad \\hat{x}\\in\\mathbf{R}^n.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This suggests taking the first basis vector $\\hat{p}_1$ \n", - "to be the gradient of $f$ at $\\hat{x}=\\hat{x}_0$, \n", - "which equals" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{A}\\hat{x}_0-\\hat{b},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and \n", - "$\\hat{x}_0=0$ it is equal $-\\hat{b}$.\n", - "The other vectors in the basis will be conjugate to the gradient, \n", - "hence the name conjugate gradient method.\n", - "\n", - "\n", - "\n", - "\n", - "## Conjugate gradient method\n", - "\n", - "Let $\\hat{r}_k$ be the residual at the $k$-th step:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{r}_k=\\hat{b}-\\hat{A}\\hat{x}_k.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that $\\hat{r}_k$ is the negative gradient of $f$ at \n", - "$\\hat{x}=\\hat{x}_k$, \n", - "so the gradient descent method would be to move in the direction $\\hat{r}_k$. \n", - "Here, we insist that the directions $\\hat{p}_k$ are conjugate to each other, \n", - "so we take the direction closest to the gradient $\\hat{r}_k$ \n", - "under the conjugacy constraint. \n", - "This gives the following expression" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{p}_{k+1}=\\hat{r}_k-\\frac{\\hat{p}_k^T \\hat{A}\\hat{r}_k}{\\hat{p}_k^T\\hat{A}\\hat{p}_k} \\hat{p}_k.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conjugate gradient method\n", - "\n", - "We can also compute the residual iteratively as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{r}_{k+1}=\\hat{b}-\\hat{A}\\hat{x}_{k+1},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which equals" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{b}-\\hat{A}(\\hat{x}_k+\\alpha_k\\hat{p}_k),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "(\\hat{b}-\\hat{A}\\hat{x}_k)-\\alpha_k\\hat{A}\\hat{p}_k,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which gives" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{r}_{k+1}=\\hat{r}_k-\\hat{A}\\hat{p}_{k},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Review of probability theory\n", - "\n", - "## Domains and probabilities\n", - "\n", - "Consider the following simple example, namely the tossing of a dice, resulting in the following possible values" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\{2,3,4,5,6,7,8,9,10,11,12\\}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These values are called the *domain*. \n", - "To this domain we have the corresponding *probabilities*" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\{1/36,2/36/3/36,4/36,5/36,6/36,5/36,4/36,3/36,2/36,1/36\\}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Tossing a dice\n", - "\n", - "The numbers in the domain are the outcomes of the physical process tossing the dice.\n", - "We cannot tell beforehand whether the outcome is 3 or 5 or any other number in this domain.\n", - "This defines the randomness of the outcome, or unexpectedness or any other synonimous word which\n", - "encompasses the uncertitude of the final outcome. \n", - "\n", - "The only thing we can tell beforehand\n", - "is that say the outcome 2 has a certain probability. \n", - "If our favorite hobby is to spend an hour every evening throwing dice and \n", - "registering the sequence of outcomes, we will note that the numbers in the above domain" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\{2,3,4,5,6,7,8,9,10,11,12\\},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "appear in a random order. After 11 throws the results may look like" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\{10,8,6,3,6,9,11,8,12,4,5\\}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Stochastic variables\n", - "\n", - "\n", - "**Random variables are characterized by a domain which contains all possible values that the random value may take. This domain has a corresponding PDF**.\n", - "\n", - "\n", - "\n", - "## Stochastic variables and the main concepts, the discrete case\n", - "\n", - "There are two main concepts associated with a stochastic variable. The\n", - "*domain* is the set $\\mathbb D = \\{x\\}$ of all accessible values\n", - "the variable can assume, so that $X \\in \\mathbb D$. An example of a\n", - "discrete domain is the set of six different numbers that we may get by\n", - "throwing of a dice, $x\\in\\{1,\\,2,\\,3,\\,4,\\,5,\\,6\\}$.\n", - "\n", - "The *probability distribution function (PDF)* is a function\n", - "$p(x)$ on the domain which, in the discrete case, gives us the\n", - "probability or relative frequency with which these values of $X$\n", - "occur" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\mathrm{Prob}(X=x).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Stochastic variables and the main concepts, the continuous case\n", - "\n", - "In the continuous case, the PDF does not directly depict the\n", - "actual probability. Instead we define the probability for the\n", - "stochastic variable to assume any value on an infinitesimal interval\n", - "around $x$ to be $p(x)dx$. The continuous function $p(x)$ then gives us\n", - "the *density* of the probability rather than the probability\n", - "itself. The probability for a stochastic variable to assume any value\n", - "on a non-infinitesimal interval $[a,\\,b]$ is then just the integral" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathrm{Prob}(a\\leq X\\leq b) = \\int_a^b p(x)dx.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Qualitatively speaking, a stochastic variable represents the values of\n", - "numbers chosen as if by chance from some specified PDF so that the\n", - "selection of a large set of these numbers reproduces this PDF.\n", - "\n", - "\n", - "\n", - "## The cumulative probability\n", - "\n", - "Of interest to us is the *cumulative probability\n", - "distribution function* (**CDF**), $P(x)$, which is just the probability\n", - "for a stochastic variable $X$ to assume any value less than $x$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "P(x)=\\mathrm{Prob(}X\\leq x\\mathrm{)} =\n", - "\\int_{-\\infty}^x p(x^{\\prime})dx^{\\prime}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The relation between a CDF and its corresponding PDF is then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\frac{d}{dx}P(x).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Properties of PDFs\n", - "\n", - "\n", - "There are two properties that all PDFs must satisfy. The first one is\n", - "positivity (assuming that the PDF is normalized)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "0 \\leq p(x) \\leq 1.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Naturally, it would be nonsensical for any of the values of the domain\n", - "to occur with a probability greater than $1$ or less than $0$. Also,\n", - "the PDF must be normalized. That is, all the probabilities must add up\n", - "to unity. The probability of \"anything\" to happen is always unity. For\n", - "both discrete and continuous PDFs, this condition is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "\\sum_{x_i\\in\\mathbb D} p(x_i) & = 1,\\\\\n", - "\\int_{x\\in\\mathbb D} p(x)\\,dx & = 1.\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Important distributions, the uniform distribution\n", - "\n", - "The first one\n", - "is the most basic PDF; namely the uniform distribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "p(x) = \\frac{1}{b-a}\\theta(x-a)\\theta(b-x),\n", - "\\label{eq:unifromPDF} \\tag{10}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{array}{ll}\n", - "\\theta(x)=0 & x<0 \\\\\n", - "\\theta(x)=\\frac{1}{b-a} & \\in [a,b].\n", - "\\end{array}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The normal distribution with $b=1$ and $a=0$ is used to generate random numbers. \n", - "\n", - "\n", - "\n", - "## Gaussian distribution\n", - "\n", - "The second one is the Gaussian Distribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp{(-\\frac{(x-\\mu)^2}{2\\sigma^2})},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with mean value $\\mu$ and standard deviation $\\sigma$. If $\\mu=0$ and $\\sigma=1$, it is normally called the **standard normal distribution**" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\frac{1}{\\sqrt{2\\pi}} \\exp{(-\\frac{x^2}{2})},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following simple Python code plots the above distribution for different values of $\\mu$ and $\\sigma$." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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Elr2wpiao5RTKULmSdu0y36dPH3is0+ulsKTk8I7nn2dLTw+zv/GNsGVNn26V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\nX0iiZPKmHSZIJRhCFt8zsZb6HXIsV3KZtdmF+YC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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "from math import acos, exp, sqrt\n", - "from matplotlib import pyplot as plt\n", - "from matplotlib import rc, rcParams\n", - "import matplotlib.units as units\n", - "import matplotlib.ticker as ticker\n", - "rc('text',usetex=True)\n", - "rc('font',**{'family':'serif','serif':['Gaussian distribution']})\n", - "font = {'family' : 'serif',\n", - " 'color' : 'darkred',\n", - " 'weight' : 'normal',\n", - " 'size' : 16,\n", - " }\n", - "pi = acos(-1.0)\n", - "mu0 = 0.0\n", - "sigma0 = 1.0\n", - "mu1= 1.0\n", - "sigma1 = 2.0\n", - "mu2 = 2.0\n", - "sigma2 = 4.0\n", - "\n", - "x = np.linspace(-20.0, 20.0)\n", - "v0 = np.exp(-(x*x-2*x*mu0+mu0*mu0)/(2*sigma0*sigma0))/sqrt(2*pi*sigma0*sigma0)\n", - "v1 = np.exp(-(x*x-2*x*mu1+mu1*mu1)/(2*sigma1*sigma1))/sqrt(2*pi*sigma1*sigma1)\n", - "v2 = np.exp(-(x*x-2*x*mu2+mu2*mu2)/(2*sigma2*sigma2))/sqrt(2*pi*sigma2*sigma2)\n", - "plt.plot(x, v0, 'b-', x, v1, 'r-', x, v2, 'g-')\n", - "plt.title(r'{\\bf Gaussian distributions}', fontsize=20)\n", - "plt.text(-19, 0.3, r'Parameters: $\\mu = 0$, $\\sigma = 1$', fontdict=font)\n", - "plt.text(-19, 0.18, r'Parameters: $\\mu = 1$, $\\sigma = 2$', fontdict=font)\n", - "plt.text(-19, 0.08, r'Parameters: $\\mu = 2$, $\\sigma = 4$', fontdict=font)\n", - "plt.xlabel(r'$x$',fontsize=20)\n", - "plt.ylabel(r'$p(x)$ [MeV]',fontsize=20)\n", - "\n", - "# Tweak spacing to prevent clipping of ylabel \n", - "plt.subplots_adjust(left=0.15)\n", - "plt.savefig('gaussian.pdf', format='pdf')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exponential distribution\n", - "\n", - "Another important distribution in science is the exponential distribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\alpha\\exp{-(\\alpha x)}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Expectation values\n", - "\n", - "Let $h(x)$ be an arbitrary continuous function on the domain of the stochastic\n", - "variable $X$ whose PDF is $p(x)$. We define the *expectation value*\n", - "of $h$ with respect to $p$ as follows" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\langle h \\rangle_X \\equiv \\int\\! h(x)p(x)\\,dx\n", - "\\label{eq:expectation_value_of_h_wrt_p} \\tag{11}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Whenever the PDF is known implicitly, like in this case, we will drop\n", - "the index $X$ for clarity. \n", - "A particularly useful class of special expectation values are the\n", - "*moments*. The $n$-th moment of the PDF $p$ is defined as\n", - "follows" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x^n \\rangle \\equiv \\int\\! x^n p(x)\\,dx\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Stochastic variables and the main concepts, mean values\n", - "\n", - "The zero-th moment $\\langle 1\\rangle$ is just the normalization condition of\n", - "$p$. The first moment, $\\langle x\\rangle$, is called the *mean* of $p$\n", - "and often denoted by the letter $\\mu$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x\\rangle = \\mu \\equiv \\int x p(x)dx,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "for a continuous distribution and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x\\rangle = \\mu \\equiv \\frac{1}{N}\\sum_{i=1}^N x_i p(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "for a discrete distribution. \n", - "Qualitatively it represents the centroid or the average value of the\n", - "PDF and is therefore simply called the expectation value of $p(x)$.\n", - "\n", - "\n", - "\n", - "## Stochastic variables and the main concepts, central moments, the variance\n", - "\n", - "\n", - "A special version of the moments is the set of *central moments*, the n-th central moment defined as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle (x-\\langle x\\rangle )^n\\rangle \\equiv \\int\\! (x-\\langle x\\rangle)^n p(x)\\,dx\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The zero-th and first central moments are both trivial, equal $1$ and\n", - "$0$, respectively. But the second central moment, known as the\n", - "*variance* of $p$, is of particular interest. For the stochastic\n", - "variable $X$, the variance is denoted as $\\sigma^2_X$ or $\\mathrm{Var}(X)$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "\\sigma^2_X &=\\mathrm{Var}(X) = \\langle (x-\\langle x\\rangle)^2\\rangle =\n", - "\\int (x-\\langle x\\rangle)^2 p(x)dx\\\\\n", - "& = \\int\\left(x^2 - 2 x \\langle x\\rangle^{2} +\\langle x\\rangle^2\\right)p(x)dx\\\\\n", - "& = \\langle x^2\\rangle\\rangle - 2 \\langle x\\rangle\\langle x\\rangle + \\langle x\\rangle^2\\\\\n", - "& = \\langle x^2 \\rangle - \\langle x\\rangle^2\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The square root of the variance, $\\sigma =\\sqrt{\\langle (x-\\langle x\\rangle)^2\\rangle}$ is called the \n", - "**standard deviation** of $p$. It is the RMS (root-mean-square)\n", - "value of the deviation of the PDF from its mean value, interpreted\n", - "qualitatively as the \"spread\" of $p$ around its mean.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Probability Distribution Functions\n", - "\n", - "\n", - "The following table collects properties of probability distribution functions.\n", - "In our notation we reserve the label $p(x)$ for the probability of a certain event,\n", - "while $P(x)$ is the cumulative probability. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "
Discrete PDF Continuous PDF
Domain $\\left\\{x_1, x_2, x_3, \\dots, x_N\\right\\}$ $[a,b]$
Probability $p(x_i)$ $p(x)dx$
Cumulative $P_i=\\sum_{l=1}^ip(x_l)$ $P(x)=\\int_a^xp(t)dt$
Positivity $ 0\\le p(x_i)\\le 1$ $ p(x) \\ge 0$
Positivity $ 0\\le P_i\\le 1$ $ 0\\le P(x)\\le 1$
Monotonic $P_i\\ge P_j$ if $x_i\\ge x_j$ $P(x_i)\\ge P(x_j)$ if $x_i\\ge x_j$
Normalization $P_N=1$ $P(b)=1$
\n", - "\n", - "\n", - "\n", - "\n", - "## Probability Distribution Functions\n", - "\n", - "With a PDF we can compute expectation values of selected quantities such as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x^k\\rangle=\\frac{1}{N}\\sum_{i=1}^{N}x_i^kp(x_i),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "if we have a discrete PDF or" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x^k\\rangle=\\int_a^b x^kp(x)dx,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "in the case of a continuous PDF. We have already defined the mean value $\\mu$\n", - "and the variance $\\sigma^2$. \n", - "\n", - "\n", - "\n", - "## The three famous Probability Distribution Functions\n", - "\n", - "\n", - "There are at least three PDFs which one may encounter. These are the\n", - "\n", - "**Uniform distribution**" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x)=\\frac{1}{b-a}\\Theta(x-a)\\Theta(b-x),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "yielding probabilities different from zero in the interval $[a,b]$.\n", - "\n", - "**The exponential distribution**" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x)=\\alpha \\exp{(-\\alpha x)},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "yielding probabilities different from zero in the interval $[0,\\infty)$ and with mean value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu = \\int_0^{\\infty}xp(x)dx=\\int_0^{\\infty}x\\alpha \\exp{(-\\alpha x)}dx=\\frac{1}{\\alpha},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with variance" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2=\\int_0^{\\infty}x^2p(x)dx-\\mu^2 = \\frac{1}{\\alpha^2}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Probability Distribution Functions, the normal distribution\n", - "\n", - "Finally, we have the so-called univariate normal distribution, or just the **normal distribution**" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x)=\\frac{1}{b\\sqrt{2\\pi}}\\exp{\\left(-\\frac{(x-a)^2}{2b^2}\\right)}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with probabilities different from zero in the interval $(-\\infty,\\infty)$.\n", - "The integral $\\int_{-\\infty}^{\\infty}\\exp{\\left(-(x^2\\right)}dx$ appears in many calculations, its value\n", - "is $\\sqrt{\\pi}$, a result we will need when we compute the mean value and the variance.\n", - "The mean value is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu = \\int_0^{\\infty}xp(x)dx=\\frac{1}{b\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty}x \\exp{\\left(-\\frac{(x-a)^2}{2b^2}\\right)}dx,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which becomes with a suitable change of variables" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu =\\frac{1}{b\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty}b\\sqrt{2}(a+b\\sqrt{2}y)\\exp{-y^2}dy=a.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Probability Distribution Functions, the normal distribution\n", - "\n", - "Similarly, the variance becomes" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2 = \\frac{1}{b\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty}(x-\\mu)^2 \\exp{\\left(-\\frac{(x-a)^2}{2b^2}\\right)}dx,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and inserting the mean value and performing a variable change we obtain" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2 = \\frac{1}{b\\sqrt{2\\pi}}\\int_{-\\infty}^{\\infty}b\\sqrt{2}(b\\sqrt{2}y)^2\\exp{\\left(-y^2\\right)}dy=\n", - "\\frac{2b^2}{\\sqrt{\\pi}}\\int_{-\\infty}^{\\infty}y^2\\exp{\\left(-y^2\\right)}dy,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and performing a final integration by parts we obtain the well-known result $\\sigma^2=b^2$.\n", - "It is useful to introduce the standard normal distribution as well, defined by $\\mu=a=0$, viz. a distribution\n", - "centered around zero and with a variance $\\sigma^2=1$, leading to" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " p(x)=\\frac{1}{\\sqrt{2\\pi}}\\exp{\\left(-\\frac{x^2}{2}\\right)}.\n", - "\\label{_auto9} \\tag{12}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Probability Distribution Functions, the cumulative distribution\n", - "\n", - "\n", - "The exponential and uniform distributions have simple cumulative functions,\n", - "whereas the normal distribution does not, being proportional to the so-called\n", - "error function $erf(x)$, given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "P(x) = \\frac{1}{\\sqrt{2\\pi}}\\int_{-\\infty}^x\\exp{\\left(-\\frac{t^2}{2}\\right)}dt,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which is difficult to evaluate in a quick way. \n", - "\n", - "\n", - "\n", - "\n", - "## Probability Distribution Functions, other important distribution\n", - "\n", - "\n", - "Some other PDFs which one encounters often in the natural sciences are the binomial distribution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\left(\\begin{array}{c} n \\\\ x\\end{array}\\right)y^x(1-y)^{n-x} \\hspace{0.5cm}x=0,1,\\dots,n,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $y$ is the probability for a specific event, such as the tossing of a coin or moving left or right\n", - "in case of a random walker. Note that $x$ is a discrete stochastic variable. \n", - "\n", - "The sequence of binomial trials is characterized by the following definitions\n", - "\n", - " * Every experiment is thought to consist of $N$ independent trials.\n", - "\n", - " * In every independent trial one registers if a specific situation happens or not, such as the jump to the left or right of a random walker.\n", - "\n", - " * The probability for every outcome in a single trial has the same value, for example the outcome of tossing (either heads or tails) a coin is always $1/2$.\n", - "\n", - "## Probability Distribution Functions, the binomial distribution\n", - "\n", - "\n", - "In order to compute the mean and variance we need to recall Newton's binomial\n", - "formula" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "(a+b)^m=\\sum_{n=0}^m \\left(\\begin{array}{c} m \\\\ n\\end{array}\\right)a^nb^{m-n},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which can be used to show that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sum_{x=0}^n\\left(\\begin{array}{c} n \\\\ x\\end{array}\\right)y^x(1-y)^{n-x} = (y+1-y)^n = 1,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "the PDF is normalized to one. \n", - "The mean value is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu = \\sum_{x=0}^n x\\left(\\begin{array}{c} n \\\\ x\\end{array}\\right)y^x(1-y)^{n-x} =\n", - "\\sum_{x=0}^n x\\frac{n!}{x!(n-x)!}y^x(1-y)^{n-x},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "resulting in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu = \n", - "\\sum_{x=0}^n x\\frac{(n-1)!}{(x-1)!(n-1-(x-1))!}y^{x-1}(1-y)^{n-1-(x-1)},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which we rewrite as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu=ny\\sum_{\\nu=0}^n\\left(\\begin{array}{c} n-1 \\\\ \\nu\\end{array}\\right)y^{\\nu}(1-y)^{n-1-\\nu} =ny(y+1-y)^{n-1}=ny.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The variance is slightly trickier to get. It reads $\\sigma^2=ny(1-y)$. \n", - "\n", - "\n", - "## Probability Distribution Functions, Poisson's distribution\n", - "\n", - "\n", - "Another important distribution with discrete stochastic variables $x$ is \n", - "the Poisson model, which resembles the exponential distribution and reads" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p(x) = \\frac{\\lambda^x}{x!} e^{-\\lambda} \\hspace{0.5cm}x=0,1,\\dots,;\\lambda > 0.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this case both the mean value and the variance are easier to calculate," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu = \\sum_{x=0}^{\\infty} x \\frac{\\lambda^x}{x!} e^{-\\lambda} = \\lambda e^{-\\lambda}\\sum_{x=1}^{\\infty}\n", - "\\frac{\\lambda^{x-1}}{(x-1)!}=\\lambda,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and the variance is $\\sigma^2=\\lambda$. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Probability Distribution Functions, Poisson's distribution\n", - "\n", - "An example of applications of the Poisson distribution could be the counting\n", - "of the number of $\\alpha$-particles emitted from a radioactive source in a given time interval.\n", - "In the limit of $n\\rightarrow \\infty$ and for small probabilities $y$, the binomial distribution\n", - "approaches the Poisson distribution. Setting $\\lambda = ny$, with $y$ the probability for an event in\n", - "the binomial distribution we can show that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\lim_{n\\rightarrow \\infty}\\left(\\begin{array}{c} n \\\\ x\\end{array}\\right)y^x(1-y)^{n-x} e^{-\\lambda}=\\sum_{x=1}^{\\infty}\\frac{\\lambda^x}{x!} e^{-\\lambda}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Meet the covariance!\n", - "\n", - "An important quantity in a statistical analysis is the so-called covariance. \n", - "\n", - "Consider the set $\\{X_i\\}$ of $n$\n", - "stochastic variables (not necessarily uncorrelated) with the\n", - "multivariate PDF $P(x_1,\\dots,x_n)$. The *covariance* of two\n", - "of the stochastic variables, $X_i$ and $X_j$, is defined as follows" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\mathrm{Cov}(X_i,\\,X_j) = \\langle (x_i-\\langle x_i\\rangle)(x_j-\\langle x_j\\rangle)\\rangle \n", - "\\label{_auto10} \\tag{13}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation} \n", - "=\\int\\cdots\\int (x_i-\\langle x_i\\rangle)(x_j-\\langle x_j\\rangle)P(x_1,\\dots,x_n)\\,dx_1\\dots dx_n,\n", - "\\label{eq:def_covariance} \\tag{14}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x_i\\rangle =\n", - "\\int\\cdots\\int x_i P(x_1,\\dots,x_n)\\,dx_1\\dots dx_n.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Meet the covariance in matrix disguise\n", - "\n", - "If we consider the above covariance as a matrix" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "C_{ij} =\\mathrm{Cov}(X_i,\\,X_j),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "then the diagonal elements are just the familiar\n", - "variances, $C_{ii} = \\mathrm{Cov}(X_i,\\,X_i) = \\mathrm{Var}(X_i)$. It turns out that\n", - "all the off-diagonal elements are zero if the stochastic variables are\n", - "uncorrelated. \n", - "\n", - "\n", - "\n", - "## Meet the covariance, uncorrelated events\n", - "\n", - "\n", - "This is easy to show, keeping in mind the linearity of\n", - "the expectation value. Consider the stochastic variables $X_i$ and\n", - "$X_j$, ($i\\neq j$)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "\\mathrm{Cov}(X_i,\\,X_j) &= \\langle (x_i-\\langle x_i\\rangle)(x_j-\\langle x_j\\rangle)\\rangle\\\\\n", - "&=\\langle x_i x_j - x_i\\langle x_j\\rangle - \\langle x_i\\rangle x_j + \\langle x_i\\rangle\\langle x_j\\rangle\\rangle\\\\\n", - "&=\\langle x_i x_j\\rangle - \\langle x_i\\langle x_j\\rangle\\rangle - \\langle \\langle x_i\\rangle x_j \\rangle +\n", - "\\langle \\langle x_i\\rangle\\langle x_j\\rangle\\rangle\\\\\n", - "&=\\langle x_i x_j\\rangle - \\langle x_i\\rangle\\langle x_j\\rangle - \\langle x_i\\rangle\\langle x_j\\rangle +\n", - "\\langle x_i\\rangle\\langle x_j\\rangle\\\\\n", - "&=\\langle x_i x_j\\rangle - \\langle x_i\\rangle\\langle x_j\\rangle\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If $X_i$ and $X_j$ are independent, we get" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x_i x_j\\rangle =\n", - "\\langle x_i\\rangle\\langle x_j\\rangle=\\mathrm{Cov}(X_i, X_j) = 0\\ \\ (i\\neq j).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Numerical experiments and the covariance\n", - "\n", - "\n", - "Now that we have constructed an idealized mathematical framework, let\n", - "us try to apply it to empirical observations. Examples of relevant\n", - "physical phenomena may be spontaneous decays of nuclei, or a purely\n", - "mathematical set of numbers produced by some deterministic\n", - "mechanism. It is the latter we will deal with, using so-called pseudo-random\n", - "number generators. In general our observations will contain only a limited set of\n", - "observables. We remind the reader that\n", - "a *stochastic process* is a process that produces sequentially a\n", - "chain of values" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\{x_1, x_2,\\dots\\,x_k,\\dots\\}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Numerical experiments and the covariance\n", - "\n", - "We will call these\n", - "values our *measurements* and the entire set as our measured\n", - "*sample*. The action of measuring all the elements of a sample\n", - "we will call a stochastic *experiment* (since, operationally,\n", - "they are often associated with results of empirical observation of\n", - "some physical or mathematical phenomena; precisely an experiment). We\n", - "assume that these values are distributed according to some \n", - "PDF $p_X^{\\phantom X}(x)$, where $X$ is just the formal symbol for the\n", - "stochastic variable whose PDF is $p_X^{\\phantom X}(x)$. Instead of\n", - "trying to determine the full distribution $p$ we are often only\n", - "interested in finding the few lowest moments, like the mean\n", - "$\\mu_X^{\\phantom X}$ and the variance $\\sigma_X^{\\phantom X}$.\n", - "\n", - "\n", - "\n", - "\n", - "## Numerical experiments and the covariance, actual situations\n", - "\n", - "In practical situations however, a sample is always of finite size. Let that\n", - "size be $n$. The expectation value of a sample $\\alpha$, the **sample mean**, is then defined as follows" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\langle x_{\\alpha} \\rangle \\equiv \\frac{1}{n}\\sum_{k=1}^n x_{\\alpha,k}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The *sample variance* is:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mathrm{Var}(x) \\equiv \\frac{1}{n}\\sum_{k=1}^n (x_{\\alpha,k} - \\langle x_{\\alpha} \\rangle)^2,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with its square root being the *standard deviation of the sample*. \n", - "\n", - "\n", - "\n", - "\n", - "## Numerical experiments and the covariance, our observables\n", - "\n", - "You can think of the above observables as a set of quantities which define\n", - "a given experiment. This experiment is then repeated several times, say $m$ times.\n", - "The total average is then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\langle X_m \\rangle= \\frac{1}{m}\\sum_{\\alpha=1}^mx_{\\alpha}=\\frac{1}{mn}\\sum_{\\alpha, k} x_{\\alpha,k},\n", - "\\label{eq:exptmean} \\tag{15}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the last sums end at $m$ and $n$.\n", - "The total variance is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2_m= \\frac{1}{mn^2}\\sum_{\\alpha=1}^m(\\langle x_{\\alpha} \\rangle-\\langle X_m \\rangle)^2,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which we rewrite as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\sigma^2_m=\\frac{1}{m}\\sum_{\\alpha=1}^m\\sum_{kl=1}^n (x_{\\alpha,k}-\\langle X_m \\rangle)(x_{\\alpha,l}-\\langle X_m \\rangle).\n", - "\\label{eq:exptvariance} \\tag{16}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Numerical experiments and the covariance, the sample variance\n", - "\n", - "\n", - "We define also the sample variance $\\sigma^2$ of all $mn$ individual experiments as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\sigma^2=\\frac{1}{mn}\\sum_{\\alpha=1}^m\\sum_{k=1}^n (x_{\\alpha,k}-\\langle X_m \\rangle)^2.\n", - "\\label{eq:sampleexptvariance} \\tag{17}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These quantities, being known experimental values or the results from our calculations, \n", - "may differ, in some cases\n", - "significantly, from the similarly named\n", - "exact values for the mean value $\\mu_X$, the variance $\\mathrm{Var}(X)$\n", - "and the covariance $\\mathrm{Cov}(X,Y)$. \n", - "\n", - "\n", - "\n", - "## Numerical experiments and the covariance, central limit theorem\n", - "\n", - "\n", - "The central limit theorem states that the PDF $\\tilde{p}(z)$ of\n", - "the average of $m$ random values corresponding to a PDF $p(x)$ \n", - "is a normal distribution whose mean is the \n", - "mean value of the PDF $p(x)$ and whose variance is the variance\n", - "of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$.\n", - "\n", - "The central limit theorem leads then to the well-known expression for the\n", - "standard deviation, given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma_m=\n", - "\\frac{\\sigma}{\\sqrt{m}}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In many cases the above estimate for the standard deviation, in particular if correlations are strong, may be too simplistic. We need therefore a more precise defintion of the error and the variance in our results.\n", - "\n", - "\n", - "\n", - "## Definition of Correlation Functions and Standard Deviation\n", - "\n", - "Our estimate of the true average $\\mu_{X}$ is the sample mean $\\langle X_m \\rangle$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu_{X}^{\\phantom X} \\approx X_m=\\frac{1}{mn}\\sum_{\\alpha=1}^m\\sum_{k=1}^n x_{\\alpha,k}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can then use Eq. ([eq:exptvariance](#eq:exptvariance))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2_m=\\frac{1}{mn^2}\\sum_{\\alpha=1}^m\\sum_{kl=1}^n (x_{\\alpha,k}-\\langle X_m \\rangle)(x_{\\alpha,l}-\\langle X_m \\rangle),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and rewrite it as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2_m=\\frac{\\sigma^2}{n}+\\frac{2}{mn^2}\\sum_{\\alpha=1}^m\\sum_{k\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\kappa_d = \\frac{f_d}{\\sigma^2}\n", - "\\label{eq:autocorrelformal} \\tag{18}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which gives us a useful measure of the correlation pair correlation\n", - "starting always at $1$ for $d=0$.\n", - "\n", - "\n", - "\n", - "## Definition of Correlation Functions and Standard Deviation, sample variance\n", - "\n", - "\n", - "The sample variance of the $mn$ experiments can now be\n", - "written in terms of the autocorrelation function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\sigma_m^2=\\frac{\\sigma^2}{n}+\\frac{2}{n}\\cdot\\sigma^2\\sum_{d=1}^{n-1}\n", - "\\frac{f_d}{\\sigma^2}=\\left(1+2\\sum_{d=1}^{n-1}\\kappa_d\\right)\\frac{1}{n}\\sigma^2=\\frac{\\tau}{n}\\cdot\\sigma^2\n", - "\\label{eq:error_estimate_corr_time} \\tag{19}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and we see that $\\sigma_m$ can be expressed in terms of the\n", - "uncorrelated sample variance times a correction factor $\\tau$ which\n", - "accounts for the correlation between measurements. We call this\n", - "correction factor the *autocorrelation time*" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "\\tau = 1+2\\sum_{d=1}^{n-1}\\kappa_d\n", - "\\label{eq:autocorrelation_time} \\tag{20}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "\n", - "For a correlation free experiment, $\\tau$\n", - "equals 1. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Definition of Correlation Functions and Standard Deviation\n", - "\n", - "From the point of view of\n", - "Eq. ([eq:error_estimate_corr_time](#eq:error_estimate_corr_time)) we can interpret a sequential\n", - "correlation as an effective reduction of the number of measurements by\n", - "a factor $\\tau$. The effective number of measurements becomes" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "n_\\mathrm{eff} = \\frac{n}{\\tau}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To neglect the autocorrelation time $\\tau$ will always cause our\n", - "simple uncorrelated estimate of $\\sigma_m^2\\approx \\sigma^2/n$ to\n", - "be less than the true sample error. The estimate of the error will be\n", - "too \"good\". On the other hand, the calculation of the full\n", - "autocorrelation time poses an efficiency problem if the set of\n", - "measurements is very large. The solution to this problem is given by \n", - "more practically oriented methods like the blocking technique.\n", - "\n", - "\n", - "\n", - "\n", - "# Random Numbers\n", - "\n", - "\n", - "Uniform deviates are just random numbers that lie within a specified range\n", - "(typically 0 to 1), with any one number in the range just as likely as any other. They\n", - "are, in other words, what you probably think random numbers are. However,\n", - "we want to distinguish uniform deviates from other sorts of random numbers, for\n", - "example numbers drawn from a normal (Gaussian) distribution of specified mean\n", - "and standard deviation. These other sorts of deviates are almost always generated by\n", - "performing appropriate operations on one or more uniform deviates, as we will see\n", - "in subsequent sections. So, a reliable source of random uniform deviates, the subject\n", - "of this section, is an essential building block for any sort of stochastic modeling\n", - "or Monte Carlo computer work.\n", - "\n", - "\n", - "\n", - "\n", - "# Random Numbers, better name: pseudo random numbers\n", - "\n", - "\n", - "A disclaimer is however appropriate. It should be fairly obvious that \n", - "something as deterministic as a computer cannot generate purely random numbers.\n", - "\n", - "Numbers generated by any of the standard algorithms are in reality pseudo random\n", - "numbers, hopefully abiding to the following criteria:\n", - "\n", - " * they produce a uniform distribution in the interval [0,1].\n", - "\n", - " * correlations between random numbers are negligible\n", - "\n", - " * the period before the same sequence of random numbers is repeated is as large as possible and finally\n", - "\n", - " * the algorithm should be fast.\n", - "\n", - "# Random number generator RNG\n", - "\n", - " The most common random number generators are based on so-called\n", - "Linear congruential relations of the type" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "N_i=(aN_{i-1}+c) \\mathrm{MOD} (M),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which yield a number in the interval [0,1] through" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "x_i=N_i/M\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The number \n", - "$M$ is called the period and it should be as large as possible \n", - " and \n", - "$N_0$ is the starting value, or seed. The function $\\mathrm{MOD}$ means the remainder,\n", - "that is if we were to evaluate $(13)\\mathrm{MOD}(9)$, the outcome is the remainder\n", - "of the division $13/9$, namely $4$.\n", - "\n", - "\n", - "\n", - "# Random number generator RNG and periodic outputs\n", - "\n", - "\n", - "The problem with such generators is that their outputs are periodic;\n", - "they \n", - "will start to repeat themselves with a period that is at most $M$. If however\n", - "the parameters $a$ and $c$ are badly chosen, the period may be even shorter.\n", - "\n", - "Consider the following example" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "N_i=(6N_{i-1}+7) \\mathrm{MOD} (5),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with a seed $N_0=2$. This generator produces the sequence\n", - "$4,1,3,0,2,4,1,3,0,2,...\\dots$, i.e., a sequence with period $5$.\n", - "However, increasing $M$ may not guarantee a larger period as the following\n", - "example shows" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "N_i=(27N_{i-1}+11) \\mathrm{MOD} (54),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which still, with $N_0=2$, results in $11,38,11,38,11,38,\\dots$, a period of\n", - "just $2$.\n", - "\n", - "\n", - "\n", - "# Random number generator RNG and its period\n", - "\n", - "Typical periods for the random generators provided in the program library \n", - "are of the order of $\\sim 10^9$ or larger. Other random number generators which have\n", - "become increasingly popular are so-called shift-register generators.\n", - "In these generators each successive number depends on many preceding\n", - "values (rather than the last values as in the linear congruential\n", - "generator).\n", - "For example, you could make a shift register generator whose $l$th \n", - "number is the sum of the $l-i$th and $l-j$th values with modulo $M$," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "N_l=(aN_{l-i}+cN_{l-j})\\mathrm{MOD}(M).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Random number generator RNG, other examples\n", - "\n", - "Such a generator again produces a sequence of pseudorandom numbers\n", - "but this time with a period much larger than $M$.\n", - "It is also possible to construct more elaborate algorithms by including\n", - "more than two past terms in the sum of each iteration.\n", - "One example is the generator of [Marsaglia and Zaman](http://dl.acm.org/citation.cfm?id=187154)\n", - "which consists of two congruential relations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " N_l=(N_{l-3}-N_{l-1})\\mathrm{MOD}(2^{31}-69),\n", - "\\label{eq:mz1} \\tag{21}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "followed by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " N_l=(69069N_{l-1}+1013904243)\\mathrm{MOD}(2^{32}),\n", - "\\label{eq:mz2} \\tag{22}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which according to the authors has a period larger than $2^{94}$.\n", - "\n", - "\n", - "\n", - "# Random number generator RNG, other examples\n", - "\n", - "Instead of using modular addition, we could use the bitwise\n", - "exclusive-OR ($\\oplus$) operation so that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "N_l=(N_{l-i})\\oplus (N_{l-j})\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the bitwise action of $\\oplus$ means that if $N_{l-i}=N_{l-j}$ the result is\n", - "$0$ whereas if $N_{l-i}\\ne N_{l-j}$ the result is\n", - "$1$. As an example, consider the case where $N_{l-i}=6$ and $N_{l-j}=11$. The first\n", - "one has a bit representation (using 4 bits only) which reads $0110$ whereas the \n", - "second number is $1011$. Employing the $\\oplus$ operator yields \n", - "$1101$, or $2^3+2^2+2^0=13$.\n", - "\n", - "In Fortran90, the bitwise $\\oplus$ operation is coded through the intrinsic\n", - "function $\\mathrm{IEOR}(m,n)$ where $m$ and $n$ are the input numbers, while in $C$\n", - "it is given by $m\\wedge n$. \n", - "\n", - "\n", - "\n", - "\n", - "# Random number generator RNG, RAN0\n", - "\n", - "\n", - "We show here how the linear congruential algorithm can be implemented, namely" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "N_i=(aN_{i-1}) \\mathrm{MOD} (M).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "However, since $a$ and $N_{i-1}$ are integers and their multiplication \n", - "could become greater than the standard 32 bit integer, there is a trick via \n", - "Schrage's algorithm which approximates the multiplication\n", - "of large integers through the factorization" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "M=aq+r,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where we have defined" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "q=[M/a],\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "r = M\\hspace{0.1cm}\\mathrm{MOD} \\hspace{0.1cm}a.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the brackets denote integer division. In the code below the numbers \n", - "$q$ and $r$ are chosen so that $r < q$.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "# Random number generator RNG, RAN0\n", - "\n", - "\n", - "To see how this works we note first that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "(aN_{i-1}) \\mathrm{MOD} (M)= (aN_{i-1}-[N_{i-1}/q]M)\\mathrm{MOD} (M),\n", - "\\label{eq:rntrick1} \\tag{23}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "since we can add or subtract any integer multiple of $M$ from $aN_{i-1}$.\n", - "The last term $[N_{i-1}/q]M\\mathrm{MOD}(M)$ is zero since the integer division \n", - "$[N_{i-1}/q]$ just yields a constant which is multiplied with $M$. \n", - "\n", - "\n", - "\n", - "\n", - "# Random number generator RNG, RAN0\n", - "\n", - "We can now rewrite Eq. ([eq:rntrick1](#eq:rntrick1)) as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "(aN_{i-1}) \\mathrm{MOD} (M)= (aN_{i-1}-[N_{i-1}/q](aq+r))\\mathrm{MOD} (M),\n", - "\\label{eq:rntrick2} \\tag{24}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which results\n", - "in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "(aN_{i-1}) \\mathrm{MOD} (M)= \\left(a(N_{i-1}-[N_{i-1}/q]q)-[N_{i-1}/q]r)\\right)\\mathrm{MOD} (M),\n", - "\\label{eq:rntrick3} \\tag{25}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "yielding" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "(aN_{i-1}) \\mathrm{MOD} (M)= \\left(a(N_{i-1}\\mathrm{MOD} (q)) -[N_{i-1}/q]r)\\right)\\mathrm{MOD} (M).\n", - "\\label{eq:rntrick4} \\tag{26}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Random number generator RNG, RAN0\n", - "\n", - "The term $[N_{i-1}/q]r$ is always smaller or equal $N_{i-1}(r/q)$ and with $r < q$ we obtain always a \n", - "number smaller than $N_{i-1}$, which is smaller than $M$. \n", - "And since the number $N_{i-1}\\mathrm{MOD} (q)$ is between zero and $q-1$ then\n", - "$a(N_{i-1}\\mathrm{MOD} (q))< aq$. Combined with our definition of $q=[M/a]$ ensures that \n", - "this term is also smaller than $M$ meaning that both terms fit into a\n", - "32-bit signed integer. None of these two terms can be negative, but their difference could.\n", - "The algorithm below adds $M$ if their difference is negative.\n", - "Note that the program uses the bitwise $\\oplus$ operator to generate\n", - "the starting point for each generation of a random number. The period\n", - "of $ran0$ is $\\sim 2.1\\times 10^{9}$. A special feature of this\n", - "algorithm is that is should never be called with the initial seed \n", - "set to $0$. \n", - "\n", - "\n", - "\n", - "\n", - "# Random number generator RNG, RAN0 code" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " /*\n", - " ** The function\n", - " ** ran0()\n", - " ** is an \"Minimal\" random number generator of Park and Miller\n", - " ** Set or reset the input value\n", - " ** idum to any integer value (except the unlikely value MASK)\n", - " ** to initialize the sequence; idum must not be altered between\n", - " ** calls for sucessive deviates in a sequence.\n", - " ** The function returns a uniform deviate between 0.0 and 1.0.\n", - " */\n", - " double ran0(long &idum)\n", - " {\n", - " const int a = 16807, m = 2147483647, q = 127773;\n", - " const int r = 2836, MASK = 123459876;\n", - " const double am = 1./m;\n", - " long k;\n", - " double ans;\n", - " idum ^= MASK;\n", - " k = (*idum)/q;\n", - " idum = a*(idum - k*q) - r*k;\n", - " // add m if negative difference\n", - " if(idum < 0) idum += m;\n", - " ans=am*(idum);\n", - " idum ^= MASK;\n", - " return ans;\n", - " } // End: function ran0() \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Properties of Selected Random Number Generators\n", - "\n", - "\n", - "As mentioned previously, the underlying PDF for the generation of\n", - "random numbers is the uniform distribution, meaning that the \n", - "probability for finding a number $x$ in the interval [0,1] is $p(x)=1$.\n", - "\n", - "A random number generator should produce numbers which are uniformly distributed\n", - "in this interval. The table shows the distribution of $N=10000$ random\n", - "numbers generated by the functions in the program library.\n", - "We note in this table that the number of points in the various\n", - "intervals $0.0-0.1$, $0.1-0.2$ etc are fairly close to $1000$, with some minor\n", - "deviations. \n", - "\n", - "Two additional measures are the standard deviation $\\sigma$ and the mean\n", - "$\\mu=\\langle x\\rangle$.\n", - "\n", - "\n", - "\n", - "## Properties of Selected Random Number Generators\n", - "\n", - "For the uniform distribution, the mean value $\\mu$ is then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\mu=\\langle x\\rangle=\\frac{1}{2}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "while the standard deviation is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma=\\sqrt{\\langle x^2\\rangle-\\mu^2}=\\frac{1}{\\sqrt{12}}=0.2886.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Properties of Selected Random Number Generators\n", - "\n", - "The various random number generators produce results which agree rather well with\n", - "these limiting values. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "
$x$-bin ran0 ran1 ran2 ran3
0.0-0.1 1013 991 938 1047
0.1-0.2 1002 1009 1040 1030
0.2-0.3 989 999 1030 993
0.3-0.4 939 960 1023 937
0.4-0.5 1038 1001 1002 992
0.5-0.6 1037 1047 1009 1009
0.6-0.7 1005 989 1003 989
0.7-0.8 986 962 985 954
0.8-0.9 1000 1027 1009 1023
0.9-1.0 991 1015 961 1026
$\\mu$ 0.4997 0.5018 0.4992 0.4990
$\\sigma$ 0.2882 0.2892 0.2861 0.2915
\n", - "\n", - "\n", - "\n", - "## Simple demonstration of RNGs using python\n", - "\n", - "The following simple Python code plots the distribution of the produced random numbers using the linear congruential RNG employed by Python. The trend displayed in the previous table is seen rather clearly." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "#!/usr/bin/env python\n", - "import numpy as np\n", - "import matplotlib.mlab as mlab\n", - "import matplotlib.pyplot as plt\n", - "import random\n", - "\n", - "# initialize the rng with a seed\n", - "random.seed() \n", - "counts = 10000\n", - "values = np.zeros(counts) \n", - "for i in range (1, counts, 1):\n", - " values[i] = random.random()\n", - "\n", - "# the histogram of the data\n", - "n, bins, patches = plt.hist(values, 10, facecolor='green')\n", - "\n", - "plt.xlabel('$x$')\n", - "plt.ylabel('Number of counts')\n", - "plt.title(r'Test of uniform distribution')\n", - "plt.axis([0, 1, 0, 1100])\n", - "plt.grid(True)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Properties of Selected Random Number Generators\n", - "\n", - "Since our random numbers, which are typically generated via a linear congruential algorithm,\n", - "are never fully independent, we can then define \n", - "an important test which measures the degree of correlation, namely the so-called \n", - "auto-correlation function defined previously, see again Eq. ([eq:autocorrelformal](#eq:autocorrelformal)).\n", - "We rewrite it here as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "C_k=\\frac{f_d}\n", - " {\\sigma^2},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "with $C_0=1$. Recall that \n", - "$\\sigma^2=\\langle x_i^2\\rangle-\\langle x_i\\rangle^2$ and that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "f_d = \\frac{1}{nm}\\sum_{\\alpha=1}^m\\sum_{k=1}^{n-d}(x_{\\alpha,k}-\\langle X_m \\rangle)(x_{\\alpha,k+d}-\\langle X_m \\rangle),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The non-vanishing of $C_k$ for $k\\ne 0$ means that the random\n", - "numbers are not independent. The independence of the random numbers is crucial \n", - "in the evaluation of other expectation values. If they are not independent, our\n", - "assumption for approximating $\\sigma_N$ is no longer valid.\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Correlation function and which random number generators should I use\n", - "\n", - "The program here computes the correlation function for one of the standard functions included with the c++ compiler." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " // This function computes the autocorrelation function for \n", - " // the standard c++ random number generator\n", - " \n", - " #include \n", - " #include \n", - " #include \n", - " #include \n", - " using namespace std;\n", - " // output file as global variable\n", - " ofstream ofile; \n", - " \n", - " // Main function begins here \n", - " int main(int argc, char* argv[])\n", - " {\n", - " int n;\n", - " char *outfilename;\n", - " \n", - " cin >> n;\n", - " double MCint = 0.; double MCintsqr2=0.;\n", - " double invers_period = 1./RAND_MAX; // initialise the random number generator\n", - " srand(time(NULL)); // This produces the so-called seed in MC jargon\n", - " // Compute the variance and the mean value of the uniform distribution\n", - " // Compute also the specific values x for each cycle in order to be able to\n", - " // the covariance and the correlation function \n", - " // Read in output file, abort if there are too few command-line arguments\n", - " if( argc <= 2 ){\n", - " cout << \"Bad Usage: \" << argv[0] << \n", - " \t \" read also output file and number of cycles on same line\" << endl;\n", - " exit(1);\n", - " }\n", - " else{\n", - " outfilename=argv[1];\n", - " }\n", - " ofile.open(outfilename); \n", - " // Get the number of Monte-Carlo samples\n", - " n = atoi(argv[2]);\n", - " double *X; \n", - " X = new double[n];\n", - " for (int i = 0; i < n; i++){\n", - " double x = double(rand())*invers_period; \n", - " X[i] = x;\n", - " MCint += x;\n", - " MCintsqr2 += x*x;\n", - " }\n", - " double Mean = MCint/((double) n );\n", - " MCintsqr2 = MCintsqr2/((double) n );\n", - " double STDev = sqrt(MCintsqr2-Mean*Mean);\n", - " double Variance = MCintsqr2-Mean*Mean;\n", - " // Write mean value and standard deviation \n", - " cout << \" Standard deviation= \" << STDev << \" Integral = \" << Mean << endl;\n", - " \n", - " // Now we compute the autocorrelation function\n", - " double *autocor; autocor = new double[n];\n", - " for (int j = 0; j < n; j++){\n", - " double sum = 0.0;\n", - " for (int k = 0; k < (n-j); k++){\n", - " \t sum += (X[k]-Mean)*(X[k+j]-Mean); \n", - " }\n", - " autocor[j] = sum/Variance/((double) n );\n", - " ofile << setiosflags(ios::showpoint | ios::uppercase);\n", - " ofile << setw(15) << setprecision(8) << j;\n", - " ofile << setw(15) << setprecision(8) << autocor[j] << endl;\n", - " }\n", - " ofile.close(); // close output file\n", - " return 0;\n", - " } // end of main program \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Correlation function and which random number generators should I use\n", - "\n", - "The following Python code plots the results for the correlation function from the above program." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "from matplotlib import pyplot as plt\n", - "# Load in data file\n", - "data = np.loadtxt(\"datafiles/autocor.dat\")\n", - "# Make arrays containing x-axis and binding energies as function of A\n", - "x = data[:,0]\n", - "corr = data[:,1]\n", - "plt.plot(x, corr ,'ro')\n", - "plt.axis([0,1000,-0.2, 1.1])\n", - "plt.xlabel(r'$d$')\n", - "plt.ylabel(r'$C_d$')\n", - "plt.title(r'autocorrelation function for RNG')\n", - "plt.savefig('autocorr.pdf')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Which RNG should I use?\n", - "\n", - "* In the library files lib.cpp and lib.h we have included four popular RNGs taken from the widely used textbook [Numerical Recipes](http://numerical.recipes/). These are called ran0, ran1, ran2 and ran3.\n", - "\n", - "* C++ has a class called **random**. The [random class](http://www.cplusplus.com/reference/random/) contains a large selection of RNGs and is highly recommended. Some of these RNGs have very large periods making it thereby very safe to use these RNGs in case one is performing large calculations. In particular, the [Mersenne twister random number engine](http://www.cplusplus.com/reference/random/mersenne_twister_engine/) has a period of $2^{19937}$. \n", - "\n", - "## How to use the Mersenne generator\n", - "\n", - "The following part of a c++ code (from project 4) sets up the uniform distribution for $x\\in [0,1]$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " /*\n", - " \n", - " // You need this \n", - " #include \n", - " \n", - " // Initialize the seed and call the Mersienne algo\n", - " std::random_device rd;\n", - " std::mt19937_64 gen(rd());\n", - " // Set up the uniform distribution for x \\in [[0, 1]\n", - " std::uniform_real_distribution RandomNumberGenerator(0.0,1.0);\n", - " \n", - " // Now use the RNG\n", - " int ix = (int) (RandomNumberGenerator(gen)*NSpins);\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Why blocking?\n", - " Statistical analysis\n", - " * Monte Carlo simulations can be treated as *computer experiments*\n", - "\n", - " * The results can be analysed with the same statistical tools as we would use analysing experimental data.\n", - "\n", - " * As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors.\n", - "\n", - "A very good article which explains blocking is H. Flyvbjerg and H. G. Petersen, *Error estimates on averages of correlated data*, [Journal of Chemical Physics 91, 461-466 (1989)](http://scitation.aip.org/content/aip/journal/jcp/91/1/10.1063/1.457480).\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Why blocking?\n", - " Statistical analysis\n", - " * As in other experiments, Monte Carlo experiments have two classes of errors:\n", - "\n", - " * Statistical errors\n", - "\n", - " * Systematical errors\n", - "\n", - "\n", - " * Statistical errors can be estimated using standard tools from statistics\n", - "\n", - " * Systematical errors are method specific and must be treated differently from case to case. (In VMC a common source is the step length or time step in importance sampling)\n", - "\n", - "## Code to demonstrate the calculation of the autocorrelation function\n", - "The following code computes the autocorrelation function, the covariance and the standard deviation\n", - "for standard RNG. \n", - "The [following file](https://github.com/CompPhysics/ComputationalPhysics2/tree/gh-pages/doc/Programs/LecturePrograms/programs/Blocking/autocorrelation.cpp) gives the code." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " // This function computes the autocorrelation function for \n", - " // the Mersenne random number generator with a uniform distribution\n", - " #include \n", - " #include \n", - " #include \n", - " #include \n", - " #include \n", - " #include \n", - " #include \n", - " #include \n", - " using namespace std;\n", - " using namespace arma;\n", - " // output file\n", - " ofstream ofile;\n", - " \n", - " // Main function begins here \n", - " int main(int argc, char* argv[])\n", - " {\n", - " int MonteCarloCycles;\n", - " string filename;\n", - " if (argc > 1) {\n", - " filename=argv[1];\n", - " MonteCarloCycles = atoi(argv[2]);\n", - " string fileout = filename;\n", - " string argument = to_string(MonteCarloCycles);\n", - " fileout.append(argument);\n", - " ofile.open(fileout);\n", - " }\n", - " \n", - " // Compute the variance and the mean value of the uniform distribution\n", - " // Compute also the specific values x for each cycle in order to be able to\n", - " // compute the covariance and the correlation function \n", - " \n", - " vec X = zeros(MonteCarloCycles);\n", - " double MCint = 0.; double MCintsqr2=0.;\n", - " std::random_device rd;\n", - " std::mt19937_64 gen(rd());\n", - " // Set up the uniform distribution for x \\in [[0, 1]\n", - " std::uniform_real_distribution RandomNumberGenerator(0.0,1.0);\n", - " for (int i = 0; i < MonteCarloCycles; i++){\n", - " double x = RandomNumberGenerator(gen); \n", - " X(i) = x;\n", - " MCint += x;\n", - " MCintsqr2 += x*x;\n", - " }\n", - " double Mean = MCint/((double) MonteCarloCycles );\n", - " MCintsqr2 = MCintsqr2/((double) MonteCarloCycles );\n", - " double STDev = sqrt(MCintsqr2-Mean*Mean);\n", - " double Variance = MCintsqr2-Mean*Mean;\n", - " // Write mean value and variance\n", - " cout << \" Sample variance= \" << Variance << \" Mean value = \" << Mean << endl;\n", - " // Now we compute the autocorrelation function\n", - " vec autocorrelation = zeros(MonteCarloCycles);\n", - " for (int j = 0; j < MonteCarloCycles; j++){\n", - " double sum = 0.0;\n", - " for (int k = 0; k < (MonteCarloCycles-j); k++){\n", - " sum += (X(k)-Mean)*(X(k+j)-Mean); \n", - " }\n", - " autocorrelation(j) = sum/Variance/((double) MonteCarloCycles );\n", - " ofile << setiosflags(ios::showpoint | ios::uppercase);\n", - " ofile << setw(15) << setprecision(8) << j;\n", - " ofile << setw(15) << setprecision(8) << autocorrelation(j) << endl;\n", - " }\n", - " // Now compute the exact covariance using the autocorrelation function\n", - " double Covariance = 0.0;\n", - " for (int j = 0; j < MonteCarloCycles; j++){\n", - " Covariance += autocorrelation(j);\n", - " }\n", - " Covariance *= 2.0/((double) MonteCarloCycles);\n", - " // Compute now the total variance, including the covariance, and obtain the standard deviation\n", - " double TotalVariance = (Variance/((double) MonteCarloCycles ))+Covariance;\n", - " cout << \"Covariance =\" << Covariance << \"Totalvariance= \" << TotalVariance << \"Sample Variance/n= \" << (Variance/((double) MonteCarloCycles )) << endl;\n", - " cout << \" STD from sample variance= \" << sqrt(Variance/((double) MonteCarloCycles )) << \" STD with covariance = \" << sqrt(TotalVariance) << endl;\n", - " \n", - " ofile.close(); // close output file\n", - " return 0;\n", - " } // end of main program \n", - " \n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## What is blocking?\n", - " Blocking\n", - " * Say that we have a set of samples from a Monte Carlo experiment\n", - "\n", - " * Assuming (wrongly) that our samples are uncorrelated our best estimate of the standard deviation of the mean $\\langle \\mathbf{M}\\rangle$ is given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma=\\sqrt{\\frac{1}{n}\\left(\\langle \\mathbf{M}^2\\rangle-\\langle \\mathbf{M}\\rangle^2\\right)}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "* If the samples are correlated we can rewrite our results to show that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma=\\sqrt{\\frac{1+2\\tau/\\Delta t}{n}\\left(\\langle \\mathbf{M}^2\\rangle-\\langle \\mathbf{M}\\rangle^2\\right)}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\tau$ is the correlation time (the time between a sample and the next uncorrelated sample) and $\\Delta t$ is time between each sample\n", - "\n", - "\n", - "\n", - "## What is blocking?\n", - " Blocking \n", - " * If $\\Delta t\\gg\\tau$ our first estimate of $\\sigma$ still holds\n", - "\n", - " * Much more common that $\\Delta t<\\tau$\n", - "\n", - " * In the method of data blocking we divide the sequence of samples into blocks\n", - "\n", - " * We then take the mean $\\langle \\mathbf{M}_i\\rangle$ of block $i=1\\ldots n_{blocks}$ to calculate the total mean and variance\n", - "\n", - " * The size of each block must be so large that sample $j$ of block $i$ is not correlated with sample $j$ of block $i+1$\n", - "\n", - " * The correlation time $\\tau$ would be a good choice\n", - "\n", - "## What is blocking?\n", - " Blocking\n", - " * Problem: We don't know $\\tau$ or it is too expensive to compute\n", - "\n", - " * Solution: Make a plot of std. dev. as a function of blocksize\n", - "\n", - " * The estimate of std. dev. of correlated data is too low $\\to$ the error will increase with increasing block size until the blocks are uncorrelated, where we reach a plateau\n", - "\n", - " * When the std. dev. stops increasing the blocks are uncorrelated\n", - "\n", - "## Implementation\n", - "\n", - " * Do a Monte Carlo simulation, storing all samples to file\n", - "\n", - " * Do the statistical analysis on this file, independently of your Monte Carlo program\n", - "\n", - " * Read the file into an array\n", - "\n", - " * Loop over various block sizes\n", - "\n", - " * For each block size $n_b$, loop over the array in steps of $n_b$ taking the mean of elements $i n_b,\\ldots,(i+1) n_b$\n", - "\n", - " * Take the mean and variance of the resulting array\n", - "\n", - " * Write the results for each block size to file for later\n", - " analysis\n", - "\n", - "## Actual implementation with code, main function\n", - "When the file gets large, it can be useful to write your data in binary mode instead of ascii characters.\n", - "The [following python file](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py) reads data from file with the output from every Monte Carlo cycle." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# Blocking\n", - " @timeFunction\n", - " def blocking(self, blockSizeMax = 500):\n", - " blockSizeMin = 1\n", - "\n", - " self.blockSizes = []\n", - " self.meanVec = []\n", - " self.varVec = []\n", - "\n", - " for i in range(blockSizeMin, blockSizeMax):\n", - " if(len(self.data) % i != 0):\n", - " pass#continue\n", - " blockSize = i\n", - " meanTempVec = []\n", - " varTempVec = []\n", - " startPoint = 0\n", - " endPoint = blockSize\n", - "\n", - " while endPoint <= len(self.data):\n", - " meanTempVec.append(np.average(self.data[startPoint:endPoint]))\n", - " startPoint = endPoint\n", - " endPoint += blockSize\n", - " mean, var = np.average(meanTempVec), np.var(meanTempVec)/len(meanTempVec)\n", - " self.meanVec.append(mean)\n", - " self.varVec.append(var)\n", - " self.blockSizes.append(blockSize)\n", - "\n", - " self.blockingAvg = np.average(self.meanVec[-200:])\n", - " self.blockingVar = (np.average(self.varVec[-200:]))\n", - " self.blockingStd = np.sqrt(self.blockingVar)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Bootstrap method\n", - "\n", - "The Bootstrap resampling method is also very popular. It is very simple:\n", - "\n", - "1. Start with your sample of measurements and compute the sample variance and the mean values\n", - "\n", - "2. Then start again but pick in a random way the numbers in the sample and recalculate the mean and the sample variance.\n", - "\n", - "3. Repeat this $K$ times.\n", - "\n", - "It can be shown, see the article by [Efron](https://projecteuclid.org/download/pdf_1/euclid.aos/1176344552)\n", - "that it produces the correct standard deviation.\n", - "\n", - "This method is very useful for small ensembles of data points. \n", - "\n", - "\n", - "## Bootstrapping\n", - "Given a set of $N$ data, assume that we are interested in some \n", - "observable $\\theta$ which may be estimated from that set. This observable can also be for example the result of a fit based on all $N$ raw data. \n", - "Let us call the value of the observable obtained from the original \n", - "data set $\\hat{\\theta}$. One recreates from the sample repeatedly \n", - "other samples by choosing randomly $N$ data out of the original set. \n", - "This costs essentially nothing, since we just recycle the original data set for the building of new sets. \n", - "\n", - "\n", - "## Bootstrapping, recipe\n", - "Let us assume we have done this $K$ times and thus have $K$ sets of $N$ \n", - "data values each. \n", - "Of course some values will enter more than once in the new sets. For each of these sets one computes the observable $\\theta$ resulting in values $\\theta_k$ with $k = 1,...,K$. Then one determines" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\tilde{\\theta} = \\frac{1}{K} \\sum_{k=1}^K \\theta_k,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "sigma^2_{\\tilde{\\theta}} = \\frac{1}{K} \\sum_{k=1}^K \\left(\\theta_k-\\tilde{\\theta}\\right)^2.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These are estimators for $\\angle\\theta\\rangle$ and its variance. They are not unbiased and therefore \n", - "$\\tilde{\\theta}\\neq\\hat{\\theta}$ for finite K. \n", - "\n", - "The difference is called bias and gives an idea on how far away the result may be from \n", - "the true $\\angle\\theta\\rangle$. As final result for the observable one quotes $\\angle\\theta\\rangle = \\tilde{\\theta} \\pm \\sigma_{\\tilde{\\theta}}$ .\n", - "\n", - "\n", - "\n", - "## Bootstrapping, [code](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " # Bootstrap\n", - " @timeFunction\n", - " def bootstrap(self, nBoots = 1000):\n", - " bootVec = np.zeros(nBoots)\n", - " for k in range(0,nBoots):\n", - " bootVec[k] = np.average(np.random.choice(self.data, len(self.data)))\n", - " self.bootAvg = np.average(bootVec)\n", - " self.bootVar = np.var(bootVec)\n", - " self.bootStd = np.std(bootVec)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Jackknife, [code](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " # Jackknife\n", - " @timeFunction\n", - " def jackknife(self):\n", - " jackknVec = np.zeros(len(self.data))\n", - " for k in range(0,len(self.data)):\n", - " jackknVec[k] = np.average(np.delete(self.data, k))\n", - " self.jackknAvg = self.avg - (len(self.data) - 1) * (np.average(jackknVec) - self.avg)\n", - " self.jackknVar = float(len(self.data) - 1) * np.var(jackknVec)\n", - " self.jackknStd = np.sqrt(self.jackknVar)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Regression analysis, overarching aims\n", - "\n", - "\n", - "Regression modeling deals with the description of the sampling distribution of a given random variable $y$ varies as function of another variable or a set of such variables $\\hat{x} =[x_0, x_1,\\dots, x_p]^T$. \n", - "The first variable is called the **dependent**, the **outcome** or the **response** variable while the set of variables $\\hat{x}$ is called the independent variable, or the predictor variable or the explanatory variable. \n", - "\n", - "A regression model aims at finding a likelihood function $p(y\\vert \\hat{x})$, that is the conditional distribution for $y$ with a given $\\hat{x}$. The estimation of $p(y\\vert \\hat{x})$ is made using a data set with \n", - "* $n$ cases $i = 0, 1, 2, \\dots, n-1$ \n", - "\n", - "* Response (dependent or outcome) variable $y_i$ with $i = 0, 1, 2, \\dots, n-1$ \n", - "\n", - "* $p$ Explanatory (independent or predictor) variables $\\hat{x}_i=[x_{i0}, x_{i1}, \\dots, x_{ip}]$ with $i = 0, 1, 2, \\dots, n-1$ \n", - "\n", - " The goal of the regression analysis is to extract/exploit relationship between $y_i$ and $\\hat{x}_i$ in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .\n", - "\n", - "\n", - "\n", - "\n", - "## General linear models\n", - "\n", - "Before we proceed let us study a case from linear algebra where we aim at fitting a set of data $\\hat{y}=[y_0,y_1,\\dots,y_{n-1}]$. We could think of these data as a result of an experiment or a complicated numerical experiment. These data are functions of a series of variables $\\hat{x}=[x_0,x_1,\\dots,x_{n-1}]$, that is $y_i = y(x_i)$ with $i=0,1,2,\\dots,n-1$. The variables $x_i$ could represent physical quantities like time, temperature, position etc. We assume that $y(x)$ is a smooth function. \n", - "\n", - "Since obtaining these data points may not be trivial, we want to use these data to fit a function which can allow us to make predictions for values of $y$ which are not in the present set. The perhaps simplest approach is to assume we can parametrize our function in terms of a polynomial of degree $n-1$ with $n$ points, that is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "y=y(x) \\rightarrow y(x_i)=\\tilde{y}_i+\\epsilon_i=\\sum_{j=0}^{n-1} \\beta_i x_i^j+\\epsilon_i,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\epsilon_i$ is the error in our approximation. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## Rewriting the fitting procedure as a linear algebra problem\n", - "\n", - "For every set of values $y_i,x_i$ we have thus the corresponding set of equations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "y_0&=\\beta_0+\\beta_1x_0^1+\\beta_2x_0^2+\\dots+\\beta_{n-1}x_0^{n-1}+\\epsilon_0\\\\\n", - "y_1&=\\beta_0+\\beta_1x_1^1+\\beta_2x_1^2+\\dots+\\beta_{n-1}x_1^{n-1}+\\epsilon_1\\\\\n", - "y_2&=\\beta_0+\\beta_1x_2^1+\\beta_2x_2^2+\\dots+\\beta_{n-1}x_2^{n-1}+\\epsilon_2\\\\\n", - "\\dots & \\dots \\\\\n", - "y_{n-1}&=\\beta_0+\\beta_1x_{n-1}^1+\\beta_2x_{n-1}^2+\\dots+\\beta_1x_{n-1}^{n-1}+\\epsilon_{n-1}.\\\\\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Rewriting the fitting procedure as a linear algebra problem, follows\n", - "\n", - "Defining the vectors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "2\n", - "9\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "3\n", - "0\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{\\epsilon} = [\\epsilon_0,\\epsilon_1, \\epsilon_2,\\dots, \\epsilon_{n-1}]^T,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and the matrix" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{X}=\n", - "\\begin{bmatrix} \n", - "1& x_{0}^1 &x_{0}^2& \\dots & \\dots &x_{0}^{n-1}\\\\\n", - "1& x_{1}^1 &x_{1}^2& \\dots & \\dots &x_{1}^{n-1}\\\\\n", - "1& x_{2}^1 &x_{2}^2& \\dots & \\dots &x_{2}^{n-1}\\\\ \n", - "\\dots& \\dots &\\dots& \\dots & \\dots &\\dots\\\\\n", - "1& x_{n-1}^1 &x_{n-1}^2& \\dots & \\dots &x_{n-1}^{n-1}\\\\\n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "we can rewrite our equations as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{y} = \\hat{X}\\hat{\\beta}+\\hat{\\epsilon}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Generalizing the fitting procedure as a linear algebra problem\n", - "\n", - "We are obviously not limited to the above polynomial. We could replace the various powers of $x$ with elements of Fourier series, that is, instead of $x_i^j$ we could have $\\cos{(j x_i)}$ or $\\sin{(j x_i)}$, or time series or other orthogonal functions.\n", - "For every set of values $y_i,x_i$ we can then generalize the equations to" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "y_0&=\\beta_0x_{00}+\\beta_1x_{01}+\\beta_2x_{02}+\\dots+\\beta_{n-1}x_{0n-1}+\\epsilon_0\\\\\n", - "y_1&=\\beta_0x_{10}+\\beta_1x_{11}+\\beta_2x_{12}+\\dots+\\beta_{n-1}x_{1n-1}+\\epsilon_1\\\\\n", - "y_2&=\\beta_0x_{20}+\\beta_1x_{21}+\\beta_2x_{22}+\\dots+\\beta_{n-1}x_{2n-1}+\\epsilon_2\\\\\n", - "\\dots & \\dots \\\\\n", - "y_{i}&=\\beta_0x_{i0}+\\beta_1x_{i1}+\\beta_2x_{i2}+\\dots+\\beta_{n-1}x_{in-1}+\\epsilon_i\\\\\n", - "\\dots & \\dots \\\\\n", - "y_{n-1}&=\\beta_0x_{n-1,0}+\\beta_1x_{n-1,2}+\\beta_2x_{n-1,2}+\\dots+\\beta_1x_{n-1,n-1}+\\epsilon_{n-1}.\\\\\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Generalizing the fitting procedure as a linear algebra problem\n", - "\n", - "We redefine in turn the matrix $\\hat{X}$ as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{X}=\n", - "\\begin{bmatrix} \n", - "x_{00}& x_{01} &x_{02}& \\dots & \\dots &x_{0,n-1}\\\\\n", - "x_{10}& x_{11} &x_{12}& \\dots & \\dots &x_{1,n-1}\\\\\n", - "x_{20}& x_{21} &x_{22}& \\dots & \\dots &x_{2,n-1}\\\\ \n", - "\\dots& \\dots &\\dots& \\dots & \\dots &\\dots\\\\\n", - "x_{n-1,0}& x_{n-1,1} &x_{n-1,2}& \\dots & \\dots &x_{n-1,n-1}\\\\\n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and without loss of generality we rewrite again our equations as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{y} = \\hat{X}\\hat{\\beta}+\\hat{\\epsilon}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The left-hand side of this equation forms know. Our error vector $\\hat{\\epsilon}$ and the parameter vector $\\hat{\\beta}$ are our unknow quantities. How can we obtain the optimal set of $\\beta_i$ values? \n", - "\n", - "\n", - "\n", - "\n", - "## Optimizing our parameters\n", - "\n", - "We have defined the matrix $\\hat{X}$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "y_0&=\\beta_0x_{00}+\\beta_1x_{01}+\\beta_2x_{02}+\\dots+\\beta_{n-1}x_{0n-1}+\\epsilon_0\\\\\n", - "y_1&=\\beta_0x_{10}+\\beta_1x_{11}+\\beta_2x_{12}+\\dots+\\beta_{n-1}x_{1n-1}+\\epsilon_1\\\\\n", - "y_2&=\\beta_0x_{20}+\\beta_1x_{21}+\\beta_2x_{22}+\\dots+\\beta_{n-1}x_{2n-1}+\\epsilon_1\\\\\n", - "\\dots & \\dots \\\\\n", - "y_{i}&=\\beta_0x_{i0}+\\beta_1x_{i1}+\\beta_2x_{i2}+\\dots+\\beta_{n-1}x_{in-1}+\\epsilon_1\\\\\n", - "\\dots & \\dots \\\\\n", - "y_{n-1}&=\\beta_0x_{n-1,0}+\\beta_1x_{n-1,2}+\\beta_2x_{n-1,2}+\\dots+\\beta_1x_{n-1,n-1}+\\epsilon_{n-1}.\\\\\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Optimizing our parameters, more details\n", - "\n", - "We well use this matrix to define the approximation $\\hat{\\tilde{y}}$ via the unknown quantity $\\hat{\\beta}$ as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{\\tilde{y}}= \\hat{X}\\hat{\\beta},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and in order to find the optimal parameters $\\beta_i$ instead of solving the above linear algebra problem, we define a function which gives a measure of the spread between the values $y_i$ (which represent hopefully the exact values) and the parametrized values $\\tilde{y}_i$, namely" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "Q(\\hat{\\beta})=\\sum_{i=0}^{n-1}\\left(y_i-\\tilde{y}_i\\right)^2=\\left(\\hat{y}-\\hat{\\tilde{y}}\\right)^T\\left(\\hat{y}-\\hat{\\tilde{y}}\\right),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or using the matrix $\\hat{X}$ as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "Q(\\hat{\\beta})=\\left(\\hat{y}-\\hat{X}\\hat{\\beta}\\right)^T\\left(\\hat{y}-\\hat{X}\\hat{\\beta}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Interpretations and optimizing our parameters\n", - "\n", - "The function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "Q(\\hat{\\beta})=\\left(\\hat{y}-\\hat{X}\\hat{\\beta}\\right)^T\\left(\\hat{y}-\\hat{X}\\hat{\\beta}\\right),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "can be linked to the variance of the quantity $y_i$ if we interpret the latter as the mean value of for example a numerical experiment. When linking below with the maximum likelihood approach below, we will indeed interpret $y_i$ as a mean value" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "y_{i}=\\langle y_i \\rangle = \\beta_0x_{i,0}+\\beta_1x_{i,1}+\\beta_2x_{i,2}+\\dots+\\beta_{n-1}x_{i,n-1}+\\epsilon_i,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $\\langle y_i \\rangle$ is the mean value. Keep in mind also that till now we have treated $y_i$ as the exact value. Normally, the response (dependent or outcome) variable $y_i$ the outcome of a numerical experiment or another type of experiment and is thus only an approximation to the true value. It is then always accompanied by an error estimate, often limited to a statistical error estimate given by the standard deviation discussed earlier. In the discussion here we will treat $y_i$ as our exact value for the response variable.\n", - "\n", - "In order to find the parameters $\\beta_i$ we will then minimize the spread of $Q(\\hat{\\beta})$ by requiring" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial Q(\\hat{\\beta})}{\\partial \\beta_j} = \\frac{\\partial }{\\partial \\beta_j}\\left[ \\sum_{i=0}^{n-1}\\left(y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}\\right)^2\\right]=0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which results in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial Q(\\hat{\\beta})}{\\partial \\beta_j} = -2\\left[ \\sum_{i=0}^{n-1}x_{ij}\\left(y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}\\right)\\right]=0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or in a matrix-vector form as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial Q(\\hat{\\beta})}{\\partial \\hat{\\beta}} = 0 = \\hat{X}^T\\left( \\hat{y}-\\hat{X}\\hat{\\beta}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Interpretations and optimizing our parameters\n", - "\n", - "We can rewrite" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial Q(\\hat{\\beta})}{\\partial \\hat{\\beta}} = 0 = \\hat{X}^T\\left( \\hat{y}-\\hat{X}\\hat{\\beta}\\right),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{X}^T\\hat{y} = \\hat{X}^T\\hat{X}\\hat{\\beta},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and if the matrix $\\hat{X}^T\\hat{X}$ is invertible we have the solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{\\beta} =\\left(\\hat{X}^T\\hat{X}\\right)^{-1}\\hat{X}^T\\hat{y}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Interpretations and optimizing our parameters\n", - "\n", - "The residuals $\\hat{\\epsilon}$ are in turn given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{\\epsilon} = \\hat{y}-\\hat{\\tilde{y}} = \\hat{y}-\\hat{X}\\hat{\\beta},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and with" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{X}^T\\left( \\hat{y}-\\hat{X}\\hat{\\beta}\\right)= 0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "we have" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{X}^T\\hat{\\epsilon}=\\hat{X}^T\\left( \\hat{y}-\\hat{X}\\hat{\\beta}\\right)= 0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "meaning that the solution for $\\hat{\\beta}$ is the one which minimizes the residuals. Later we will link this with the maximum likelihood approach.\n", - "\n", - "\n", - "\n", - "\n", - "## The $\\chi^2$ function\n", - "\n", - "\n", - "Normally, the response (dependent or outcome) variable $y_i$ the outcome of a numerical experiment or another type of experiment and is thus only an approximation to the true value. It is then always accompanied by an error estimate, often limited to a statistical error estimate given by the standard deviation discussed earlier. In the discussion here we will treat $y_i$ as our exact value for the response variable.\n", - "\n", - "Introducing the standard deviation $\\sigma_i$ for each measurement $y_i$, we define now the $\\chi^2$ function as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\chi^2(\\hat{\\beta})=\\sum_{i=0}^{n-1}\\frac{\\left(y_i-\\tilde{y}_i\\right)^2}{\\sigma_i^2}=\\left(\\hat{y}-\\hat{\\tilde{y}}\\right)^T\\frac{1}{\\hat{\\Sigma^2}}\\left(\\hat{y}-\\hat{\\tilde{y}}\\right),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the matrix $\\hat{\\Sigma}$ is a diagonal matrix with $\\sigma_i$ as matrix elements. \n", - "\n", - "\n", - "\n", - "\n", - "## The $\\chi^2$ function\n", - "\n", - "\n", - "In order to find the parameters $\\beta_i$ we will then minimize the spread of $\\chi^2(\\hat{\\beta})$ by requiring" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\chi^2(\\hat{\\beta})}{\\partial \\beta_j} = \\frac{\\partial }{\\partial \\beta_j}\\left[ \\sum_{i=0}^{n-1}\\left(\\frac{y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}}{\\sigma_i}\\right)^2\\right]=0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which results in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\chi^2(\\hat{\\beta})}{\\partial \\beta_j} = -2\\left[ \\sum_{i=0}^{n-1}\\frac{x_{ij}}{\\sigma_i}\\left(\\frac{y_i-\\beta_0x_{i,0}-\\beta_1x_{i,1}-\\beta_2x_{i,2}-\\dots-\\beta_{n-1}x_{i,n-1}}{\\sigma_i}\\right)\\right]=0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "or in a matrix-vector form as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\chi^2(\\hat{\\beta})}{\\partial \\hat{\\beta}} = 0 = \\hat{A}^T\\left( \\hat{b}-\\hat{A}\\hat{\\beta}\\right).\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where we have defined the matrix $\\hat{A} =\\hat{X}/\\hat{\\Sigma}$ with matrix elements $a_{ij} = x_{ij}/\\sigma_i$ and the vector $\\hat{b}$ with elements $b_i = y_i/\\sigma_i$. \n", - "\n", - "\n", - "\n", - "## The $\\chi^2$ function\n", - "\n", - "\n", - "We can rewrite" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\chi^2(\\hat{\\beta})}{\\partial \\hat{\\beta}} = 0 = \\hat{A}^T\\left( \\hat{b}-\\hat{A}\\hat{\\beta}\\right),\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{A}^T\\hat{b} = \\hat{A}^T\\hat{A}\\hat{\\beta},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and if the matrix $\\hat{A}^T\\hat{A}$ is invertible we have the solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{\\beta} =\\left(\\hat{A}^T\\hat{A}\\right)^{-1}\\hat{A}^T\\hat{b}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The $\\chi^2$ function\n", - "\n", - "\n", - "If we then introduce the matrix" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{H} = \\hat{A}^T\\hat{A},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "we have then the following expression for the parameters $\\beta_j$ (the matrix elements of $\\hat{H}$ are $h_{ij}$)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\beta_j = \\sum_{k=0}^{p-1}h_{jk}\\sum_{i=0}^{n-1}\\frac{y_i}{\\sigma_i}\\frac{x_{ik}}{\\sigma_i} = \\sum_{k=0}^{p-1}h_{jk}\\sum_{i=0}^{n-1}b_ia_{ik}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We state without proof the expression for the uncertainty in the parameters $\\beta_j$ as" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2(\\beta_j) = \\sum_{i=0}^{n-1}\\sigma_i^2\\left( \\frac{\\partial \\beta_j}{\\partial y_i}\\right)^2,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "resulting in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\sigma^2(\\beta_j) = \\left(\\sum_{k=0}^{p-1}h_{jk}\\sum_{i=0}^{n-1}a_{ik}\\right)\\left(\\sum_{l=0}^{p-1}h_{jl}\\sum_{m=0}^{n-1}a_{ml}\\right) = h_{jj}!\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The $\\chi^2$ function\n", - "\n", - "The first step here is to approximate the function $y$ with a first-order polynomial, that is we write" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "y=y(x) \\rightarrow y(x_i) \\approx \\beta_0+\\beta_1 x_i.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "By computing the derivatives of $\\chi^2$ with respect to $\\beta_0$ and $\\beta_1$ show that these are given by" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\chi^2(\\hat{\\beta})}{\\partial \\beta_0} = -2\\left[ \\sum_{i=0}^{1}\\left(\\frac{y_i-\\beta_0-\\beta_1x_{i}}{\\sigma_i^2}\\right)\\right]=0,\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\frac{\\partial \\chi^2(\\hat{\\beta})}{\\partial \\beta_0} = -2\\left[ \\sum_{i=0}^{1}x_i\\left(\\frac{y_i-\\beta_0-\\beta_1x_{i}}{\\sigma_i^2}\\right)\\right]=0.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The $\\chi^2$ function\n", - "\n", - "\n", - "We define then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\gamma = \\sum_{i=0}^{1}\\frac{1}{\\sigma_i^2},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "6\n", - "7\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "6\n", - "8\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "6\n", - "9\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\gamma_{xy} = \\sum_{i=0}^{1}\\frac{y_ix_{i}}{\\sigma_i^2},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and show that" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\n", - "7\n", - "1\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "M\n", - "A\n", - "T\n", - "H\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\beta_1 = \\frac{\\gamma_{xy}\\gamma-\\gamma_x\\gamma_y}{\\gamma\\gamma_{xx}-\\gamma_x^2}.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients $\\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "## The singular value decompostion\n", - "\n", - "How can we use the singular value decomposition to find the parameters $\\beta_j$? More details will come. We first note that a general $m\\times n$ matrix $\\hat{A}$ can be written in terms of a diagonal matrix $\\hat{\\Sigma}$ of dimensionality $n\\times n$ and two orthognal matrices $\\hat{U}$ and $\\hat{V}$, where the first has dimensionality $m \\times n$ and the last dimensionality $n\\times n$. We have then" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\hat{A} = \\hat{U}\\hat{\\Sigma}\\hat{V}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Neural Networks\n", - "\n", - "## Artificial neurons\n", - "The field of artificial neural networks has a long history of development, and is closely connected with \n", - "the advancement of computer science and computers in general. A model of artificial neurons \n", - "was first developed by McCulloch and Pitts in 1943 to study signal processing in the brain and \n", - "has later been refined by others. The general idea is to mimic neural networks in the human brain, which\n", - "is composed of billions of neurons that communicate with each other by sending electrical signals. \n", - "Each neuron accumulates its incoming signals, \n", - "which must exceed an activation threshold to yield an output. If the threshold is not overcome, the neuron\n", - "remains inactive, i.e. has zero output. \n", - "\n", - "This behaviour has inspired a simple mathematical model for an artificial neuron." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y = f\\left(\\sum_{i=1}^n w_ix_i\\right) = f(u)\n", - "\\label{artificialNeuron} \\tag{27}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here, the output $y$ of the neuron is the value of its activation function, which have as input\n", - "a weighted sum of signals $x_i, \\dots ,x_n$ received by $n$ other neurons.\n", - "\n", - "\n", - "## Neural network types\n", - "\n", - "An artificial neural network (NN), is a computational model that consists of layers of connected neurons, or *nodes*. \n", - "It is supposed to mimic a biological nervous system by letting each neuron interact with other neurons\n", - "by sending signals in the form of mathematical functions between layers. \n", - "A wide variety of different NNs have\n", - "been developed, but most of them consist of an input layer, an output layer and eventual layers in-between, called\n", - "*hidden layers*. All layers can contain an arbitrary number of nodes, and each connection between two nodes\n", - "is associated with a weight variable. \n", - "\n", - "\n", - "\n", - "\n", - "## Feed-forward neural networks\n", - "The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, \n", - "the information moves in only one direction: forward through the layers.\n", - "\n", - "Nodes are represented by circles, while the arrows display the connections between the nodes, including the \n", - "direction of information flow. Additionally, each arrow corresponds to a weight variable, not displayed here. \n", - "We observe that each node in a layer is connected to *all* nodes in the subsequent layer, \n", - "making this a so-called *fully-connected* FFNN. \n", - "\n", - "\n", - "\n", - "A different variant of FFNNs are *convolutional neural networks* (CNNs), which have a connectivity pattern\n", - "inspired by the animal visual cortex. Individual neurons in the visual cortex only respond to stimuli from\n", - "small sub-regions of the visual field, called a receptive field. This makes the neurons well-suited to exploit the strong\n", - "spatially local correlation present in natural images. The response of each neuron can be approximated mathematically \n", - "as a convolution operation. \n", - "\n", - "CNNs emulate the behaviour of neurons in the visual cortex by enforcing a *local* connectivity pattern\n", - "between nodes of adjacent layers: Each node\n", - "in a convolutional layer is connected only to a subset of the nodes in the previous layer, \n", - "in contrast to the fully-connected FFNN.\n", - "Often, CNNs \n", - "consist of several convolutional layers that learn local features of the input, with a fully-connected layer at the end, \n", - "which gathers all the local data and produces the outputs. They have wide applications in image and video recognition\n", - "\n", - "\n", - "## Recurrent neural networks\n", - "\n", - "So far we have only mentioned NNs where information flows in one direction: forward. *Recurrent neural networks* on\n", - "the other hand, have connections between nodes that form directed *cycles*. This creates a form of \n", - "internal memory which are able to capture information on what has been calculated before; the output is dependent \n", - "on the previous computations. Recurrent NNs make use of sequential information by performing the same task for \n", - "every element in a sequence, where each element depends on previous elements. An example of such information is \n", - "sentences, making recurrent NNs especially well-suited for handwriting and speech recognition.\n", - "\n", - "\n", - "## Other types of networks\n", - "\n", - "There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation\n", - "in multidimensional space is the radial basis function (RBF) network. RBFs are typically made up of three layers: \n", - "an input layer, a hidden layer with non-linear radial symmetric activation functions and a linear output layer (''linear'' here\n", - "means that each node in the output layer has a linear activation function). The layers are normally fully-connected and \n", - "there are no cycles, thus RBFs can be viewed as a type of fully-connected FFNN. They are however usually treated as\n", - "a separate type of NN due the unusual activation functions.\n", - "\n", - "\n", - "Other types of NNs could also be mentioned, but are outside the scope of this work. We will now move on to a detailed description\n", - "of how a fully-connected FFNN works, and how it can be used to interpolate data sets. \n", - "\n", - "\n", - "## Multilayer perceptrons\n", - "\n", - "One use often so-called fully-connected feed-forward neural networks with three\n", - "or more layers (an input layer, one or more hidden layers and an output layer)\n", - "consisting of neurons that have non-linear activation functions.\n", - "\n", - "Such networks are often called *multilayer perceptrons* (MLPs)\n", - "\n", - "\n", - "## Why multilayer perceptrons?\n", - "\n", - "According to the *Universal approximation theorem*, a feed-forward neural network with just a single hidden layer containing \n", - "a finite number of neurons can approximate a continuous multidimensional function to arbitrary accuracy, \n", - "assuming the activation function for the hidden layer is a **non-constant, bounded and monotonically-increasing continuous function**.\n", - "Note that the requirements on the activation function only applies to the hidden layer, the output nodes are always\n", - "assumed to be linear, so as to not restrict the range of output values. \n", - "\n", - "We note that this theorem is only applicable to a NN with *one* hidden layer. \n", - "Therefore, we can easily construct an NN \n", - "that employs activation functions which do not satisfy the above requirements, as long as we have at least one layer\n", - "with activation functions that *do*. Furthermore, although the universal approximation theorem\n", - "lays the theoretical foundation for regression with neural networks, it does not say anything about how things work in practice: \n", - "A neural network can still be able to approximate a given function reasonably well without having the flexibility to fit *all other*\n", - "functions. \n", - "\n", - "\n", - "\n", - "\n", - "## Mathematical model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y = f\\left(\\sum_{i=1}^n w_ix_i + b_i\\right) = f(u)\n", - "\\label{artificialNeuron2} \\tag{28}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In an FFNN of such neurons, the *inputs* $x_i$\n", - "are the *outputs* of the neurons in the preceding layer. Furthermore, an MLP is fully-connected, \n", - "which means that each neuron receives a weighted sum of the outputs of *all* neurons in the previous layer. \n", - "\n", - "\n", - "## Mathematical model\n", - "\n", - "First, for each node $i$ in the first hidden layer, we calculate a weighted sum $u_i^1$ of the input coordinates $x_j$," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " u_i^1 = \\sum_{j=1}^2 w_{ij}^1 x_j + b_i^1 \n", - "\\label{_auto11} \\tag{29}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This value is the argument to the activation function $f_1$ of each neuron $i$,\n", - "producing the output $y_i^1$ of all neurons in layer 1," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y_i^1 = f_1(u_i^1) = f_1\\left(\\sum_{j=1}^2 w_{ij}^1 x_j + b_i^1\\right)\n", - "\\label{outputLayer1} \\tag{30}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where we assume that all nodes in the same layer have identical activation functions, hence the notation $f_l$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y_i^l = f_l(u_i^l) = f_l\\left(\\sum_{j=1}^{N_{l-1}} w_{ij}^l y_j^{l-1} + b_i^l\\right)\n", - "\\label{generalLayer} \\tag{31}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $N_l$ is the number of nodes in layer $l$. When the output of all the nodes in the first hidden layer are computed,\n", - "the values of the subsequent layer can be calculated and so forth until the output is obtained. \n", - "\n", - "\n", - "\n", - "\n", - "## Mathematical model\n", - "\n", - "The output of neuron $i$ in layer 2 is thus," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y_i^2 = f_2\\left(\\sum_{j=1}^3 w_{ij}^2 y_j^1 + b_i^2\\right) \n", - "\\label{_auto12} \\tag{32}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation} \n", - " = f_2\\left[\\sum_{j=1}^3 w_{ij}^2f_1\\left(\\sum_{k=1}^2 w_{jk}^1 x_k + b_j^1\\right) + b_i^2\\right]\n", - "\\label{outputLayer2} \\tag{33}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where we have substituted $y_m^1$ with. Finally, the NN output yields," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y_1^3 = f_3\\left(\\sum_{j=1}^3 w_{1m}^3 y_j^2 + b_1^3\\right) \n", - "\\label{_auto13} \\tag{34}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation} \n", - " = f_3\\left[\\sum_{j=1}^3 w_{1j}^3 f_2\\left(\\sum_{k=1}^3 w_{jk}^2 f_1\\left(\\sum_{m=1}^2 w_{km}^1 x_m + b_k^1\\right) + b_j^2\\right)\n", - " + b_1^3\\right]\n", - "\\label{_auto14} \\tag{35}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Mathematical model\n", - "\n", - "We can generalize this expression to an MLP with $l$ hidden layers. The complete functional form\n", - "is," - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - "y^{l+1}_1\\! = \\!f_{l+1}\\!\\left[\\!\\sum_{j=1}^{N_l}\\! w_{1j}^3 f_l\\!\\left(\\!\\sum_{k=1}^{N_{l-1}}\\! w_{jk}^2 f_{l-1}\\!\\left(\\!\n", - " \\dots \\!f_1\\!\\left(\\!\\sum_{n=1}^{N_0} \\!w_{mn}^1 x_n\\! + \\!b_m^1\\!\\right)\n", - " \\!\\dots \\!\\right) \\!+ \\!b_k^2\\!\\right)\n", - " \\!+ \\!b_1^3\\!\\right] \n", - "\\label{completeNN} \\tag{36}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which illustrates a basic property of MLPs: The only independent variables are the input values $x_n$. \n", - "\n", - "\n", - "## Mathematical model\n", - "\n", - "This confirms that an MLP,\n", - "despite its quite convoluted mathematical form, is nothing more than an analytic function, specifically a \n", - "mapping of real-valued vectors $\\vec{x} \\in \\mathbb{R}^n \\rightarrow \\vec{y} \\in \\mathbb{R}^m$. \n", - "In our example, $n=2$ and $m=1$. Consequentially, \n", - "the number of input and output values of the function we want to fit must be equal to the number of inputs and outputs of our MLP. \n", - "\n", - "Furthermore, the flexibility and universality of a MLP can be illustrated by realizing that \n", - "the expression is essentially a nested sum of scaled activation functions of the form" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " h(x) = c_1 f(c_2 x + c_3) + c_4\n", - "\\label{_auto15} \\tag{37}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where the parameters $c_i$ are weights and biases. By adjusting these parameters, the activation functions\n", - "can be shifted up and down or left and right, change slope or be rescaled \n", - "which is the key to the flexibility of a neural network. \n", - "\n", - "\n", - "### Matrix-vector notation\n", - "\n", - "We can introduce a more convenient notation for the activations in a NN. \n", - "\n", - "Additionally, we can represent the biases and activations\n", - "as layer-wise column vectors $\\vec{b}_l$ and $\\vec{y}_l$, so that the $i$-th element of each vector \n", - "is the bias $b_i^l$ and activation $y_i^l$ of node $i$ in layer $l$ respectively. \n", - "\n", - "We have that $\\mathrm{W}_l$ is a $N_{l-1} \\times N_l$ matrix, while $\\vec{b}_l$ and $\\vec{y}_l$ are $N_l \\times 1$ column vectors. \n", - "With this notation, the sum in becomes a matrix-vector multiplication, and we can write\n", - "the equation for the activations of hidden layer 2 in" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " \\vec{y}_2 = f_2(\\mathrm{W}_2 \\vec{y}_{1} + \\vec{b}_{2}) = \n", - " f_2\\left(\\left[\\begin{array}{ccc}\n", - " w^2_{11} &w^2_{12} &w^2_{13} \\\\\n", - " w^2_{21} &w^2_{22} &w^2_{23} \\\\\n", - " w^2_{31} &w^2_{32} &w^2_{33} \\\\\n", - " \\end{array} \\right] \\cdot\n", - " \\left[\\begin{array}{c}\n", - " y^1_1 \\\\\n", - " y^1_2 \\\\\n", - " y^1_3 \\\\\n", - " \\end{array}\\right] + \n", - " \\left[\\begin{array}{c}\n", - " b^2_1 \\\\\n", - " b^2_2 \\\\\n", - " b^2_3 \\\\\n", - " \\end{array}\\right]\\right).\n", - "\\label{_auto16} \\tag{38}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Matrix-vector notation and activation\n", - "\n", - "The activation of node $i$ in layer 2 is" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " y^2_i = f_2\\Bigr(w^2_{i1}y^1_1 + w^2_{i2}y^1_2 + w^2_{i3}y^1_3 + b^2_i\\Bigr) = \n", - " f_2\\left(\\sum_{j=1}^3 w^2_{ij} y_j^1 + b^2_i\\right).\n", - "\\label{_auto17} \\tag{39}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is not just a convenient and compact notation, but also \n", - "a useful and intuitive way to think about MLPs: The output is calculated by a series of matrix-vector multiplications\n", - "and vector additions that are used as input to the activation functions. For each operation \n", - "$\\mathrm{W}_l \\vec{y}_{l-1}$ we move forward one layer. \n", - "\n", - "\n", - "\n", - "### Activation functions\n", - "\n", - "A property that characterizes a neural network, other than its connectivity, is the choice of activation function(s). \n", - "As described in, the following restrictions are imposed on an activation function for a FFNN\n", - "to fulfill the universal approximation theorem\n", - "\n", - " * Non-constant\n", - "\n", - " * Bounded\n", - "\n", - " * Monotonically-increasing\n", - "\n", - " * Continuous\n", - "\n", - "### Activation functions, Logistic and Hyperbolic ones\n", - "\n", - "The second requirement excludes all linear functions. Furthermore, in a MLP with only linear activation functions, each \n", - "layer simply performs a linear transformation of its inputs.\n", - "\n", - "Regardless of the number of layers, \n", - "the output of the NN will be nothing but a linear function of the inputs. Thus we need to introduce some kind of \n", - "non-linearity to the NN to be able to fit non-linear functions\n", - "Typical examples are the logistic *Sigmoid*" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " f(x) = \\frac{1}{1 + e^{-x}},\n", - "\\label{sigmoidActivationFunction} \\tag{40}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and the *hyperbolic tangent* function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "
\n", - "\n", - "$$\n", - "\\begin{equation}\n", - " f(x) = \\tanh(x)\n", - "\\label{tanhActivationFunction} \\tag{41}\n", - "\\end{equation}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Relevance\n", - "\n", - "The *sigmoid* function are more biologically plausible because \n", - "the output of inactive neurons are zero. Such activation function are called *one-sided*. However,\n", - "it has been shown that the hyperbolic tangent \n", - "performs better than the sigmoid for training MLPs. \n", - "has become the most popular for *deep neural networks*" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.4" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/doc/LectureNotes/book.do.txt b/doc/LectureNotes/book.do.txt deleted file mode 100644 index eda1009af..000000000 --- a/doc/LectureNotes/book.do.txt +++ /dev/null @@ -1,3525 +0,0 @@ -TITLE: Data Analysis and Machine Learning -AUTHOR: Morten Hjorth-Jensen {copyright, 1999-present|CC BY-NC} at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -DATE: today - -TOC: on - - -======= Introduction ======= - - -During the last two decades there has been a swift and amazing -development of Machine Learning techniques and algorithms that impact -many areas in not only Science and Technology but also the Humanities, -Social Sciences, Medicine, Law, indeed, almost all possible -disciplines. The applications are incredibly many, from self-driving -cars to solving high-dimensional differential equations or complicated -quantum mechanical many-body problems. Machine Learning is perceived -by many as one of the main disruptive techniques nowadays. - -Statistics, Data science and Machine Learning form important -fields of research in modern science. They describe how to learn and -make predictions from data, as well as allowing us to extract -important correlations about physical process and the underlying laws -of motion in large data sets. The latter, big data sets, appear -frequently in essentially all disciplines, from the traditional -Science, Technology, Mathematics and Engineering fields to Life -Science, Law, education research, the Humanities and the Social -Sciences. - -It has become more -and more common to see research projects on big data in for example -the Social Sciences where extracting patterns from complicated survey -data is one of many research directions. Having a solid grasp of data -analysis and machine learning is thus becoming central to scientific -computing in many fields, and competences and skills within the fields -of machine learning and scientific computing are nowadays strongly -requested by many potential employers. The latter cannot be -overstated, familiarity with machine learning has almost become a -prerequisite for many of the most exciting employment opportunities, -whether they are in bioinformatics, life science, physics or finance, -in the private or the public sector. This author has had several -students or met students who have been hired recently based on their -skills and competences in scientific computing and data science, often -with marginal knowledge of machine learning. - -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. Many of the methods we will study are also -strongly rooted in basic mathematics and physics research. - -Ideally, machine learning represents the science of giving computers -the ability to learn without being explicitly programmed. The idea is -that there exist generic algorithms which can be used to find patterns -in a broad class of data sets without having to write code -specifically for each problem. The algorithm will build its own logic -based on the data. You should however always keep in mind that -machines and algorithms are to a large extent developed by humans. The -insights and knowledge we have about a specific system, play a central -role when we develop a specific machine learning algorithm. - -Machine learning is an extremely rich field, in spite of its young -age. The increases we have seen during the last three decades in -computational capabilities have been followed by developments of -methods and techniques for analyzing and handling large date sets, -relying heavily on statistics, computer science and mathematics. The -field is rather new and developing rapidly. Popular software packages -written in Python for machine learning like -"Scikit-learn":"http://scikit-learn.org/stable/", -"Tensorflow":"https://www.tensorflow.org/", -"PyTorch":"http://pytorch.org/" and "Keras":"https://keras.io/", all -freely available at their respective GitHub sites, encompass -communities of developers in the thousands or more. And the number of -code developers and contributors keeps increasing. Not all the -algorithms and methods can be given a rigorous mathematical -justification, opening up thereby large rooms for experimenting and -trial and error and thereby exciting new developments. However, a -solid command of linear algebra, multivariate theory, probability -theory, statistical data analysis, understanding errors and Monte -Carlo methods are central elements in a proper understanding of many -of algorithms and methods we will discuss. - - -===== Learning outcomes ===== - -These sets of lectures aim at giving you an overview of central aspects of -statistical data analysis as well as some of the central algorithms -used in machine learning. We will introduce a variety of central -algorithms and methods essential for studies of data analysis and -machine learning. - -Hands-on projects and experimenting with data and algorithms plays a central role in -these lectures, and our hope is, through the various -projects and exercises, to expose you to fundamental -research problems in these fields, with the aim to reproduce state of -the art scientific results. You will learn to develop and -structure codes for studying these systems, get acquainted with -computing facilities and learn to handle large scientific projects. A -good scientific and ethical conduct is emphasized throughout the -course. More specifically, you will - -o Learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning; -o Be capable of extending the acquired knowledge to other systems and cases; -o Have an understanding of central algorithms used in data analysis and machine learning; -o Gain knowledge of central aspects of Monte Carlo methods, Markov chains, Gibbs samplers and their possible applications, from numerical integration to simulation of stock markets; -o Understand methods for regression and classification; -o Learn about neural network, genetic algorithms and Boltzmann machines; -o Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++, in addition to a basic knowledge of linear algebra (typically taught during the first one or two years of undergraduate studies). - -There are several topics we will cover here, spanning from -statistical data analysis and its basic concepts such as expectation -values, variance, covariance, correlation functions and errors, via -well-known probability distribution functions like the uniform -distribution, the binomial distribution, the Poisson distribution and -simple and multivariate normal distributions to central elements of -Bayesian statistics and modeling. We will also remind the reader about -central elements from linear algebra and standard methods based on -linear algebra used to optimize (minimize) functions (the family of gradient descent methods) -and the Singular-value decomposition and -least square methods for parameterizing data. - -We will also cover Monte Carlo methods, Markov chains, well-known -algorithms for sampling stochastic events like the Metropolis-Hastings -and Gibbs sampling methods. An important aspect of all our -calculations is a proper estimation of errors. Here we will also -discuss famous resampling techniques like the blocking, the bootstrapping -and the jackknife methods and the infamous bias-variance tradeoff. - -The second part of the material covers several algorithms used in -machine learning. - - - - - - -===== Types of Machine Learning ===== - - -The approaches to machine learning are many, but are often split into -two main categories. In *supervised learning* we know the answer to a -problem, and let the computer deduce the logic behind it. On the other -hand, *unsupervised learning* is a method for finding patterns and -relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely -*reinforcement learning*. This is a paradigm of learning inspired by -behavioral psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. - -Another way to categorize machine learning tasks is to consider the -desired output of a system. Some of the most common tasks are: - - * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. - - * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. - - * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. - - -The methods we cover have three main topics in common, irrespective of -whether we deal with supervised or unsupervised learning. The first -ingredient is normally our data set (which can be subdivided into -training and test data), the second item is a model which is normally -a function of some parameters. The model reflects our knowledge of -the system (or lack thereof). As an example, if we know that our data -show a behavior similar to what would be predicted by a polynomial, -fitting our data to a polynomial of some degree would then determin -our model. - -The last ingredient is a so-called _cost_ -function which allows us to present an estimate on how good our model -is in reproducing the data it is supposed to train. - -Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms - -o Linear regression and its variants -o Decision tree algorithms, from single trees to random forests -o Bayesian statistics and regression -o Support vector machines and finally various variants of -o Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks -o Networks for unsupervised learning using for example reduced Boltzmann machines. - - - -===== Choice of programming language ===== - -Python plays nowadays a central role in the development of machine -learning techniques and tools for data analysis. In particular, seen -the wealth of machine learning and data analysis libraries written in -Python, easy to use libraries with immediate visualization(and not the -least impressive galleries of existing examples), the popularity of the -Jupyter notebook framework with the possibility to run _R_ codes or -compiled programs written in C++, and much more made our choice of -programming language for this series of lectures easy. However, -since the focus here is not only on using existing Python libraries such -as _Scikit-Learn_ or _Tensorflow_, but also on developing your own -algorithms and codes, we will as far as possible present many of these -algorithms either as a Python codes or C++ or Fortran (or other languages) codes. - -The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -"Lapack":"http://www.netlib.org/lapack/" or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like "Numba":"https://numba.pydata.org/" -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. - -Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. - -===== Data handling, machine learning and ethical aspects ===== - -In most of the cases we will study, we will either generate the data -to analyze ourselves (both for supervised learning and unsupervised -learning) or we will recur again and again to data present in say -_Scikit-Learn_ or _Tensorflow_. Many of the examples we end up -dealing with are from a privacy and data protection point of view, -rather inoccuous and boring results of numerical -calculations. However, this does not hinder us from developing a sound -ethical attitude to the data we use, how we analyze the data and how -we handle the data. - -The most immediate and simplest possible ethical aspects deal with our -approach to the scientific process. Nowadays, with version control -software like "Git":"https://git-scm.com/" and various online -repositories like "Github":"https://github.com/", -"Gitlab":"https://about.gitlab.com/" etc, we can easily make our codes -and data sets we have used, freely and easily accessible to a wider -community. This helps us almost automagically in making our science -reproducible. The large open-source development communities involved -in say "Scikit-Learn":"http://scikit-learn.org/stable/", -"Tensorflow":"https://www.tensorflow.org/", -"PyTorch":"http://pytorch.org/" and "Keras":"https://keras.io/", are -all excellent examples of this. The codes can be tested and improved -upon continuosly, helping thereby our scientific community at large in -developing data analysis and machine learning tools. It is much -easier today to gain traction and acceptance for making your science -reproducible. From a societal stand, this is an important element -since many of the developers are employees of large public institutions like -universities and research labs. Our fellow taxpayers do deserve to get -something back for their bucks. - -However, this more mechanical aspect of the ethics of science (in -particular the reproducibility of scientific results) is something -which is obvious and everybody should do so as part of the dialectics of -science. The fact that many scientists are not willing to share their codes or -data is detrimental to the scientific discourse. - -Before we proceed, we should add a disclaimer. Even though -we may dream of computers developing some kind of higher learning -capabilities, at the end (even if the artificial intelligence -community keeps touting our ears full of fancy futuristic avenues), it is we, yes you reading these lines, -who end up constructing and instructing, via various algorithms, the -machine learning approaches. Self-driving cars for example, rely on sofisticated -programs which take into account all possible situations a car can -encounter. In addition, extensive usage of training data from GPS -information, maps etc, are typically fed into the software for -self-driving cars. Adding to this various sensors and cameras that -feed information to the programs, there are zillions of ethical issues -which arise from this. - -For self-driving cars, where basically many of the standard machine -learning algorithms discussed here enter into the codes, at a certain -stage we have to make choices. Yes, we , the lads and lasses who wrote -a program for a specific brand of a self-driving car. As an example, -all carmakers have as their utmost priority the security of the -driver and the accompanying passengers. A famous European carmaker, which is -one of the leaders in the market of self-driving cars, had _if_ -statements of the following type: suppose there are two obstacles in -front of you and you cannot avoid to collide with one of them. One of -the obstacles is a monstertruck while the other one is a kindergarten -class trying to cross the road. The self-driving car algo would then -opt for the hitting the small folks instead of the monstertruck, since -the likelihood of surving a collision with our future citizens, is -much higher. - -This leads to serious ethical aspects. Why should we opt for such an -option? Who decides and who is entitled to make such choices? Keep in -mind that many of the algorithms you will encounter in this series of -lectures or hear about later, are indeed based on simple programming -instructions. And you are very likely to be one of the people who may -end up writing such a code. Thus, developing a sound ethical attitude -to what we do, an approach well beyond the simple mechanistic one of -making our science available and reproducible, is much needed. The -example of the self-driving cars is just one of infinitely many cases -where we have to make choices. When you analyze data on economic -inequalities, who guarantees that you are not weighting some data in a -particular way, perhaps because you dearly want a specific conclusion -which may support your political views? Or what about the recent -claims that a famous IT company like Apple has a sexist bias on the -their recently "launched credit card":"https://qz.com/1748321/the-role-of-goldman-sachs-algorithms-in-the-apple-credit-card-scandal/"? - -We do not have the answers here, nor will we venture into a deeper -discussions of these aspects, but we want you think over these topics -in a more overarching way. A statistical data analysis with its dry -numbers and graphs meant to guide the eye, does not necessarily -reflect the truth, whatever that is. As a scientist, and after a -university education, you are supposedly a better citizen, with an -improved critical view and understanding of the scientific method, and -perhaps some deeper understanding of the ethics of science at -large. Use these insights. Be a critical citizen. You owe it to our -society. - - -======= Machine Learning Overview with Selectec Examples ======= - - -===== Introduction ===== - -Our emphasis throughout this series of lectures -is on understanding the mathematical aspects of -different algorithms used in the fields of data analysis and machine learning. - -However, where possible we will emphasize the -importance of using available software. We start thus with a hands-on -and top-down approach to machine learning. The aim is thus to start with -relevant data or data we have produced -and use these to introduce statistical data analysis -concepts and machine learning algorithms before we delve into the -algorithms themselves. The examples we will use in the beginning, start with simple -polynomials with random noise added. We will use the Python -software package "Scikit-Learn":"http://scikit-learn.org/stable/" and -introduce various machine learning algorithms to make fits of -the data and predictions. We move thereafter to more interesting -cases such as data from say experiments (below we will look at experimental nuclear binding energies as an example). -These are examples where we can easily set up the data and -then use machine learning algorithms included in for example -_Scikit-Learn_. - -These examples will serve us the purpose of getting -started. Furthermore, they allow us to catch more than two birds with -a stone. They will allow us to bring in some programming specific -topics and tools as well as showing the power of various Python -libraries for machine learning and statistical data analysis. - -Here, we will mainly focus on two -specific Python packages for Machine Learning, Scikit-Learn and -Tensorflow (see below for links etc). Moreover, the examples we -introduce will serve as inputs to many of our discussions later, as -well as allowing you to set up models and produce your own data and -get started with programming. - - - -===== What is Machine Learning? ===== - -Statistics, data science and machine learning form important fields of -research in modern science. They describe how to learn and make -predictions from data, as well as allowing us to extract important -correlations about physical process and the underlying laws of motion -in large data sets. The latter, big data sets, appear frequently in -essentially all disciplines, from the traditional Science, Technology, -Mathematics and Engineering fields to Life Science, Law, education -research, the Humanities and the Social Sciences. - -It has become more -and more common to see research projects on big data in for example -the Social Sciences where extracting patterns from complicated survey -data is one of many research directions. Having a solid grasp of data -analysis and machine learning is thus becoming central to scientific -computing in many fields, and competences and skills within the fields -of machine learning and scientific computing are nowadays strongly -requested by many potential employers. The latter cannot be -overstated, familiarity with machine learning has almost become a -prerequisite for many of the most exciting employment opportunities, -whether they are in bioinformatics, life science, physics or finance, -in the private or the public sector. This author has had several -students or met students who have been hired recently based on their -skills and competences in scientific computing and data science, often -with marginal knowledge of machine learning. - -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. Many of the methods we will study are also -strongly rooted in basic mathematics and physics research. - -Ideally, machine learning represents the science of giving computers -the ability to learn without being explicitly programmed. The idea is -that there exist generic algorithms which can be used to find patterns -in a broad class of data sets without having to write code -specifically for each problem. The algorithm will build its own logic -based on the data. You should however always keep in mind that -machines and algorithms are to a large extent developed by humans. The -insights and knowledge we have about a specific system, play a central -role when we develop a specific machine learning algorithm. - -Machine learning is an extremely rich field, in spite of its young -age. The increases we have seen during the last three decades in -computational capabilities have been followed by developments of -methods and techniques for analyzing and handling large date sets, -relying heavily on statistics, computer science and mathematics. The -field is rather new and developing rapidly. Popular software packages -written in Python for machine learning like -"Scikit-learn":"http://scikit-learn.org/stable/", -"Tensorflow":"https://www.tensorflow.org/", -"PyTorch":"http://pytorch.org/" and "Keras":"https://keras.io/", all -freely available at their respective GitHub sites, encompass -communities of developers in the thousands or more. And the number of -code developers and contributors keeps increasing. Not all the -algorithms and methods can be given a rigorous mathematical -justification, opening up thereby large rooms for experimenting and -trial and error and thereby exciting new developments. However, a -solid command of linear algebra, multivariate theory, probability -theory, statistical data analysis, understanding errors and Monte -Carlo methods are central elements in a proper understanding of many -of algorithms and methods we will discuss. - - - -===== Types of Machine Learning ===== - - -The approaches to machine learning are many, but are often split into -two main categories. In *supervised learning* we know the answer to a -problem, and let the computer deduce the logic behind it. On the other -hand, *unsupervised learning* is a method for finding patterns and -relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely -*reinforcement learning*. This is a paradigm of learning inspired by -behavioral psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. - -Another way to categorize machine learning tasks is to consider the -desired output of a system. Some of the most common tasks are: - - * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. - - * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. - - * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. - - -The methods we cover have three main topics in common, irrespective of -whether we deal with supervised or unsupervised learning. The first -ingredient is normally our data set (which can be subdivided into -training and test data), the second item is a model which is normally a -function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model. - -The last ingredient is a so-called _cost_ -function which allows us to present an estimate on how good our model -is in reproducing the data it is supposed to train. -At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of _gradient_ methods. - - - - - - - -===== Software and needed installations ===== - -We will make extensive use of Python as programming language and its -myriad of available libraries. You will find -Jupyter notebooks invaluable in your work. You can run _R_ -codes in the Jupyter/IPython notebooks, with the immediate benefit of -visualizing your data. You can also use compiled languages like C++, -Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be -on Python. - - -If you have Python installed (we strongly recommend Python3) and you feel -pretty familiar with installing different packages, we recommend that -you install the following Python packages via _pip_ as - -o pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow - -For Python3, replace _pip_ with _pip3_. - -For OSX users we recommend, after having installed Xcode, to -install _brew_. Brew allows for a seamless installation of additional -software via for example - -o brew install python3 - -For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution, -you can use _pip_ as well and simply install Python as - -o sudo apt-get install python3 (or python for pyhton2.7) - -etc etc. - - - -===== Python installers ===== - -If you don't want to perform these operations separately and venture -into the hassle of exploring how to set up dependencies and paths, we -recommend two widely used distrubutions which set up all relevant -dependencies for Python, namely - -* "Anaconda":"https://docs.anaconda.com/", - -which is an open source -distribution of the Python and R programming languages for large-scale -data processing, predictive analytics, and scientific computing, that -aims to simplify package management and deployment. Package versions -are managed by the package management system _conda_. - -* "Enthought canopy":"https://www.enthought.com/product/canopy/" - -is a Python -distribution for scientific and analytic computing distribution and -analysis environment, available for free and under a commercial -license. - -Furthermore, "Google's Colab":"https://colab.research.google.com/notebooks/welcome.ipynb" is a free Jupyter notebook environment that requires -no setup and runs entirely in the cloud. Try it out! - -===== Useful Python libraries ===== -Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there) - -* "NumPy":"https://www.numpy.org/" is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays -* "The pandas":"https://pandas.pydata.org/" library provides high-performance, easy-to-use data structures and data analysis tools -* "Xarray":"http://xarray.pydata.org/en/stable/" is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun! -* "Scipy":"https://www.scipy.org/" (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering. -* "Matplotlib":"https://matplotlib.org/" is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. -* "Autograd":"https://github.com/HIPS/autograd" can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives -* "SymPy":"https://www.sympy.org/en/index.html" is a Python library for symbolic mathematics. -* "scikit-learn":"https://scikit-learn.org/stable/" has simple and efficient tools for machine learning, data mining and data analysis -* "TensorFlow":"https://www.tensorflow.org/" is a Python library for fast numerical computing created and released by Google -* "Keras":"https://keras.io/" is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano -* And many more such as "pytorch":"https://pytorch.org/", "Theano":"https://pypi.org/project/Theano/" etc - -===== Installing R, C++, cython or Julia ===== - -You will also find it convenient to utilize _R_. We will mainly -use Python during our lectures and in various projects and exercises. -Those of you -already familiar with _R_ should feel free to continue using _R_, keeping -however an eye on the parallel Python set ups. Similarly, if you are a -Python afecionado, feel free to explore _R_ as well. Jupyter/Ipython -notebook allows you to run _R_ codes interactively in your -browser. The software library _R_ is really tailored for statistical data analysis -and allows for an easy usage of the tools and algorithms we will discuss in these -lectures. - -To install _R_ with Jupyter notebook -"follow the link here":"https://mpacer.org/maths/r-kernel-for-ipython-notebook" - - - - -===== Installing R, C++, cython, Numba etc ===== - - -For the C++ aficionados, Jupyter/IPython notebook allows you also to -install C++ and run codes written in this language interactively in -the browser. Since we will emphasize writing many of the algorithms -yourself, you can thus opt for either Python or C++ (or Fortran or other compiled languages) as programming -languages. - -To add more entropy, _cython_ can also be used when running your -notebooks. It means that Python with the jupyter notebook -setup allows you to integrate widely popular softwares and tools for -scientific computing. Similarly, the -"Numba Python package":"https://numba.pydata.org/" delivers increased performance -capabilities with minimal rewrites of your codes. With its -versatility, including symbolic operations, Python offers a unique -computational environment. Your jupyter notebook can easily be -converted into a nicely rendered _PDF_ file or a Latex file for -further processing. For example, convert to latex as - -!bc -pycod jupyter nbconvert filename.ipynb --to latex -!ec - -And to add more versatility, the Python package "SymPy":"http://www.sympy.org/en/index.html" is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) and is entirely written in Python. - -Finally, if you wish to use the light mark-up language -"doconce":"https://github.com/hplgit/doconce" you can convert a standard ascii text file into various HTML -formats, ipython notebooks, latex files, pdf files etc with minimal edits. These lectures were generated using _doconce_. - - - -===== Numpy examples and Important Matrix and vector handling packages ===== - -There are several central software libraries for linear algebra and eigenvalue problems. Several of the more -popular ones have been wrapped into ofter software packages like those from the widely used text _Numerical Recipes_. The original source codes in many of the available packages are often taken from the widely used -software package LAPACK, which follows two other popular packages -developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here. - - * LINPACK: package for linear equations and least square problems. - * LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website URL: "http://www.netlib.org" it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available. - * BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from URL: "http://www.netlib.org". - - -===== Basic Matrix Features ===== - -!bblock Matrix properties reminder -!bt -\[ - \mathbf{A} = - \begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\ - a_{21} & a_{22} & a_{23} & a_{24} \\ - a_{31} & a_{32} & a_{33} & a_{34} \\ - a_{41} & a_{42} & a_{43} & a_{44} - \end{bmatrix}\qquad -\mathbf{I} = - \begin{bmatrix} 1 & 0 & 0 & 0 \\ - 0 & 1 & 0 & 0 \\ - 0 & 0 & 1 & 0 \\ - 0 & 0 & 0 & 1 - \end{bmatrix} -\] -!et - - - -The inverse of a matrix is defined by - -!bt -\[ -\mathbf{A}^{-1} \cdot \mathbf{A} = I -\] -!et - - -|----------------------------------------------------------------------| -| Relations | Name | matrix elements | -|----------------------------------------------------------------------| -| $A = A^{T}$ | symmetric | $a_{ij} = a_{ji}$ | -| $A = \left (A^{T} \right )^{-1}$ | real orthogonal | $\sum_k a_{ik} a_{jk} = \sum_k a_{ki} a_{kj} = \delta_{ij}$ | -| $A = A^{ * }$ | real matrix | $a_{ij} = a_{ij}^{ * }$ | -| $A = A^{\dagger}$ | hermitian | $a_{ij} = a_{ji}^{ * }$ | -| $A = \left (A^{\dagger} \right )^{-1}$ | unitary | $\sum_k a_{ik} a_{jk}^{ * } = \sum_k a_{ki}^{ * } a_{kj} = \delta_{ij}$ | -|----------------------------------------------------------------------| - -!eblock - - -=== Some famous Matrices === - - * Diagonal if $a_{ij}=0$ for $i\ne j$ - * Upper triangular if $a_{ij}=0$ for $i > j$ - * Lower triangular if $a_{ij}=0$ for $i < j$ - * Upper Hessenberg if $a_{ij}=0$ for $i > j+1$ - * Lower Hessenberg if $a_{ij}=0$ for $i < j+1$ - * Tridiagonal if $a_{ij}=0$ for $|i -j| > 1$ - * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i > j+p$ - * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i < j+p$ - * Banded, block upper triangular, block lower triangular.... - - -=== More Basic Matrix Features === - -!bblock Some Equivalent Statements -For an $N\times N$ matrix $\mathbf{A}$ the following properties are all equivalent - - * If the inverse of $\mathbf{A}$ exists, $\mathbf{A}$ is nonsingular. - * The equation $\mathbf{Ax}=0$ implies $\mathbf{x}=0$. - * The rows of $\mathbf{A}$ form a basis of $R^N$. - * The columns of $\mathbf{A}$ form a basis of $R^N$. - * $\mathbf{A}$ is a product of elementary matrices. - * $0$ is not eigenvalue of $\mathbf{A}$. -!eblock - - -===== Numpy and arrays ===== -"Numpy":"http://www.numpy.org/" provides an easy way to handle arrays in Python. The standard way to import this library is as - -!bc pycod -import numpy as np -!ec -Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution, -!bc pycod -n = 10 -x = np.random.normal(size=n) -print(x) -!ec -We defined a vector $x$ with $n=10$ elements with its values given by the Normal distribution $N(0,1)$. -Another alternative is to declare a vector as follows -!bc pycod -import numpy as np -x = np.array([1, 2, 3]) -print(x) -!ec -Here we have defined a vector with three elements, with $x_0=1$, $x_1=2$ and $x_2=3$. Note that both Python and C++ -start numbering array elements from $0$ and on. This means that a vector with $n$ elements has a sequence of entities $x_0, x_1, x_2, \dots, x_{n-1}$. We could also let (recommended) Numpy to compute the logarithms of a specific array as -!bc pycod -import numpy as np -x = np.log(np.array([4, 7, 8])) -print(x) -!ec - -In the last example we used Numpy's unary function $np.log$. This function is -highly tuned to compute array elements since the code is vectorized -and does not require looping. We normaly recommend that you use the -Numpy intrinsic functions instead of the corresponding _log_ function -from Python's _math_ module. The looping is done explicitely by the -_np.log_ function. The alternative, and slower way to compute the -logarithms of a vector would be to write - -!bc pycod -import numpy as np -from math import log -x = np.array([4, 7, 8]) -for i in range(0, len(x)): - x[i] = log(x[i]) -print(x) -!ec -We note that our code is much longer already and we need to import the _log_ function from the _math_ module. -The attentive reader will also notice that the output is $[1, 1, 2]$. Python interprets automagically our numbers as integers (like the _automatic_ keyword in C++). To change this we could define our array elements to be double precision numbers as -!bc pycod -import numpy as np -x = np.log(np.array([4, 7, 8], dtype = np.float64)) -print(x) -!ec -or simply write them as double precision numbers (Python uses 64 bits as default for floating point type variables), that is -!bc pycod -import numpy as np -x = np.log(np.array([4.0, 7.0, 8.0]) -print(x) -!ec -To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the _itemsize_ functionality (the array $x$ is actually an object which inherits the functionalities defined in Numpy) as -!bc pycod -import numpy as np -x = np.log(np.array([4.0, 7.0, 8.0]) -print(x.itemsize) -!ec - - -===== Matrices in Python ===== - -Having defined vectors, we are now ready to try out matrices. We can -define a $3 \times 3 $ real matrix $\hat{A}$ as (recall that we user -lowercase letters for vectors and uppercase letters for matrices) - -!bc pycod -import numpy as np -A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ])) -print(A) -!ec -If we use the _shape_ function we would get $(3, 3)$ as output, that is verifying that our matrix is a $3\times 3$ matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as -!bc pycod -import numpy as np -A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ])) -# print the first column, row-major order and elements start with 0 -print(A[:,0]) -!ec -We can continue this was by printing out other columns or rows. The example here prints out the second column -!bc pycod -import numpy as np -A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ])) -# print the first column, row-major order and elements start with 0 -print(A[1,:]) -!ec -Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the "Numpy website for more details":"http://www.numpy.org/". Useful functions when defining a matrix are the _np.zeros_ function which declares a matrix of a given dimension and sets all elements to zero -!bc pycod -import numpy as np -n = 10 -# define a matrix of dimension 10 x 10 and set all elements to zero -A = np.zeros( (n, n) ) -print(A) -!ec -or initializing all elements to -!bc pycod -import numpy as np -n = 10 -# define a matrix of dimension 10 x 10 and set all elements to one -A = np.ones( (n, n) ) -print(A) -!ec -or as unitarily distributed random numbers (see the material on random number generators in the statistics part) -!bc pycod -import numpy as np -n = 10 -# define a matrix of dimension 10 x 10 and set all elements to random numbers with x \in [0, 1] -A = np.random.rand(n, n) -print(A) -!ec - -As we will see throughout these lectures, there are several extremely useful functionalities in Numpy. -As an example, consider the discussion of the covariance matrix. Suppose we have defined three vectors -$\hat{x}, \hat{y}, \hat{z}$ with $n$ elements each. The covariance matrix is defined as -!bt -\[ -\hat{\Sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ - \sigma_{yx} & \sigma_{yy} & \sigma_{yz} \\ - \sigma_{zx} & \sigma_{zy} & \sigma_{zz} - \end{bmatrix}, -\] -!et -where for example -!bt -\[ -\sigma_{xy} =\frac{1}{n} \sum_{i=0}^{n-1}(x_i- \overline{x})(y_i- \overline{y}). -\] -!et -The Numpy function _np.cov_ calculates the covariance elements using the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have the exact mean values. -The following simple function uses the _np.vstack_ function which takes each vector of dimension $1\times n$ and produces a $3\times n$ matrix $\hat{W}$ -!bt -\[ -\hat{W} = \begin{bmatrix} x_0 & y_0 & z_0 \\ - x_1 & y_1 & z_1 \\ - x_2 & y_2 & z_2 \\ - \dots & \dots & \dots \\ - x_{n-2} & y_{n-2} & z_{n-2} \\ - x_{n-1} & y_{n-1} & z_{n-1} - \end{bmatrix}, -\] -!et - -which in turn is converted into into the $3\times 3$ covariance matrix -$\hat{\Sigma}$ via the Numpy function _np.cov()_. We note that we can also calculate -the mean value of each set of samples $\hat{x}$ etc using the Numpy -function _np.mean(x)_. We can also extract the eigenvalues of the -covariance matrix through the _np.linalg.eig()_ function. - -!bc pycod -# Importing various packages -import numpy as np - -n = 100 -x = np.random.normal(size=n) -print(np.mean(x)) -y = 4+3*x+np.random.normal(size=n) -print(np.mean(y)) -z = x**3+np.random.normal(size=n) -print(np.mean(z)) -W = np.vstack((x, y, z)) -Sigma = np.cov(W) -print(Sigma) -Eigvals, Eigvecs = np.linalg.eig(Sigma) -print(Eigvals) -!ec - - -!bc pycod -import numpy as np -import matplotlib.pyplot as plt -from scipy import sparse -eye = np.eye(4) -print(eye) -sparse_mtx = sparse.csr_matrix(eye) -print(sparse_mtx) -x = np.linspace(-10,10,100) -y = np.sin(x) -plt.plot(x,y,marker='x') -plt.show() -!ec - - -===== Meet the Pandas ===== - - -FIGURE: [fig/pandas.jpg, width=600 frac=0.8] - -Another useful Python package is -"pandas":"https://pandas.pydata.org/", which is an open source library -providing high-performance, easy-to-use data structures and data -analysis tools for Python. _pandas_ stands for panel data, a term borrowed from econometrics and is an efficient library for data analysis with an emphasis on tabular data. -_pandas_ has two major classes, the _DataFrame_ class with two-dimensional data objects and tabular data organized in columns and the class _Series_ with a focus on one-dimensional data objects. Both classes allow you to index data easily as we will see in the examples below. -_pandas_ allows you also to perform mathematical operations on the data, spanning from simple reshapings of vectors and matrices to statistical operations. - -The following simple example shows how we can, in an easy way make tables of our data. Here we define a data set which includes names, place of birth and date of birth, and displays the data in an easy to read way. We will see repeated use of _pandas_, in particular in connection with classification of data. - -!bc pycod -import pandas as pd -from IPython.display import display -data = {'First Name': ["Frodo", "Bilbo", "Aragorn II", "Samwise"], - 'Last Name': ["Baggins", "Baggins","Elessar","Gamgee"], - 'Place of birth': ["Shire", "Shire", "Eriador", "Shire"], - 'Date of Birth T.A.': [2968, 2890, 2931, 2980] - } -data_pandas = pd.DataFrame(data) -display(data_pandas) -!ec - -In the above we have imported _pandas_ with the shorthand _pd_, the latter has become the standard way we import _pandas_. We make then a list of various variables -and reorganize the aboves lists into a _DataFrame_ and then print out a neat table with specific column labels as *Name*, *place of birth* and *date of birth*. -Displaying these results, we see that the indices are given by the default numbers from zero to three. -_pandas_ is extremely flexible and we can easily change the above indices by defining a new type of indexing as -!bc pycod -data_pandas = pd.DataFrame(data,index=['Frodo','Bilbo','Aragorn','Sam']) -display(data_pandas) -!ec -Thereafter we display the content of the row which begins with the index _Aragorn_ -!bc pycod -display(data_pandas.loc['Aragorn']) -!ec - -We can easily append data to this, for example -!bc pycod -new_hobbit = {'First Name': ["Peregrin"], - 'Last Name': ["Took"], - 'Place of birth': ["Shire"], - 'Date of Birth T.A.': [2990] - } -data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin'])) -display(data_pandas) -!ec - - -Here are other examples where we use the _DataFrame_ functionality to handle arrays, now with more interesting features for us, namely numbers. We set up a matrix -of dimensionality $10\times 5$ and compute the mean value and standard deviation of each column. Similarly, we can perform mathematial operations like squaring the matrix elements and many other operations. -!bc pycod -import numpy as np -import pandas as pd -from IPython.display import display -np.random.seed(100) -# setting up a 10 x 5 matrix -rows = 10 -cols = 5 -a = np.random.randn(rows,cols) -df = pd.DataFrame(a) -display(df) -print(df.mean()) -print(df.std()) -display(df**2) -!ec - -Thereafter we can select specific columns only and plot final results -!bc pycod -df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth'] -df.index = np.arange(10) - -display(df) -print(df['Second'].mean() ) -print(df.info()) -print(df.describe()) - -from pylab import plt, mpl -plt.style.use('seaborn') -mpl.rcParams['font.family'] = 'serif' - -df.cumsum().plot(lw=2.0, figsize=(10,6)) -plt.show() - - -df.plot.bar(figsize=(10,6), rot=15) -plt.show() -!ec -We can produce a $4\times 4$ matrix -!bc pycod -b = np.arange(16).reshape((4,4)) -print(b) -df1 = pd.DataFrame(b) -print(df1) -!ec -and many other operations. - -The _Series_ class is another important class included in -_pandas_. You can view it as a specialization of _DataFrame_ but where -we have just a single column of data. It shares many of the same features as _DataFrame. As with _DataFrame_, -most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays. -As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in. -For multidimensional arrays, we recommend strongly "xarray":"http://xarray.pydata.org/en/stable/". _xarray_ has much of the same flexibility as _pandas_, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both _pandas_ and _xarray_. - - - -===== Reading Data and fitting ===== - -In order to study various Machine Learning algorithms, we need to -access data. Acccessing data is an essential step in all machine -learning algorithms. In particular, setting up the so-called _design -matrix_ (to be defined below) is often the first element we need in -order to perform our calculations. To set up the design matrix means -reading (and later, when the calculations are done, writing) data -in various formats, The formats span from reading files from disk, -loading data from databases and interacting with online sources -like web application programming interfaces (APIs). - -In handling various input formats, as discussed above, we will mainly stay with _pandas_, -a Python package which allows us, in a seamless and painless way, to -deal with a multitude of formats, from standard _csv_ (comma separated -values) files, via _excel_, _html_ to _hdf5_ formats. With _pandas_ -and the _DataFrame_ and _Series_ functionalities we are able to convert text data -into the calculational formats we need for a specific algorithm. And our code is going to be -pretty close the basic mathematical expressions. - -Our first data set is going to be a classic from nuclear physics, namely all -available data on binding energies. Don't be intimidated if you are not familiar with nuclear physics. It serves simply as an example here of a data set. - -We will show some of the -strengths of packages like _Scikit-Learn_ in fitting nuclear binding energies to -specific functions using linear regression first. Then, as a teaser, we will show you how -you can easily implement other algorithms like decision trees and random forests and neural networks. - -But before we really start with nuclear physics data, let's just look at some simpler polynomial fitting cases, such as, -(don't be offended) fitting straight lines! - - -=== Simple linear regression model using _scikit-learn_ === - -We start with perhaps our simplest possible example, using _Scikit-Learn_ to perform linear regression analysis on a data set produced by us. - -What follows is a simple Python code where we have defined a function -$y$ in terms of the variable $x$. Both are defined as vectors with $100$ entries. -The numbers in the vector $\hat{x}$ are given -by random numbers generated with a uniform distribution with entries -$x_i \in [0,1]$ (more about probability distribution functions -later). These values are then used to define a function $y(x)$ -(tabulated again as a vector) with a linear dependence on $x$ plus a -random noise added via the normal distribution. - - -The Numpy functions are imported used the _import numpy as np_ -statement and the random number generator for the uniform distribution -is called using the function _np.random.rand()_, where we specificy -that we want $100$ random variables. Using Numpy we define -automatically an array with the specified number of elements, $100$ in -our case. With the Numpy function _randn()_ we can compute random -numbers with the normal distribution (mean value $\mu$ equal to zero and -variance $\sigma^2$ set to one) and produce the values of $y$ assuming a linear -dependence as function of $x$ - -!bt -\[ -y = 2x+N(0,1), -\] -!et - -where $N(0,1)$ represents random numbers generated by the normal -distribution. From _Scikit-Learn_ we import then the -_LinearRegression_ functionality and make a prediction $\tilde{y} = -\alpha + \beta x$ using the function _fit(x,y)_. We call the set of -data $(\hat{x},\hat{y})$ for our training data. The Python package -_scikit-learn_ has also a functionality which extracts the above -fitting parameters $\alpha$ and $\beta$ (see below). Later we will -distinguish between training data and test data. - -For plotting we use the Python package -"matplotlib":"https://matplotlib.org/" which produces publication -quality figures. Feel free to explore the extensive -"gallery":"https://matplotlib.org/gallery/index.html" of examples. In -this example we plot our original values of $x$ and $y$ as well as the -prediction _ypredict_ ($\tilde{y}$), which attempts at fitting our -data with a straight line. - -The Python code follows here. -!bc pycod -# Importing various packages -import numpy as np -import matplotlib.pyplot as plt -from sklearn.linear_model import LinearRegression - -x = np.random.rand(100,1) -y = 2*x+np.random.randn(100,1) -linreg = LinearRegression() -linreg.fit(x,y) -xnew = np.array([[0],[1]]) -ypredict = linreg.predict(xnew) - -plt.plot(xnew, ypredict, "r-") -plt.plot(x, y ,'ro') -plt.axis([0,1.0,0, 5.0]) -plt.xlabel(r'$x$') -plt.ylabel(r'$y$') -plt.title(r'Simple Linear Regression') -plt.show() -!ec - -This example serves several aims. It allows us to demonstrate several -aspects of data analysis and later machine learning algorithms. The -immediate visualization shows that our linear fit is not -impressive. It goes through the data points, but there are many -outliers which are not reproduced by our linear regression. We could -now play around with this small program and change for example the -factor in front of $x$ and the normal distribution. Try to change the -function $y$ to - -!bt -\[ -y = 10x+0.01 \times N(0,1), -\] -!et - -where $x$ is defined as before. Does the fit look better? Indeed, by -reducing the role of the noise given by the normal distribution we see immediately that -our linear prediction seemingly reproduces better the training -set. However, this testing 'by the eye' is obviouly not satisfactory in the -long run. Here we have only defined the training data and our model, and -have not discussed a more rigorous approach to the _cost_ function. - -We need more rigorous criteria in defining whether we have succeeded or -not in modeling our training data. You will be surprised to see that -many scientists seldomly venture beyond this 'by the eye' approach. A -standard approach for the *cost* function is the so-called $\chi^2$ -function (a variant of the mean-squared error (MSE)) - -!bt -\[ \chi^2 = \frac{1}{n} -\sum_{i=0}^{n-1}\frac{(y_i-\tilde{y}_i)^2}{\sigma_i^2}, -\] -!et - -where $\sigma_i^2$ is the variance (to be defined later) of the entry -$y_i$. We may not know the explicit value of $\sigma_i^2$, it serves -however the aim of scaling the equations and make the cost function -dimensionless. - -Minimizing the cost function is a central aspect of -our discussions to come. Finding its minima as function of the model -parameters ($\alpha$ and $\beta$ in our case) will be a recurring -theme in these series of lectures. Essentially all machine learning -algorithms we will discuss center around the minimization of the -chosen cost function. This depends in turn on our specific -model for describing the data, a typical situation in supervised -learning. Automatizing the search for the minima of the cost function is a -central ingredient in all algorithms. Typical methods which are -employed are various variants of _gradient_ methods. These will be -discussed in more detail later. Again, you'll be surprised to hear that -many practitioners minimize the above function ''by the eye', popularly dubbed as -'chi by the eye'. That is, change a parameter and see (visually and numerically) that -the $\chi^2$ function becomes smaller. - -There are many ways to define the cost function. A simpler approach is to look at the relative difference between the training data and the predicted data, that is we define -the relative error (why would we prefer the MSE instead of the relative error?) as - -!bt -\[ -\epsilon_{\mathrm{relative}}= \frac{\vert \hat{y} -\hat{\tilde{y}}\vert}{\vert \hat{y}\vert}. -\] -!et - -The squared cost function results in an arithmetic mean-unbiased -estimator, and the absolute-value cost function results in a -median-unbiased estimator (in the one-dimensional case, and a -geometric median-unbiased estimator for the multi-dimensional -case). The squared cost function has the disadvantage that it has the tendency -to be dominated by outliers. - -We can modify easily the above Python code and plot the relative error instead -!bc pycod -import numpy as np -import matplotlib.pyplot as plt -from sklearn.linear_model import LinearRegression - -x = np.random.rand(100,1) -y = 5*x+0.01*np.random.randn(100,1) -linreg = LinearRegression() -linreg.fit(x,y) -ypredict = linreg.predict(x) - -plt.plot(x, np.abs(ypredict-y)/abs(y), "ro") -plt.axis([0,1.0,0.0, 0.5]) -plt.xlabel(r'$x$') -plt.ylabel(r'$\epsilon_{\mathrm{relative}}$') -plt.title(r'Relative error') -plt.show() -!ec - -Depending on the parameter in front of the normal distribution, we may -have a small or larger relative error. Try to play around with -different training data sets and study (graphically) the value of the -relative error. - -As mentioned above, _Scikit-Learn_ has an impressive functionality. -We can for example extract the values of $\alpha$ and $\beta$ and -their error estimates, or the variance and standard deviation and many -other properties from the statistical data analysis. - -Here we show an -example of the functionality of _Scikit-Learn_. -!bc pycod -import numpy as np -import matplotlib.pyplot as plt -from sklearn.linear_model import LinearRegression -from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error - -x = np.random.rand(100,1) -y = 2.0+ 5*x+0.5*np.random.randn(100,1) -linreg = LinearRegression() -linreg.fit(x,y) -ypredict = linreg.predict(x) -print('The intercept alpha: \n', linreg.intercept_) -print('Coefficient beta : \n', linreg.coef_) -# The mean squared error -print("Mean squared error: %.2f" % mean_squared_error(y, ypredict)) -# Explained variance score: 1 is perfect prediction -print('Variance score: %.2f' % r2_score(y, ypredict)) -# Mean squared log error -print('Mean squared log error: %.2f' % mean_squared_log_error(y, ypredict) ) -# Mean absolute error -print('Mean absolute error: %.2f' % mean_absolute_error(y, ypredict)) -plt.plot(x, ypredict, "r-") -plt.plot(x, y ,'ro') -plt.axis([0.0,1.0,1.5, 7.0]) -plt.xlabel(r'$x$') -plt.ylabel(r'$y$') -plt.title(r'Linear Regression fit ') -plt.show() - -!ec -The function _coef_ gives us the parameter $\beta$ of our fit while _intercept_ yields -$\alpha$. Depending on the constant in front of the normal distribution, we get values near or far from $alpha =2$ and $\beta =5$. Try to play around with different parameters in front of the normal distribution. The function _meansquarederror_ gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as -!bt -\[ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n} -\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2, -\] -!et - -The smaller the value, the better the fit. Ideally we would like to -have an MSE equal zero. The attentive reader has probably recognized -this function as being similar to the $\chi^2$ function defined above. - -The _r2score_ function computes $R^2$, the coefficient of -determination. It provides a measure of how well future samples are -likely to be predicted by the model. Best possible score is 1.0 and it -can be negative (because the model can be arbitrarily worse). A -constant model that always predicts the expected value of $\hat{y}$, -disregarding the input features, would get a $R^2$ score of $0.0$. - -If $\tilde{\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as -!bt -\[ -R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2}, -\] -!et -where we have defined the mean value of $\hat{y}$ as -!bt -\[ -\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i. -\] -!et -Another quantity taht we will meet again in our discussions of regression analysis is - the mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the $l1$-norm loss. In our discussion above we presented the relative error. -The MAE is defined as follows -!bt -\[ -\text{MAE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \tilde{y}_i \right|. -\] -!et -We present the -squared logarithmic (quadratic) error -!bt -\[ -\text{MSLE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n - 1} (\log_e (1 + y_i) - \log_e (1 + \tilde{y}_i) )^2, -\] -!et - -where $\log_e (x)$ stands for the natural logarithm of $x$. This error -estimate is best to use when targets having exponential growth, such -as population counts, average sales of a commodity over a span of -years etc. - - -Finally, another cost function is the Huber cost function used in robust regression. -It is less sensitive to outliers in data than the squared error cost function. -A variant for classification is also sometimes used, a quantity we will meet later. -!bt -\[ -L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}} -\] -!et - -We will discuss in more -detail these and other functions in the various lectures. We conclude this part with another example. Instead of -a linear $x$-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn. - -!bc pycod -import matplotlib.pyplot as plt -import numpy as np -import random -from sklearn.linear_model import Ridge -from sklearn.preprocessing import PolynomialFeatures -from sklearn.pipeline import make_pipeline -from sklearn.linear_model import LinearRegression - -x=np.linspace(0.02,0.98,200) -noise = np.asarray(random.sample((range(200)),200)) -y=x**3*noise -yn=x**3*100 -poly3 = PolynomialFeatures(degree=3) -X = poly3.fit_transform(x[:,np.newaxis]) -clf3 = LinearRegression() -clf3.fit(X,y) - -Xplot=poly3.fit_transform(x[:,np.newaxis]) -poly3_plot=plt.plot(x, clf3.predict(Xplot), label='Cubic Fit') -plt.plot(x,yn, color='red', label="True Cubic") -plt.scatter(x, y, label='Data', color='orange', s=15) -plt.legend() -plt.show() - -def error(a): - for i in y: - err=(y-yn)/yn - return abs(np.sum(err))/len(err) - -print (error(y)) -!ec - - - - -=== To our real data: nuclear binding energies. Brief reminder on masses and binding energies === - -Let us now dive into nuclear physics and remind ourselves briefly about some basic features about binding -energies. A basic quantity which can be measured for the ground -states of nuclei is the atomic mass $M(N, Z)$ of the neutral atom with -atomic mass number $A$ and charge $Z$. The number of neutrons is $N$. There are indeed several sophisticated experiments worldwide which allow us to measure this quantity to high precision (parts per million even). - -Atomic masses are usually tabulated in terms of the mass excess defined by -!bt -\[ -\Delta M(N, Z) = M(N, Z) - uA, -\] -!et -where $u$ is the Atomic Mass Unit -!bt -\[ -u = M(^{12}\mathrm{C})/12 = 931.4940954(57) \hspace{0.1cm} \mathrm{MeV}/c^2. -\] -!et -The nucleon masses are -!bt -\[ -m_p = 1.00727646693(9)u, -\] -!et -and -!bt -\[ -m_n = 939.56536(8)\hspace{0.1cm} \mathrm{MeV}/c^2 = 1.0086649156(6)u. -\] -!et - -In the "2016 mass evaluation of by W.J.Huang, G.Audi, M.Wang, F.G.Kondev, S.Naimi and X.Xu":"http://nuclearmasses.org/resources_folder/Wang_2017_Chinese_Phys_C_41_030003.pdf" -there are data on masses and decays of 3437 nuclei. - -The nuclear binding energy is defined as the energy required to break -up a given nucleus into its constituent parts of $N$ neutrons and $Z$ -protons. In terms of the atomic masses $M(N, Z)$ the binding energy is -defined by - - -!bt -\[ -BE(N, Z) = ZM_H c^2 + Nm_n c^2 - M(N, Z)c^2 , -\] -!et -where $M_H$ is the mass of the hydrogen atom and $m_n$ is the mass of the neutron. -In terms of the mass excess the binding energy is given by -!bt -\[ -BE(N, Z) = Z\Delta_H c^2 + N\Delta_n c^2 -\Delta(N, Z)c^2 , -\] -!et -where $\Delta_H c^2 = 7.2890$ MeV and $\Delta_n c^2 = 8.0713$ MeV. - - -A popular and physically intuitive model which can be used to parametrize -the experimental binding energies as function of $A$, is the so-called -_liquid drop model_. The ansatz is based on the following expression - -!bt -\[ -BE(N,Z) = a_1A-a_2A^{2/3}-a_3\frac{Z^2}{A^{1/3}}-a_4\frac{(N-Z)^2}{A}, -\] -!et - -where $A$ stands for the number of nucleons and the $a_i$s are parameters which are determined by a fit -to the experimental data. - - - - -To arrive at the above expression we have assumed that we can make the following assumptions: - - * There is a volume term $a_1A$ proportional with the number of nucleons (the energy is also an extensive quantity). When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. This contribution is proportional to the volume. - - * There is a surface energy term $a_2A^{2/3}$. The assumption here is that a nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area. - - - * There is a Coulomb energy term $a_3\frac{Z^2}{A^{1/3}}$. The electric repulsion between each pair of protons in a nucleus yields less binding. - - * There is an asymmetry term $a_4\frac{(N-Z)^2}{A}$. This term is associated with the Pauli exclusion principle and reflects the fact that the proton-neutron interaction is more attractive on the average than the neutron-neutron and proton-proton interactions. - -We could also add a so-called pairing term, which is a correction term that -arises from the tendency of proton pairs and neutron pairs to -occur. An even number of particles is more stable than an odd number. - - -=== Organizing our data === - -Let us start with reading and organizing our data. -We start with the compilation of masses and binding energies from 2016. -After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data. - - -We start with preparing folders for storing our calculations and the data file over masses and binding energies. We import also various modules that we will find useful in order to present various Machine Learning methods. Here we focus mainly on the functionality of _scikit-learn_. -!bc pycod -# Common imports -import numpy as np -import pandas as pd -import matplotlib.pyplot as plt -import sklearn.linear_model as skl -from sklearn.model_selection import train_test_split -from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error -import os - -# Where to save the figures and data files -PROJECT_ROOT_DIR = "Results" -FIGURE_ID = "Results/FigureFiles" -DATA_ID = "DataFiles/" - -if not os.path.exists(PROJECT_ROOT_DIR): - os.mkdir(PROJECT_ROOT_DIR) - -if not os.path.exists(FIGURE_ID): - os.makedirs(FIGURE_ID) - -if not os.path.exists(DATA_ID): - os.makedirs(DATA_ID) - -def image_path(fig_id): - return os.path.join(FIGURE_ID, fig_id) - -def data_path(dat_id): - return os.path.join(DATA_ID, dat_id) - -def save_fig(fig_id): - plt.savefig(image_path(fig_id) + ".png", format='png') - -infile = open(data_path("MassEval2016.dat"),'r') -!ec - - -Before we proceed, we define also a function for making our plots. You can obviously avoid this and simply set up various _matplotlib_ commands every time you need them. You may however find it convenient to collect all such commands in one function and simply call this function. -!bc pycod -from pylab import plt, mpl -plt.style.use('seaborn') -mpl.rcParams['font.family'] = 'serif' - -def MakePlot(x,y, styles, labels, axlabels): - plt.figure(figsize=(10,6)) - for i in range(len(x)): - plt.plot(x[i], y[i], styles[i], label = labels[i]) - plt.xlabel(axlabels[0]) - plt.ylabel(axlabels[1]) - plt.legend(loc=0) -!ec - -Our next step is to read the data on experimental binding energies and -reorganize them as functions of the mass number $A$, the number of -protons $Z$ and neutrons $N$ using _pandas_. Before we do this it is -always useful (unless you have a binary file or other types of compressed -data) to actually open the file and simply take a look at it! - - -In particular, the program that outputs the final nuclear masses is written in Fortran with a specific format. It means that we need to figure out the format and which columns contain the data we are interested in. Pandas comes with a function that reads formatted output. After having admired the file, we are now ready to start massaging it with _pandas_. The file begins with some basic format information. -!bc pycod -""" -This is taken from the data file of the mass 2016 evaluation. -All files are 3436 lines long with 124 character per line. - Headers are 39 lines long. - col 1 : Fortran character control: 1 = page feed 0 = line feed - format : a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5 - These formats are reflected in the pandas widths variable below, see the statement - widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), - Pandas has also a variable header, with length 39 in this case. -""" -!ec - -The data we are interested in are in columns 2, 3, 4 and 11, giving us -the number of neutrons, protons, mass numbers and binding energies, -respectively. We add also for the sake of completeness the element name. The data are in fixed-width formatted lines and we will -covert them into the _pandas_ DataFrame structure. - -!bc pycod -# Read the experimental data with Pandas -Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11), - names=('N', 'Z', 'A', 'Element', 'Ebinding'), - widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1), - header=39, - index_col=False) - -# Extrapolated values are indicated by '#' in place of the decimal place, so -# the Ebinding column won't be numeric. Coerce to float and drop these entries. -Masses['Ebinding'] = pd.to_numeric(Masses['Ebinding'], errors='coerce') -Masses = Masses.dropna() -# Convert from keV to MeV. -Masses['Ebinding'] /= 1000 - -# Group the DataFrame by nucleon number, A. -Masses = Masses.groupby('A') -# Find the rows of the grouped DataFrame with the maximum binding energy. -Masses = Masses.apply(lambda t: t[t.Ebinding==t.Ebinding.max()]) -!ec - -We have now read in the data, grouped them according to the variables we are interested in. -We see how easy it is to reorganize the data using _pandas_. If we -were to do these operations in C/C++ or Fortran, we would have had to -write various functions/subroutines which perform the above -reorganizations for us. Having reorganized the data, we can now start -to make some simple fits using both the functionalities in _numpy_ and -_Scikit-Learn_ afterwards. - -Now we define five variables which contain -the number of nucleons $A$, the number of protons $Z$ and the number of neutrons $N$, the element name and finally the energies themselves. -!bc pycod -A = Masses['A'] -Z = Masses['Z'] -N = Masses['N'] -Element = Masses['Element'] -Energies = Masses['Ebinding'] -print(Masses) -!ec -The next step, and we will define this mathematically later, is to set up the so-called _design matrix_. We will throughout call this matrix $\bm{X}$. -It has dimensionality $p\times n$, where $n$ is the number of data points and $p$ are the so-called predictors. In our case here they are given by the number of polynomials in $A$ we wish to include in the fit. -!bc pycod -# Now we set up the design matrix X -X = np.zeros((len(A),5)) -X[:,0] = 1 -X[:,1] = A -X[:,2] = A**(2.0/3.0) -X[:,3] = A**(-1.0/3.0) -X[:,4] = A**(-1.0) -!ec -With _scikitlearn_ we are now ready to use linear regression and fit our data. -!bc pycod -clf = skl.LinearRegression().fit(X, Energies) -fity = clf.predict(X) -!ec -Pretty simple! -Now we can print measures of how our fit is doing, the coefficients from the fits and plot the final fit together with our data. -!bc pycod -# The mean squared error -print("Mean squared error: %.2f" % mean_squared_error(Energies, fity)) -# Explained variance score: 1 is perfect prediction -print('Variance score: %.2f' % r2_score(Energies, fity)) -# Mean absolute error -print('Mean absolute error: %.2f' % mean_absolute_error(Energies, fity)) -print(clf.coef_, clf.intercept_) - -Masses['Eapprox'] = fity -# Generate a plot comparing the experimental with the fitted values values. -fig, ax = plt.subplots() -ax.set_xlabel(r'$A = N + Z$') -ax.set_ylabel(r'$E_\mathrm{bind}\,/\mathrm{MeV}$') -ax.plot(Masses['A'], Masses['Ebinding'], alpha=0.7, lw=2, - label='Ame2016') -ax.plot(Masses['A'], Masses['Eapprox'], alpha=0.7, lw=2, c='m', - label='Fit') -ax.legend() -save_fig("Masses2016") -plt.show() -!ec - - -=== Seeing the wood for the trees === - -As a teaser, let us now see how we can do this with decision trees using _scikit-learn_. Later we will switch to so-called _random forests_! - - -!bc pycod - -#Decision Tree Regression -from sklearn.tree import DecisionTreeRegressor -regr_1=DecisionTreeRegressor(max_depth=5) -regr_2=DecisionTreeRegressor(max_depth=7) -regr_3=DecisionTreeRegressor(max_depth=9) -regr_1.fit(X, Energies) -regr_2.fit(X, Energies) -regr_3.fit(X, Energies) - - -y_1 = regr_1.predict(X) -y_2 = regr_2.predict(X) -y_3=regr_3.predict(X) -Masses['Eapprox'] = y_3 -# Plot the results -plt.figure() -plt.plot(A, Energies, color="blue", label="Data", linewidth=2) -plt.plot(A, y_1, color="red", label="max_depth=5", linewidth=2) -plt.plot(A, y_2, color="green", label="max_depth=7", linewidth=2) -plt.plot(A, y_3, color="m", label="max_depth=9", linewidth=2) - -plt.xlabel("$A$") -plt.ylabel("$E$[MeV]") -plt.title("Decision Tree Regression") -plt.legend() -save_fig("Masses2016Trees") -plt.show() -print(Masses) -print(np.mean( (Energies-y_1)**2)) -!ec - - -=== And what about using neural networks? === -The _seaborn_ package allows us to visualize data in an efficient way. Note that we use _scikit-learn_'s multi-layer perceptron (or feed forward neural network) -functionality. -!bc pycod -from sklearn.neural_network import MLPRegressor -from sklearn.metrics import accuracy_score -import seaborn as sns - -X_train = X -Y_train = Energies -n_hidden_neurons = 100 -epochs = 100 -# store models for later use -eta_vals = np.logspace(-5, 1, 7) -lmbd_vals = np.logspace(-5, 1, 7) -# store the models for later use -DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object) -train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals))) -sns.set() -for i, eta in enumerate(eta_vals): - for j, lmbd in enumerate(lmbd_vals): - dnn = MLPRegressor(hidden_layer_sizes=(n_hidden_neurons), activation='logistic', - alpha=lmbd, learning_rate_init=eta, max_iter=epochs) - dnn.fit(X_train, Y_train) - DNN_scikit[i][j] = dnn - train_accuracy[i][j] = dnn.score(X_train, Y_train) - -fig, ax = plt.subplots(figsize = (10, 10)) -sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis") -ax.set_title("Training Accuracy") -ax.set_ylabel("$\eta$") -ax.set_xlabel("$\lambda$") -plt.show() - - - -!ec - - -===== A first summary ===== - -The aim behind these introductory words was to present to you various -Python libraries and their functionalities, in particular libraries like -_numpy_, _pandas_, _xarray_ and _matplotlib_ and other that make our life much easier -in handling various data sets and visualizing data. - -Furthermore, -_Scikit-Learn_ allows us with few lines of code to implement popular -Machine Learning algorithms for supervised learning. Later we will meet _Tensorflow_, a powerful library for deep learning. -Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails. - - -======= Review of Basic Statistics ======= - - -===== Domains and probabilities ===== -!bblock -Consider the following simple example, namely the tossing of two dice, resulting in the following possible values -!bt -\begin{equation*} -\{2,3,4,5,6,7,8,9,10,11,12\}. -\end{equation*} -!et -These values are called the *domain*. -To this domain we have the corresponding *probabilities* -!bt -\begin{equation*} -\{1/36,2/36/,3/36,4/36,5/36,6/36,5/36,4/36,3/36,2/36,1/36\}. -\end{equation*} -!et -!eblock - - -===== Tossing the dice ===== -!bblock -The numbers in the domain are the outcomes of the physical process of tossing say two dice. -We cannot tell beforehand whether the outcome is 3 or 5 or any other number in this domain. -This defines the randomness of the outcome, or unexpectedness or any other synonimous word which -encompasses the uncertitude of the final outcome. - -The only thing we can tell beforehand -is that say the outcome 2 has a certain probability. -If our favorite hobby is to spend an hour every evening throwing dice and -registering the sequence of outcomes, we will note that the numbers in the above domain -!bt -\begin{equation*} -\{2,3,4,5,6,7,8,9,10,11,12\}, -\end{equation*} -!et -appear in a random order. After 11 throws the results may look like - -!bt -\begin{equation*} -\{10,8,6,3,6,9,11,8,12,4,5\}. -\end{equation*} -!et -!eblock - - -===== Stochastic variables ===== -!bblock - -_Random variables are characterized by a domain which contains all possible values that the random value may take. This domain has a corresponding probability distribution function(PDF)_. -!eblock - - -===== Stochastic variables and the main concepts, the discrete case ===== -!bblock -There are two main concepts associated with a stochastic variable. The -*domain* is the set $\mathbb D = \{x\}$ of all accessible values -the variable can assume, so that $X \in \mathbb D$. An example of a -discrete domain is the set of six different numbers that we may get by -throwing of a dice, $x\in\{1,\,2,\,3,\,4,\,5,\,6\}$. - -The *probability distribution function (PDF)* is a function -$p(x)$ on the domain which, in the discrete case, gives us the -probability or relative frequency with which these values of $X$ -occur -!bt -\begin{equation*} -p(x) = \mathrm{Prob}(X=x). -\end{equation*} -!et -!eblock - - - -===== Stochastic variables and the main concepts, the continuous case ===== -!bblock -In the continuous case, the PDF does not directly depict the -actual probability. Instead we define the probability for the -stochastic variable to assume any value on an infinitesimal interval -around $x$ to be $p(x)dx$. The continuous function $p(x)$ then gives us -the *density* of the probability rather than the probability -itself. The probability for a stochastic variable to assume any value -on a non-infinitesimal interval $[a,\,b]$ is then just the integral - -!bt -\begin{equation*} -\mathrm{Prob}(a\leq X\leq b) = \int_a^b p(x)dx. -\end{equation*} -!et -Qualitatively speaking, a stochastic variable represents the values of -numbers chosen as if by chance from some specified PDF so that the -selection of a large set of these numbers reproduces this PDF. -!eblock - - -===== The cumulative probability ===== -!bblock -Of interest to us is the *cumulative probability -distribution function* (_CDF_), $P(x)$, which is just the probability -for a stochastic variable $X$ to assume any value less than $x$ -!bt -\begin{equation*} -P(x)=\mathrm{Prob(}X\leq x\mathrm{)} = -\int_{-\infty}^x p(x^{\prime})dx^{\prime}. -\end{equation*} -!et -The relation between a CDF and its corresponding PDF is then - -!bt -\begin{equation*} -p(x) = \frac{d}{dx}P(x). -\end{equation*} -!et -!eblock - - -===== Properties of PDFs ===== -!bblock - -There are two properties that all PDFs must satisfy. The first one is -positivity (assuming that the PDF is normalized) - -!bt -\begin{equation*} -0 \leq p(x) \leq 1. -\end{equation*} -!et -Naturally, it would be nonsensical for any of the values of the domain -to occur with a probability greater than $1$ or less than $0$. Also, -the PDF must be normalized. That is, all the probabilities must add up -to unity. The probability of ``anything'' to happen is always unity. For -both discrete and continuous PDFs, this condition is -!bt -\begin{align*} -\sum_{x_i\in\mathbb D} p(x_i) & = 1,\\ -\int_{x\in\mathbb D} p(x)\,dx & = 1. -\end{align*} -!et -!eblock - - -===== Important distributions, the uniform distribution ===== -!bblock -The first one -is the most basic PDF; namely the uniform distribution -!bt -\begin{equation} -p(x) = \frac{1}{b-a}\theta(x-a)\theta(b-x). -label{eq:unifromPDF} -\end{equation} -!et -For $a=0$ and $b=1$ we have -!bt -\[ -\begin{array}{ll} -p(x)dx = dx & \in [0,1]. -\end{array} -\] -!et -The latter distribution is used to generate random numbers. For other PDFs, one needs normally a mapping from this distribution to say for example the exponential distribution. -!eblock - - -===== Gaussian distribution ===== -!bblock -The second one is the Gaussian Distribution -!bt -\begin{equation*} -p(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp{(-\frac{(x-\mu)^2}{2\sigma^2})}, -\end{equation*} -!et -with mean value $\mu$ and standard deviation $\sigma$. If $\mu=0$ and $\sigma=1$, it is normally called the _standard normal distribution_ -!bt -\begin{equation*} -p(x) = \frac{1}{\sqrt{2\pi}} \exp{(-\frac{x^2}{2})}, -\end{equation*} -!et - -The following simple Python code plots the above distribution for different values of $\mu$ and $\sigma$. -!bc pyscpro -import numpy as np -from math import acos, exp, sqrt -from matplotlib import pyplot as plt -from matplotlib import rc, rcParams -import matplotlib.units as units -import matplotlib.ticker as ticker -rc('text',usetex=True) -rc('font',**{'family':'serif','serif':['Gaussian distribution']}) -font = {'family' : 'serif', - 'color' : 'darkred', - 'weight' : 'normal', - 'size' : 16, - } -pi = acos(-1.0) -mu0 = 0.0 -sigma0 = 1.0 -mu1= 1.0 -sigma1 = 2.0 -mu2 = 2.0 -sigma2 = 4.0 - -x = np.linspace(-20.0, 20.0) -v0 = np.exp(-(x*x-2*x*mu0+mu0*mu0)/(2*sigma0*sigma0))/sqrt(2*pi*sigma0*sigma0) -v1 = np.exp(-(x*x-2*x*mu1+mu1*mu1)/(2*sigma1*sigma1))/sqrt(2*pi*sigma1*sigma1) -v2 = np.exp(-(x*x-2*x*mu2+mu2*mu2)/(2*sigma2*sigma2))/sqrt(2*pi*sigma2*sigma2) -plt.plot(x, v0, 'b-', x, v1, 'r-', x, v2, 'g-') -plt.title(r'{\bf Gaussian distributions}', fontsize=20) -plt.text(-19, 0.3, r'Parameters: $\mu = 0$, $\sigma = 1$', fontdict=font) -plt.text(-19, 0.18, r'Parameters: $\mu = 1$, $\sigma = 2$', fontdict=font) -plt.text(-19, 0.08, r'Parameters: $\mu = 2$, $\sigma = 4$', fontdict=font) -plt.xlabel(r'$x$',fontsize=20) -plt.ylabel(r'$p(x)$ [MeV]',fontsize=20) - -# Tweak spacing to prevent clipping of ylabel -plt.subplots_adjust(left=0.15) -plt.savefig('gaussian.pdf', format='pdf') -plt.show() -!ec -!eblock - - - -===== Exponential distribution ===== -!bblock -Another important distribution in science is the exponential distribution -!bt -\begin{equation*} -p(x) = \alpha\exp{-(\alpha x)}. -\end{equation*} -!et -!eblock - - -===== Expectation values ===== -!bblock -Let $h(x)$ be an arbitrary continuous function on the domain of the stochastic -variable $X$ whose PDF is $p(x)$. We define the *expectation value* -of $h$ with respect to $p$ as follows - -!bt -\begin{equation} -\langle h \rangle_X \equiv \int\! h(x)p(x)\,dx -label{eq:expectation_value_of_h_wrt_p} -\end{equation} -!et -Whenever the PDF is known implicitly, like in this case, we will drop -the index $X$ for clarity. -A particularly useful class of special expectation values are the -*moments*. The $n$-th moment of the PDF $p$ is defined as -follows -!bt -\begin{equation*} -\langle x^n \rangle \equiv \int\! x^n p(x)\,dx -\end{equation*} -!et -!eblock - - -===== Stochastic variables and the main concepts, mean values ===== -!bblock -The zero-th moment $\langle 1\rangle$ is just the normalization condition of -$p$. The first moment, $\langle x\rangle$, is called the *mean* of $p$ -and often denoted by the letter $\mu$ -!bt -\begin{equation*} -\langle x\rangle = \mu \equiv \int x p(x)dx, -\end{equation*} -!et -for a continuous distribution and -!bt -\begin{equation*} -\langle x\rangle = \mu \equiv \sum_{i=1}^N x_i p(x_i), -\end{equation*} -!et -for a discrete distribution. -Qualitatively it represents the centroid or the average value of the -PDF and is therefore simply called the expectation value of $p(x)$. -!eblock - - -===== Stochastic variables and the main concepts, central moments, the variance ===== -!bblock - -A special version of the moments is the set of *central moments*, the n-th central moment defined as -!bt -\begin{equation*} -\langle (x-\langle x\rangle )^n\rangle \equiv \int\! (x-\langle x\rangle)^n p(x)\,dx -\end{equation*} -!et -The zero-th and first central moments are both trivial, equal $1$ and -$0$, respectively. But the second central moment, known as the -*variance* of $p$, is of particular interest. For the stochastic -variable $X$, the variance is denoted as $\sigma^2_X$ or $\mathrm{Var}(X)$ -!bt -\begin{align*} -\sigma^2_X &=\mathrm{Var}(X) = \langle (x-\langle x\rangle)^2\rangle = -\int (x-\langle x\rangle)^2 p(x)dx\\ -& = \int\left(x^2 - 2 x \langle x\rangle^{2} +\langle x\rangle^2\right)p(x)dx\\ -& = \langle x^2\rangle - 2 \langle x\rangle\langle x\rangle + \langle x\rangle^2\\ -& = \langle x^2 \rangle - \langle x\rangle^2 -\end{align*} -!et -The square root of the variance, $\sigma =\sqrt{\langle (x-\langle x\rangle)^2\rangle}$ is called the -_standard deviation_ of $p$. It is the RMS (root-mean-square) -value of the deviation of the PDF from its mean value, interpreted -qualitatively as the ``spread'' of $p$ around its mean. -!eblock - - - - -===== Probability Distribution Functions ===== -!bblock - -The following table collects properties of probability distribution functions. -In our notation we reserve the label $p(x)$ for the probability of a certain event, -while $P(x)$ is the cumulative probability. - - -|--------------------------------------------------------------------------------------------------------------------------------------| -| | Discrete PDF | Continuous PDF | -|---------------------l-------------------------------------------c-------------------------------------------c------------------------| -| Domain | $\left\{x_1, x_2, x_3, \dots, x_N\right\}$ | $[a,b]$ | -| Probability | $p(x_i)$ | $p(x)dx$ | -| Cumulative | $P_i=\sum_{l=1}^ip(x_l)$ | $P(x)=\int_a^xp(t)dt$ | -| Positivity | $0 \le p(x_i) \le 1$ | $p(x) \ge 0$ | -| Positivity | $0 \le P_i \le 1$ | $0 \le P(x) \le 1$ | -| Monotonic | $P_i \ge P_j$ if $x_i \ge x_j$ | $P(x_i) \ge P(x_j)$ if $x_i \ge x_j$ | -| Normalization | $P_N=1$ | $P(b)=1$ | -|--------------------------------------------------------------------------------------------------------------------------------------| - -!eblock - - - -===== Probability Distribution Functions ===== -!bblock -With a PDF we can compute expectation values of selected quantities such as - -!bt -\begin{equation*} - \langle x^k\rangle=\sum_{i=1}^{N}x_i^kp(x_i), -\end{equation*} -!et -if we have a discrete PDF or - -!bt -\begin{equation*} - \langle x^k\rangle=\int_a^b x^kp(x)dx, -\end{equation*} -!et -in the case of a continuous PDF. We have already defined the mean value $\mu$ -and the variance $\sigma^2$. -!eblock - - -===== The three famous Probability Distribution Functions ===== -!bblock - -There are at least three PDFs which one may encounter. These are the - -_Uniform distribution_ -!bt -\begin{equation*} -p(x)=\frac{1}{b-a}\Theta(x-a)\Theta(b-x), -\end{equation*} -!et -yielding probabilities different from zero in the interval $[a,b]$. - -_The exponential distribution_ -!bt -\begin{equation*} -p(x)=\alpha \exp{(-\alpha x)}, -\end{equation*} -!et -yielding probabilities different from zero in the interval $[0,\infty)$ and with mean value -!bt -\begin{equation*} -\mu = \int_0^{\infty}xp(x)dx=\int_0^{\infty}x\alpha \exp{(-\alpha x)}dx=\frac{1}{\alpha}, -\end{equation*} -!et -!eblock -with variance -!bt -\begin{equation*} -\sigma^2=\int_0^{\infty}x^2p(x)dx-\mu^2 = \frac{1}{\alpha^2}. -\end{equation*} -!et - - -===== Probability Distribution Functions, the normal distribution ===== -!bblock -Finally, we have the so-called univariate normal distribution, or just the _normal distribution_ -!bt -\begin{equation*} -p(x)=\frac{1}{b\sqrt{2\pi}}\exp{\left(-\frac{(x-a)^2}{2b^2}\right)} -\end{equation*} -!et -with probabilities different from zero in the interval $(-\infty,\infty)$. -The integral $\int_{-\infty}^{\infty}\exp{\left(-(x^2\right)}dx$ appears in many calculations, its value -is $\sqrt{\pi}$, a result we will need when we compute the mean value and the variance. -The mean value is -!bt -\begin{equation*} - \mu = \int_0^{\infty}xp(x)dx=\frac{1}{b\sqrt{2\pi}}\int_{-\infty}^{\infty}x \exp{\left(-\frac{(x-a)^2}{2b^2}\right)}dx, -\end{equation*} -!et -which becomes with a suitable change of variables -!bt -\begin{equation*} - \mu =\frac{1}{b\sqrt{2\pi}}\int_{-\infty}^{\infty}b\sqrt{2}(a+b\sqrt{2}y)\exp{-y^2}dy=a. -\end{equation*} -!et -!eblock - - -===== Probability Distribution Functions, the normal distribution ===== -!bblock -Similarly, the variance becomes -!bt -\begin{equation*} - \sigma^2 = \frac{1}{b\sqrt{2\pi}}\int_{-\infty}^{\infty}(x-\mu)^2 \exp{\left(-\frac{(x-a)^2}{2b^2}\right)}dx, -\end{equation*} -!et -and inserting the mean value and performing a variable change we obtain - -!bt -\begin{equation*} - \sigma^2 = \frac{1}{b\sqrt{2\pi}}\int_{-\infty}^{\infty}b\sqrt{2}(b\sqrt{2}y)^2\exp{\left(-y^2\right)}dy= -\frac{2b^2}{\sqrt{\pi}}\int_{-\infty}^{\infty}y^2\exp{\left(-y^2\right)}dy, -\end{equation*} -!et -and performing a final integration by parts we obtain the well-known result $\sigma^2=b^2$. -It is useful to introduce the standard normal distribution as well, defined by $\mu=a=0$, viz. a distribution -centered around zero and with a variance $\sigma^2=1$, leading to - -!bt -\begin{equation} - p(x)=\frac{1}{\sqrt{2\pi}}\exp{\left(-\frac{x^2}{2}\right)}. -\end{equation} -!et -!eblock - - -===== Probability Distribution Functions, the cumulative distribution ===== -!bblock - -The exponential and uniform distributions have simple cumulative functions, -whereas the normal distribution does not, being proportional to the so-called -error function $erf(x)$, given by - -!bt -\begin{equation*} -P(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^x\exp{\left(-\frac{t^2}{2}\right)}dt, -\end{equation*} -!et -which is difficult to evaluate in a quick way. -!eblock - - - -===== Probability Distribution Functions, other important distribution ===== -!bblock - -Some other PDFs which one encounters often in the natural sciences are the binomial distribution -!bt -\begin{equation*} - p(x) = \left(\begin{array}{c} n \\ x\end{array}\right)y^x(1-y)^{n-x} \hspace{0.5cm}x=0,1,\dots,n, -\end{equation*} -!et -where $y$ is the probability for a specific event, such as the tossing of a coin or moving left or right -in case of a random walker. Note that $x$ is a discrete stochastic variable. - -The sequence of binomial trials is characterized by the following definitions - - * Every experiment is thought to consist of $N$ independent trials. - - * In every independent trial one registers if a specific situation happens or not, such as the jump to the left or right of a random walker. - - * The probability for every outcome in a single trial has the same value, for example the outcome of tossing (either heads or tails) a coin is always $1/2$. -!eblock - - -===== Probability Distribution Functions, the binomial distribution ===== -!bblock - -In order to compute the mean and variance we need to recall Newton's binomial -formula -!bt -\begin{equation*} - (a+b)^m=\sum_{n=0}^m \left(\begin{array}{c} m \\ n\end{array}\right)a^nb^{m-n}, -\end{equation*} -!et -which can be used to show that - -!bt -\begin{equation*} -\sum_{x=0}^n\left(\begin{array}{c} n \\ x\end{array}\right)y^x(1-y)^{n-x} = (y+1-y)^n = 1, -\end{equation*} -!et -the PDF is normalized to one. -The mean value is -!bt -\begin{equation*} -\mu = \sum_{x=0}^n x\left(\begin{array}{c} n \\ x\end{array}\right)y^x(1-y)^{n-x} = -\sum_{x=0}^n x\frac{n!}{x!(n-x)!}y^x(1-y)^{n-x}, -\end{equation*} -!et -resulting in -!bt -\begin{equation*} -\mu = -\sum_{x=0}^n x\frac{(n-1)!}{(x-1)!(n-1-(x-1))!}y^{x-1}(1-y)^{n-1-(x-1)}, -\end{equation*} -!et -which we rewrite as - -!bt -\begin{equation*} -\mu=ny\sum_{\nu=0}^n\left(\begin{array}{c} n-1 \\ \nu\end{array}\right)y^{\nu}(1-y)^{n-1-\nu} =ny(y+1-y)^{n-1}=ny. -\end{equation*} -!et -!eblock -The variance is slightly trickier to get. It reads $\sigma^2=ny(1-y)$. - - -===== Probability Distribution Functions, Poisson's distribution ===== -!bblock - -Another important distribution with discrete stochastic variables $x$ is -the Poisson model, which resembles the exponential distribution and reads -!bt -\begin{equation*} - p(x) = \frac{\lambda^x}{x!} e^{-\lambda} \hspace{0.5cm}x=0,1,\dots,;\lambda > 0. -\end{equation*} -!et -In this case both the mean value and the variance are easier to calculate, - -!bt -\begin{equation*} -\mu = \sum_{x=0}^{\infty} x \frac{\lambda^x}{x!} e^{-\lambda} = \lambda e^{-\lambda}\sum_{x=1}^{\infty} -\frac{\lambda^{x-1}}{(x-1)!}=\lambda, -\end{equation*} -!et -and the variance is $\sigma^2=\lambda$. -!eblock - - - - -===== Probability Distribution Functions, Poisson's distribution ===== -!bblock -An example of applications of the Poisson distribution could be the counting -of the number of $\alpha$-particles emitted from a radioactive source in a given time interval. -In the limit of $n\rightarrow \infty$ and for small probabilities $y$, the binomial distribution -approaches the Poisson distribution. Setting $\lambda = ny$, with $y$ the probability for an event in -the binomial distribution we can show that - -!bt -\begin{equation*} -\lim_{n\rightarrow \infty}\left(\begin{array}{c} n \\ x\end{array}\right)y^x(1-y)^{n-x} e^{-\lambda}=\sum_{x=1}^{\infty}\frac{\lambda^x}{x!} e^{-\lambda}. -\end{equation*} -!et -!eblock - - - -===== Meet the covariance! ===== -!bblock -An important quantity in a statistical analysis is the so-called covariance. - -Consider the set $\{X_i\}$ of $n$ -stochastic variables (not necessarily uncorrelated) with the -multivariate PDF $P(x_1,\dots,x_n)$. The *covariance* of two -of the stochastic variables, $X_i$ and $X_j$, is defined as follows - -!bt -\begin{align} -\mathrm{Cov}(X_i,\,X_j) & = \langle (x_i-\langle x_i\rangle)(x_j-\langle x_j\rangle)\rangle \\ -&=\int\cdots\int (x_i-\langle x_i\rangle)(x_j-\langle x_j\rangle)P(x_1,\dots,x_n)\,dx_1\dots dx_n, -label{eq:def_covariance} -\end{align} -!et -with -!bt -\begin{equation*} -\langle x_i\rangle = -\int\cdots\int x_i P(x_1,\dots,x_n)\,dx_1\dots dx_n. -\end{equation*} -!et -!eblock - - - - -===== Meet the covariance in matrix disguise ===== -!bblock -If we consider the above covariance as a matrix -!bt -\[ -C_{ij} =\mathrm{Cov}(X_i,\,X_j), -\] -!et -then the diagonal elements are just the familiar -variances, $C_{ii} = \mathrm{Cov}(X_i,\,X_i) = \mathrm{Var}(X_i)$. It turns out that -all the off-diagonal elements are zero if the stochastic variables are -uncorrelated. -!eblock - - -===== Covariance ===== -!bc pycod -# Importing various packages -from math import exp, sqrt -from random import random, seed -import numpy as np -import matplotlib.pyplot as plt - -def covariance(x, y, n): - sum = 0.0 - mean_x = np.mean(x) - mean_y = np.mean(y) - for i in range(0, n): - sum += (x[(i)]-mean_x)*(y[i]-mean_y) - return sum/n - -n = 10 - -x=np.random.normal(size=n) -y = 4+3*x+np.random.normal(size=n) -covxy = covariance(x,y,n) -print(covxy) -z = np.vstack((x, y)) -c = np.cov(z.T) - -print(c) - -!ec - - - - -===== Meet the covariance, uncorrelated events ===== -!bblock - -Consider the stochastic variables $X_i$ and $X_j$, ($i\neq j$). We have -!bt -\begin{align*} -Cov(X_i,\,X_j) &= \langle (x_i-\langle x_i\rangle)(x_j-\langle x_j\rangle)\rangle\\ -&=\langle x_i x_j - x_i\langle x_j\rangle - \langle x_i\rangle x_j + \langle x_i\rangle\langle x_j\rangle\rangle\\ -&=\langle x_i x_j\rangle - \langle x_i\langle x_j\rangle\rangle - \langle \langle x_i\rangle x_j \rangle + -\langle \langle x_i\rangle\langle x_j\rangle\rangle \\ -&=\langle x_i x_j\rangle - \langle x_i\rangle\langle x_j\rangle - \langle x_i\rangle\langle x_j\rangle + -\langle x_i\rangle\langle x_j\rangle \\ -&=\langle x_i x_j\rangle - \langle x_i\rangle\langle x_j\rangle -\end{align*} -!et -If $X_i$ and $X_j$ are independent (assuming $i \neq j$), we have that -!bt -\[ -\langle x_i x_j\rangle = \langle x_i\rangle\langle x_j\rangle, -\] -!et -leading to -!bt -\[ -Cov(X_i, X_j) = 0 \hspace{0.1cm} (i\neq j). -\] -!et -!eblock - - - - -===== Numerical experiments and the covariance ===== -!bblock - -Now that we have constructed an idealized mathematical framework, let -us try to apply it to empirical observations. Examples of relevant -physical phenomena may be spontaneous decays of nuclei, or a purely -mathematical set of numbers produced by some deterministic -mechanism. It is the latter we will deal with, using so-called pseudo-random -number generators. In general our observations will contain only a limited set of -observables. We remind the reader that -a *stochastic process* is a process that produces sequentially a -chain of values -!bt -\begin{equation*} -\{x_1, x_2,\dots\,x_k,\dots\}. -\end{equation*} -!et -!eblock - - - -===== Numerical experiments and the covariance ===== -!bblock -We will call these -values our *measurements* and the entire set as our measured -*sample*. The action of measuring all the elements of a sample -we will call a stochastic *experiment* (since, operationally, -they are often associated with results of empirical observation of -some physical or mathematical phenomena; precisely an experiment). We -assume that these values are distributed according to some -PDF $p_X^{\phantom X}(x)$, where $X$ is just the formal symbol for the -stochastic variable whose PDF is $p_X^{\phantom X}(x)$. Instead of -trying to determine the full distribution $p$ we are often only -interested in finding the few lowest moments, like the mean -$\mu_X^{\phantom X}$ and the variance $\sigma_X^{\phantom X}$. -!eblock - - - -===== Numerical experiments and the covariance, actual situations ===== -!bblock -In practical situations however, a sample is always of finite size. Let that -size be $n$. The expectation value of a sample $\alpha$, the _sample mean_, is then defined as follows -!bt -\begin{equation*} -\langle x_{\alpha} \rangle \equiv \frac{1}{n}\sum_{k=1}^n x_{\alpha,k}. -\end{equation*} -!et -The *sample variance* is: -!bt -\begin{equation*} -\mathrm{Var}(x) \equiv \frac{1}{n}\sum_{k=1}^n (x_{\alpha,k} - \langle x_{\alpha} \rangle)^2, -\end{equation*} -!et -with its square root being the *standard deviation of the sample*. -!eblock - - - -===== Numerical experiments and the covariance, our observables ===== -!bblock -You can think of the above observables as a set of quantities which define -a given experiment. This experiment is then repeated several times, say $m$ times. -The total average is then -!bt -\begin{equation} -\langle X_m \rangle= \frac{1}{m}\sum_{\alpha=1}^mx_{\alpha}=\frac{1}{mn}\sum_{\alpha, k} x_{\alpha,k}, -label{eq:exptmean} -\end{equation} -!et -where the last sums end at $m$ and $n$. -The total variance is -!bt -\begin{equation*} -\sigma^2_m= \frac{1}{mn^2}\sum_{\alpha=1}^m(\langle x_{\alpha} \rangle-\langle X_m \rangle)^2, -\end{equation*} -!et -which we rewrite as -!bt -\begin{equation} -\sigma^2_m=\frac{1}{m}\sum_{\alpha=1}^m\sum_{kl=1}^n (x_{\alpha,k}-\langle X_m \rangle)(x_{\alpha,l}-\langle X_m \rangle). -label{eq:exptvariance} -\end{equation} -!et -!eblock - - -===== Numerical experiments and the covariance, the sample variance ===== -!bblock - -We define also the sample variance $\sigma^2$ of all $mn$ individual experiments as -!bt -\begin{equation} -\sigma^2=\frac{1}{mn}\sum_{\alpha=1}^m\sum_{k=1}^n (x_{\alpha,k}-\langle X_m \rangle)^2. -label{eq:sampleexptvariance} -\end{equation} -!et - - - -These quantities, being known experimental values or the results from our calculations, -may differ, in some cases -significantly, from the similarly named -exact values for the mean value $\mu_X$, the variance $\mathrm{Var}(X)$ -and the covariance $\mathrm{Cov}(X,Y)$. -!eblock - - -===== Numerical experiments and the covariance, central limit theorem ===== -!bblock - -The central limit theorem states that the PDF $\tilde{p}(z)$ of -the average of $m$ random values corresponding to a PDF $p(x)$ -is a normal distribution whose mean is the -mean value of the PDF $p(x)$ and whose variance is the variance -of the PDF $p(x)$ divided by $m$, the number of values used to compute $z$. - -The central limit theorem leads then to the well-known expression for the -standard deviation, given by -!bt -\begin{equation*} - \sigma_m= -\frac{\sigma}{\sqrt{m}}. -\end{equation*} -!et - -In many cases the above estimate for the standard deviation, in particular if correlations are strong, may be too simplistic. We need therefore a more precise defintion of the error and the variance in our results. -!eblock - - -===== Definition of Correlation Functions and Standard Deviation ===== -!bblock -Our estimate of the true average $\mu_{X}$ is the sample mean $\langle X_m \rangle$ - -!bt -\begin{equation*} -\mu_{X}^{\phantom X} \approx X_m=\frac{1}{mn}\sum_{\alpha=1}^m\sum_{k=1}^n x_{\alpha,k}. -\end{equation*} -!et - - -We can then use Eq. (ref{eq:exptvariance}) -!bt -\begin{equation*} -\sigma^2_m=\frac{1}{mn^2}\sum_{\alpha=1}^m\sum_{kl=1}^n (x_{\alpha,k}-\langle X_m \rangle)(x_{\alpha,l}-\langle X_m \rangle), -\end{equation*} -!et -and rewrite it as -!bt -\begin{equation*} -\sigma^2_m=\frac{\sigma^2}{n}+\frac{2}{mn^2}\sum_{\alpha=1}^m\sum_{k -#include -#include -#include -using namespace std; -// output file as global variable -ofstream ofile; - -// Main function begins here -int main(int argc, char* argv[]) -{ - int n; - char *outfilename; - - cin >> n; - double MCint = 0.; double MCintsqr2=0.; - double invers_period = 1./RAND_MAX; // initialise the random number generator - srand(time(NULL)); // This produces the so-called seed in MC jargon - // Compute the variance and the mean value of the uniform distribution - // Compute also the specific values x for each cycle in order to be able to - // the covariance and the correlation function - // Read in output file, abort if there are too few command-line arguments - if( argc <= 2 ){ - cout << "Bad Usage: " << argv[0] << - " read also output file and number of cycles on same line" << endl; - exit(1); - } - else{ - outfilename=argv[1]; - } - ofile.open(outfilename); - // Get the number of Monte-Carlo samples - n = atoi(argv[2]); - double *X; - X = new double[n]; - for (int i = 0; i < n; i++){ - double x = double(rand())*invers_period; - X[i] = x; - MCint += x; - MCintsqr2 += x*x; - } - double Mean = MCint/((double) n ); - MCintsqr2 = MCintsqr2/((double) n ); - double STDev = sqrt(MCintsqr2-Mean*Mean); - double Variance = MCintsqr2-Mean*Mean; -// Write mean value and standard deviation - cout << " Standard deviation= " << STDev << " Integral = " << Mean << endl; - - // Now we compute the autocorrelation function - double *autocor; autocor = new double[n]; - for (int j = 0; j < n; j++){ - double sum = 0.0; - for (int k = 0; k < (n-j); k++){ - sum += (X[k]-Mean)*(X[k+j]-Mean); - } - autocor[j] = sum/Variance/((double) n ); - ofile << setiosflags(ios::showpoint | ios::uppercase); - ofile << setw(15) << setprecision(8) << j; - ofile << setw(15) << setprecision(8) << autocor[j] << endl; - } - ofile.close(); // close output file - return 0; -} // end of main program -!ec -!eblock - - - - -======= Which RNG should I use? ======= -!bblock -* C++ has a class called _random_. The "random class":"http://www.cplusplus.com/reference/random/" contains a large selection of RNGs and is highly recommended. Some of these RNGs have very large periods making it thereby very safe to use these RNGs in case one is performing large calculations. In particular, the "Mersenne twister random number engine":"http://www.cplusplus.com/reference/random/mersenne_twister_engine/" has a period of $2^{19937}$. -* Add RNGs in Python - -!eblock - - - -===== How to use the Mersenne generator ===== -!bblock -The following part of a c++ code (from project 4) sets up the uniform distribution for $x\in [0,1]$. -!bc cppcod -/* - -// You need this -#include - -// Initialize the seed and call the Mersienne algo -std::random_device rd; -std::mt19937_64 gen(rd()); -// Set up the uniform distribution for x \in [[0, 1] -std::uniform_real_distribution RandomNumberGenerator(0.0,1.0); - -// Now use the RNG -int ix = (int) (RandomNumberGenerator(gen)*NSpins); -!ec -!eblock - - - - - -===== Why blocking? ===== -!bblock Statistical analysis - * Monte Carlo simulations can be treated as *computer experiments* - * The results can be analysed with the same statistical tools as we would use analysing experimental data. - * As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors. - -A very good article which explains blocking is H. Flyvbjerg and H. G. Petersen, *Error estimates on averages of correlated data*, "Journal of Chemical Physics 91, 461-466 (1989)":"http://scitation.aip.org/content/aip/journal/jcp/91/1/10.1063/1.457480". - -!eblock - - - - -===== Why blocking? ===== -!bblock Statistical analysis - * As in other experiments, Monte Carlo experiments have two classes of errors: - * Statistical errors - * Systematical errors - * Statistical errors can be estimated using standard tools from statistics - * Systematical errors are method specific and must be treated differently from case to case. (In VMC a common source is the step length or time step in importance sampling) -!eblock - - - -===== Code to demonstrate the calculation of the autocorrelation function ===== -The following code computes the autocorrelation function, the covariance and the standard deviation -for standard RNG. -The "following file":"https://github.com/CompPhysics/ComputationalPhysics2/tree/gh-pages/doc/Programs/LecturePrograms/programs/Blocking/autocorrelation.cpp" gives the code. -!bc cppcod -// This function computes the autocorrelation function for -// the Mersenne random number generator with a uniform distribution -#include -#include -#include -#include -#include -#include -#include -#include -using namespace std; -using namespace arma; -// output file -ofstream ofile; - -// Main function begins here -int main(int argc, char* argv[]) -{ - int MonteCarloCycles; - string filename; - if (argc > 1) { - filename=argv[1]; - MonteCarloCycles = atoi(argv[2]); - string fileout = filename; - string argument = to_string(MonteCarloCycles); - fileout.append(argument); - ofile.open(fileout); - } - - // Compute the variance and the mean value of the uniform distribution - // Compute also the specific values x for each cycle in order to be able to - // compute the covariance and the correlation function - - vec X = zeros(MonteCarloCycles); - double MCint = 0.; double MCintsqr2=0.; - std::random_device rd; - std::mt19937_64 gen(rd()); - // Set up the uniform distribution for x \in [[0, 1] - std::uniform_real_distribution RandomNumberGenerator(0.0,1.0); - for (int i = 0; i < MonteCarloCycles; i++){ - double x = RandomNumberGenerator(gen); - X(i) = x; - MCint += x; - MCintsqr2 += x*x; - } - double Mean = MCint/((double) MonteCarloCycles ); - MCintsqr2 = MCintsqr2/((double) MonteCarloCycles ); - double STDev = sqrt(MCintsqr2-Mean*Mean); - double Variance = MCintsqr2-Mean*Mean; - // Write mean value and variance - cout << " Sample variance= " << Variance << " Mean value = " << Mean << endl; - // Now we compute the autocorrelation function - vec autocorrelation = zeros(MonteCarloCycles); - for (int j = 0; j < MonteCarloCycles; j++){ - double sum = 0.0; - for (int k = 0; k < (MonteCarloCycles-j); k++){ - sum += (X(k)-Mean)*(X(k+j)-Mean); - } - autocorrelation(j) = sum/Variance/((double) MonteCarloCycles ); - ofile << setiosflags(ios::showpoint | ios::uppercase); - ofile << setw(15) << setprecision(8) << j; - ofile << setw(15) << setprecision(8) << autocorrelation(j) << endl; - } - // Now compute the exact covariance using the autocorrelation function - double Covariance = 0.0; - for (int j = 0; j < MonteCarloCycles; j++){ - Covariance += autocorrelation(j); - } - Covariance *= 2.0/((double) MonteCarloCycles); - // Compute now the total variance, including the covariance, and obtain the standard deviation - double TotalVariance = (Variance/((double) MonteCarloCycles ))+Covariance; - cout << "Covariance =" << Covariance << "Totalvariance= " << TotalVariance << "Sample Variance/n= " << (Variance/((double) MonteCarloCycles )) << endl; - cout << " STD from sample variance= " << sqrt(Variance/((double) MonteCarloCycles )) << " STD with covariance = " << sqrt(TotalVariance) << endl; - - ofile.close(); // close output file - return 0; -} // end of main program - - -!ec - - - -===== What is blocking? ===== -!bblock Blocking - * Say that we have a set of samples from a Monte Carlo experiment - * Assuming (wrongly) that our samples are uncorrelated our best estimate of the standard deviation of the mean $\langle \mathbf{M}\rangle$ is given by -!bt -\[ -\sigma=\sqrt{\frac{1}{n}\left(\langle \mathbf{M}^2\rangle-\langle \mathbf{M}\rangle^2\right)} -\] -!et - * If the samples are correlated we can rewrite our results to show that -!bt -\[ -\sigma=\sqrt{\frac{1+2\tau/\Delta t}{n}\left(\langle \mathbf{M}^2\rangle-\langle \mathbf{M}\rangle^2\right)} -\] -!et - where $\tau$ is the correlation time (the time between a sample and the next uncorrelated sample) and $\Delta t$ is time between each sample -!eblock - - -===== What is blocking? ===== -!bblock Blocking - * If $\Delta t\gg\tau$ our first estimate of $\sigma$ still holds - * Much more common that $\Delta t<\tau$ - * In the method of data blocking we divide the sequence of samples into blocks - * We then take the mean $\langle \mathbf{M}_i\rangle$ of block $i=1\ldots n_{blocks}$ to calculate the total mean and variance - * The size of each block must be so large that sample $j$ of block $i$ is not correlated with sample $j$ of block $i+1$ - * The correlation time $\tau$ would be a good choice -!eblock - - -===== What is blocking? ===== -!bblock Blocking - * Problem: We don't know $\tau$ or it is too expensive to compute - * Solution: Make a plot of std. dev. as a function of blocksize - * The estimate of std. dev. of correlated data is too low $\to$ the error will increase with increasing block size until the blocks are uncorrelated, where we reach a plateau - * When the std. dev. stops increasing the blocks are uncorrelated -!eblock - - -===== Implementation ===== -!bblock - * Do a Monte Carlo simulation, storing all samples to file - * Do the statistical analysis on this file, independently of your Monte Carlo program - * Read the file into an array - * Loop over various block sizes - * For each block size $n_b$, loop over the array in steps of $n_b$ taking the mean of elements $i n_b,\ldots,(i+1) n_b$ - * Take the mean and variance of the resulting array - * Write the results for each block size to file for later - analysis -!eblock - - - - - - -===== Actual implementation with code, main function ===== -When the file gets large, it can be useful to write your data in binary mode instead of ascii characters. -The "following python file":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py" reads data from file with the output from every Monte Carlo cycle. -!bc pycod -# Blocking - @timeFunction - def blocking(self, blockSizeMax = 500): - blockSizeMin = 1 - - self.blockSizes = [] - self.meanVec = [] - self.varVec = [] - - for i in range(blockSizeMin, blockSizeMax): - if(len(self.data) % i != 0): - pass#continue - blockSize = i - meanTempVec = [] - varTempVec = [] - startPoint = 0 - endPoint = blockSize - - while endPoint <= len(self.data): - meanTempVec.append(np.average(self.data[startPoint:endPoint])) - startPoint = endPoint - endPoint += blockSize - mean, var = np.average(meanTempVec), np.var(meanTempVec)/len(meanTempVec) - self.meanVec.append(mean) - self.varVec.append(var) - self.blockSizes.append(blockSize) - - self.blockingAvg = np.average(self.meanVec[-200:]) - self.blockingVar = (np.average(self.varVec[-200:])) - self.blockingStd = np.sqrt(self.blockingVar) - -!ec - - - - - -===== The Bootstrap method ===== - -The Bootstrap resampling method is also very popular. It is very simple: - -o Start with your sample of measurements and compute the sample variance and the mean values -o Then start again but pick in a random way the numbers in the sample and recalculate the mean and the sample variance. -o Repeat this $K$ times. - -It can be shown, see the article by "Efron":"https://projecteuclid.org/download/pdf_1/euclid.aos/1176344552" -that it produces the correct standard deviation. - -This method is very useful for small ensembles of data points. - - -===== Bootstrapping ===== -Given a set of $N$ data, assume that we are interested in some -observable $\theta$ which may be estimated from that set. This observable can also be for example the result of a fit based on all $N$ raw data. -Let us call the value of the observable obtained from the original -data set $\hat{\theta}$. One recreates from the sample repeatedly -other samples by choosing randomly $N$ data out of the original set. -This costs essentially nothing, since we just recycle the original data set for the building of new sets. - - -===== Bootstrapping, recipe ===== -Let us assume we have done this $K$ times and thus have $K$ sets of $N$ -data values each. -Of course some values will enter more than once in the new sets. For each of these sets one computes the observable $\theta$ resulting in values $\theta_k$ with $k = 1,...,K$. Then one determines -!bt -\[ -\tilde{\theta} = \frac{1}{K} \sum_{k=1}^K \theta_k, -\] -!et -and -!bt -\[ -sigma^2_{\tilde{\theta}} = \frac{1}{K} \sum_{k=1}^K \left(\theta_k-\tilde{\theta}\right)^2. -\] -!et - -These are estimators for $\angle\theta\rangle$ and its variance. They are not unbiased and therefore -$\tilde{\theta}\neq\hat{\theta}$ for finite K. - -The difference is called bias and gives an idea on how far away the result may be from -the true $\angle\theta\rangle$. As final result for the observable one quotes $\angle\theta\rangle = \tilde{\theta} \pm \sigma_{\tilde{\theta}}$ . - - - -===== Bootstrapping, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py" ===== -!bc -# Bootstrap - @timeFunction - def bootstrap(self, nBoots = 1000): - bootVec = np.zeros(nBoots) - for k in range(0,nBoots): - bootVec[k] = np.average(np.random.choice(self.data, len(self.data))) - self.bootAvg = np.average(bootVec) - self.bootVar = np.var(bootVec) - self.bootStd = np.std(bootVec) -!ec - - -===== Jackknife, "code":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Programs/Sampling/analysis.py" ===== -!bc -# Jackknife - @timeFunction - def jackknife(self): - jackknVec = np.zeros(len(self.data)) - for k in range(0,len(self.data)): - jackknVec[k] = np.average(np.delete(self.data, k)) - self.jackknAvg = self.avg - (len(self.data) - 1) * (np.average(jackknVec) - self.avg) - self.jackknVar = 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'bash make.sh slides1|slides2' -exit 1 -fi - -name=$1 -rm -f *.tar.gz - -opt="--encoding=utf-8" -# Note: Makefile examples contain constructions like ${PROG} which -# looks like Mako constructions, but they are not. Use --no_mako -# to turn off Mako processing. -opt="--no_mako" - -rm -f *.aux - -# IPython notebook -system doconce format ipynb $name $opt - - -# Ordinary plain LaTeX document -rm -f *.aux # important after beamer -system doconce format pdflatex $name --minted_latex_style=trac --latex_admon=paragraph $opt -system doconce ptex2tex $name envir=minted -# Add special packages -doconce subst "% Add user's preamble" "\g<1>\n\\usepackage{simplewick}" $name.tex -doconce replace 'section{' 'section*{' $name.tex -pdflatex -shell-escape $name -pdflatex -shell-escape $name -mv -f $name.pdf ${name}-minted.pdf -cp $name.tex ${name}-plain-minted.tex diff --git a/doc/LectureNotes/src/Hudson_Bay.csv b/doc/LectureNotes/src/Hudson_Bay.csv deleted file mode 100644 index fd9d4767f..000000000 --- a/doc/LectureNotes/src/Hudson_Bay.csv +++ /dev/null @@ -1,22 +0,0 @@ -Year,Hares (x1000),Lynx (x1000) -1900,30.0,4.0 -1901,47.2,6.1 -1902,70.2,9.8 -1903,77.4,35.2 -1904,36.3,59.4 -1905,20.6,41.7 -1906,18.1,19.0 -1907,21.4,13.0 -1908,22.0,8.3 -1909,25.4,9.1 -1910,27.1,7.4 -1911,40.3,8.0 -1912,57,12.3 -1913,76.6,19.5 -1914,52.3,45.7 -1915,19.5,51.1 -1916,11.2,29.7 -1917,7.6,15.8 -1918,14.6,9.7 -1919,16.2,10.1 -1920,24.7,8.6 diff --git a/doc/LectureNotes/src/Hudson_Bay.py b/doc/LectureNotes/src/Hudson_Bay.py deleted file mode 100644 index bff849971..000000000 --- a/doc/LectureNotes/src/Hudson_Bay.py +++ /dev/null @@ -1,43 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -def solver(m, H0, L0, dt, a, b, c, d, t0): - """Solve the difference equations for H and L over m years - with time step dt (measured in years.""" - - num_intervals = int(m/float(dt)) - t = np.linspace(t0, t0 + m, num_intervals+1) - H = np.zeros(t.size) - L = np.zeros(t.size) - - print('Init:', H0, L0, dt) - H[0] = H0 - L[0] = L0 - - for n in range(0, len(t)-1): - H[n+1] = H[n] + a*dt*H[n] - b*dt*H[n]*L[n] - L[n+1] = L[n] + d*dt*H[n]*L[n] - c*dt*L[n] - return H, L, t - -# Load in data file -data = np.loadtxt('src/Hudson_Bay.csv', delimiter=',', skiprows=1) -# Make arrays containing x-axis and hares and lynx populations -t_e = data[:,0] -H_e = data[:,1] -L_e = data[:,2] - -# Simulate using the model -H, L, t = solver(m=20, H0=34.91, L0=3.857, dt=0.1, - a=0.4807, b=0.02482, c=0.9272, d=0.02756, - t0=1900) - -# Visualize simulations and data -plt.plot(t_e, H_e, 'b-+', t_e, L_e, 'r-o', t, H, 'm--', t, L, 'k--') -plt.xlabel('Year') -plt.ylabel('Numbers of hares and lynx') -plt.axis([1900, 1920, 0, 140]) -plt.title(r'Population of hares and lynx 1900-1920 (x1000)') -plt.legend(('H_e', 'L_e', 'H', 'L'), loc='upper left') -plt.savefig('Hudson_Bay_sim.pdf') -plt.savefig('Hudson_Bay_sim.png') -plt.show() diff --git a/doc/LectureNotes/src/Hudson_Bay.py~ b/doc/LectureNotes/src/Hudson_Bay.py~ deleted file mode 100644 index acd44518e..000000000 --- a/doc/LectureNotes/src/Hudson_Bay.py~ +++ /dev/null @@ -1,43 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -def solver(m, H0, L0, dt, a, b, c, d, t0): - """Solve the difference equations for H and L over m years - with time step dt (measured in years.""" - - num_intervals = int(m/float(dt)) - t = np.linspace(t0, t0 + m, num_intervals+1) - H = np.zeros(t.size) - L = np.zeros(t.size) - - print 'Init:', H0, L0, dt - H[0] = H0 - L[0] = L0 - - for n in range(0, len(t)-1): - H[n+1] = H[n] + a*dt*H[n] - b*dt*H[n]*L[n] - L[n+1] = L[n] + d*dt*H[n]*L[n] - c*dt*L[n] - return H, L, t - -# Load in data file -data = np.loadtxt('Hudson_Bay.csv', delimiter=',', skiprows=1) -# Make arrays containing x-axis and hares and lynx populations -t_e = data[:,0] -H_e = data[:,1] -L_e = data[:,2] - -# Simulate using the model -H, L, t = solver(m=20, H0=34.91, L0=3.857, dt=0.1, - a=0.4807, b=0.02482, c=0.9272, d=0.02756, - t0=1900) - -# Visualize simulations and data -plt.plot(t_e, H_e, 'b-+', t_e, L_e, 'r-o', t, H, 'm--', t, L, 'k--') -plt.xlabel('Year') -plt.ylabel('Numbers of hares and lynx') -plt.axis([1900, 1920, 0, 140]) 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\n", + "image/png": 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\n", 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\n", 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\n", 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AWIwgBwDAYgQ5AAAWI8gBALAYQQ4AgMUIcgAALEaQAwBgMYIcAACLEeQAAFiMIAcAwGIEOQAAFiPIAQCwmN+C/Pz587r11lu1YMECfxUJAECz57cgX7x4seLi4vxVHAAAAcEvQb527VpdffXViomJ8UdxAAAEDMeD/Ouvv9a3336rm266yemiAAAIOC5jjHGygOeff15ut1stW7bUli1bdOHCBd14442aNGmSk8UCABAQQpwuYNq0aZ4/FxQUKC8vz6sQT08/52CtEBXVmjZ2GG3sPNrYP2hn50VFta73uX6b7LZhwwbt2LFDX3zxhd5//31/FQsAQLPmeI+81LBhwzRs2DB/FQcAQEBgQRgAACxGkAMAYDGCHAAAixHkAABYjCAHAMBiBDkAABYjyAEAsBhBDgCAxQhyAAAsRpADAGAxghwAAIsR5AAAWIwgBwDAYgQ5AAAWI8gBALAYQQ4AgMUIcgAALEaQAwBgMYIcAACLEeQAAFiMIAcAwGIEOQAAFiPIAQCwGEEOAIDFCHIAACxGkAMAYDGCHAAAixHkAABYjCAHAMBiBDkAABYjyAEAsBhBDgCAxQhyAAAsRpADAGAxghwAAIsR5AAAWIwgBwDAYgQ5AAAWI8gBALAYQQ4AgMUIcgAALEaQAwBgMYIcAACLEeQAAFiMIAcAwGIEOQAAFiPIAQCwGEEOAIDFCHIAACxGkAMAYDGCHAAAixHkAABYLMTpAoqLi3X33Xerd+/eunDhgo4dO6b58+erVatWThcNAECz55ceed++fTV9+nQ98MADys/P18aNG/1RLAAAzZ7jQR4UFKR77rlHklRUVKRTp07psssuc7pYAAACgssYY/xR0CeffKKXX35Zffr00X333eePIgEAaPb8FuSl/vCHP6hPnz4aP358jcelp5/zU40CU1RUa9rYYbSx82hj/6CdnRcV1bre5zo+tP71118rJSXF8zomJkbHjx93ulgAAAKC47PWW7ZsqdWrV2v//v0qKirSN998oz/+8Y9OFwsAQEBwPMi7deumpUuXOl0MAAABiQVhAACwGEEOAIDFCHIAACxGkAMAYDGCHAAAixHkAABYjCAHAMBiBDkAABYjyAEAsBhBDgCAxQhyAAAsRpADAGAxghwAAIsR5AAAWIwgBwDAYgQ5AAAWI8gBALAYQQ4AgMUIcgAALEaQAwBgMYIcAACLEeQAAFiMIAcAwGK1BvnGjRv9UQ8AAFAPtQb522+/rcTERKWmpvqjPgAAoA5qDfIVK1Zo5MiRmjRpkpYvX66ioiJ/1AsAAHjBq3vkI0aM0DvvvKO0tDSNHj1aO3fudLpeAADAC14F+eHDh7V+/Xrl5OTo1KlTmjp1qubMmaP8/Hyn6wcAAGpQa5D3799fv//977Vnzx797Gc/0+rVq7Vz505dfvnluu+++/xRRwAAUI2Q2g7YuHGjIiMjK70/efJkvf32245UCgAAeKfWHnlVIV5q6dKlPq0MAAComwYtCHP55Zf7qh4AAKAeWNkNAACLEeQAAFiMIAcAwGIEOQAAFiPIAQCwGEEOAIDFCHIAACxGkAMAYDGCHAAAixHkAABYjCAHAMBiBDkAABYjyAEAsBhBDgCAxQhyAAAsRpADAGAxghwAAIsR5AAAWIwgBwDAYgQ5AAAWC3G6gKNHj2rx4sWKi4vTyZMn1a5dO02fPt3pYgEAaNJCk1crbPFfFHz4oBQXJ335Zb2u43iQnzlzRiNGjNDQoUMlSSNGjNDgwYMVHx/vdNEAADQpocmrFTHrIblOZ8lV9oM9e+p9TceDvHfv3uVeFxcX66KLLnK6WAAAmpTQ5NVqk3iHz6/rMsYYn1+1Gh9++KG2bdumP/7xj/4qEgAA/3rzTWn+fGn/fqlLl5L3UlNL/ut2V39ePePYb0H+6aef6qOPPtIjjzyioKDa59ilp5/zQ60CV1RUa9rYYbSx82hj/6Cda1b2XndxdGcFpx6v34XqGceOD61LUkpKinbu3KnZs2crLS1Nqamp6tevnz+KBgDAp8oF98WdFXzix+Cud4g3gONBvnfvXj3wwAOKj4/X7bffrry8PI0fP54gBwBYJTR5tcIfSyof3Cd8FNwdOtT7VMeDPD4+Xp9//rnTxQAA4FPhj8zQRatelgoKpJAWchVdcKScgiE3KPSfH9X7fBaEAQCggvBHZihs5TK5Cgrkknwa4u6YGJmQEBXFxSt72YvKfiu5Qdfzyz1yAACakrL3ud2xPZR3/4MqGHWbJCmqU5sGX98dE6OgkydVfPHFkpGCTp0sKef3/+0px1cIcgBAQKn4PHfIgX0lrxvwjLe7a4yjYV0TghwAEFDC5j/us2u5u8YoN+kxvwZ3RdwjBwA0C6HJq9V+0EB17Nxe7QcNVGjy6pIP3G5FdWrj+Qn593fVXuPck39Welq28qYkVvl5cfvIcve3sz7f36ghLvl5Zbe6YPEBZ7HAg/NoY+fRxv5hQzv7YvnTorh4nU7Z4nldMmv9FangvBTaSvkTJip3/tMNrWqVoqJa1/tceuQAAOtFPPh7r4/NXvZile/n/f6/y73Onf+0Mo6lKSMtWxnH0hwL8YbiHjkAwDrB+/cpcvBAr47N3LVXxZd0K/detqSwZxf9OGvdzxPUfIkgBwA0fcYoKrptnU8riouvFOKSVDDqNmuDuyKG1gEAjaq6SWplJ6jVFuLeDpc3R/TIAQCNpr7PdKefOiu5XOXea07D5XVBkAMAGkXQ8WNezzQ//b//VNHV/Ws8pjkNl9cFQQ4A8Btvlz81LpcyTp11uDbNA0EOAHBMfdctd/fs5eOaNF9MdgMA1OzNN6teMa0KFy15ptwktZqkH88I6ElqvkKPHABQrdDk1VLiHZ6wKJ2Mlq2Se9Kus2fU8crKj3dVJXvFyyoYObrcewWjbgvYSWq+whKtAcqGJRdtRxs7jzZ2XvtBAxVyYF+9z09Py/ZhbZqvhizRSo8cAFCt4MMH63Q8we1/3CMHgABT7S5hpZ+/8ZrnHrfL7a7xWhlfH1N6WrbnB/7H0HqAYkjSebSx82jjuvPFLmFSyUpq3Mf2HXY/AwBUq2wPvPV90+p+gTfeUFFcfLl9uAnxpoN75ADQjFXqgdcyVC5Vvs8dFdVap2+42ddVg48Q5ADQDIQmr1bY4r94HuEqHDREYS8srdM1TEiIMlKzHKohnEKQA4Dlqtp4pD6PjLlje/iyWvAT7pEDQBNV2+zy0pnlvpi8JrGamq0IcgBogkp72SEH9snldntWVPN2+VOpZKi82iVQpyQyga2ZYGgdABpZ+CMzdNGql6WCAik0VPkTJqnl5v9r8HXdsT1qXAI1t8EloCkgyAGgEYU/MkNhK5f9+EZBQfnX1TAtWijjRKak6p8NLx0qD9R9ugMFQ+sA0Ii8Ce2KTEiIJ8SlHzYeWfYiQ+UBih45ADio4mNhys9VyJEjDbpmVbPL6XUHLnrkAOCQqiaseRviJrSV8qYkVvkZs8tRFkEOAD5Wl8fCqgvr/AkTlTv/aYbMUSuG1gHACxWHyPPuf9ATqN48ClZRUVy8Tqds8by+aNUrUsF5KbSVJ8QlhsxRO3Y/C1DsGuU82th5/mjj0OTVCp+XpODU4z69rk3LofJddh67nwGAA8IfmaE2iXfUKcTPjx3v2Zu7usVYJJZDhe8wtA4goFU3ZF6X4fKKu4WVKhh1m/J2bKvyETMmrMFX6JEDCDieNcyj21a7DKo3iuLiqw3xUkxYg9PokQNo9sr2uosv7qzgE7653+1tr5oJa3ASPXIAzVrFZ7m9CXEjqahnr2o/d8fE0KtGk0GQA2gWqtrys75bfLrj4pV3/4NVfpY3JVFZn+0nxNFkMLQOwBqeIfJDB6QWLaTCQrXvEafCa64tN6Gs9F53fZXuDlbdrmFAU8Jz5AGK50KdRxv7VnU7fPmKCQqWu0dPwroKfJed15DnyOmRA2iSKu7RbcLC63wNExKic88tr/IfAO6uMQo6dZKeNqxHkANoMjxD5wf3y1V2sLCgQK6Cgjpfzx3bgyFyNHsEOYAmwYmh89LHw3j8C80Zs9YBNKqQHdvqPbu8rLwpiSy6goBEjxyAY3yx/GlZJqSF3LHdFXywZNa660KhinrEeYbKc31cf8AGzFoPUMxCdV4gtnG5FdSiO/t8x7C8KYme7T2lwGzjxkA7O4/dzwD4RVWLrpT9rNwKal6GePp339e4U5iRZEJbVQpxACUYWgfglYqT0UoXXSme9ZByH5ql1rP/4NV1jMuljFNnK73P7HKgfghyAJVUdW87bPFfqjw26HSW1yEuSe4a1jBndjlQdwQ5gPKLr4S0kKvoguezhi53WhH7cAO+5fg98vT0dM2ePVu/+tWvnC4KQD2EPzJDYSuXyVVQIJdULsTrwgRV/b8Td0wMj4QBDnK8R75r1y7dcMMNOnDggNNFAahF2ZXTJEk+fGjF/cNjYNzjBvzL8SAfPny4tm3b5nQxAGrR0JXTiuLiVfjza8rtMlZWaWgT3IB/Ndl75A15pg7eoY2d16TaeOkzDTo9ZM5shYwdK90wWJo5Uzp6tOSDbt2kBQvUZuzYhtexHppUGzdjtHPT1WSDnMUHnMUCD85zuo1Dk1crfF6Sgn54Xru4a4xykx4r1yMO/9M8hT1b9Wzz2hS3j5TrXPaPQ+Q33Cyln5NuuFnaeXPlExrh+8T32D9oZ+exjSnQTIUmr1b4Y0kKOvFDWHeJUe7cxySp0jB58InjJe/Vc/jcc7c8tJXyJ0xk8RXAEo4H+fbt2/Xuu+8qPT1df/vb33THHXeoVatWThcLWK+qe9rBqSVh7e4S4/Py8lk5DbCS40GekJCghIQEp4sBmp3qFmCR5P3yp2nZ5V6HJq8umVV+YF/JG8bQAwcsx9A60EQFHz5Y73NNSIgyUrMqvc+scqD5IciBJqi+23yWcsf28FFNADR1BDnQBDQ0uCtiGVQgcBDkgANCk1dLS59Rx/375Y7tocJrrlXLzf/nWfEspPQetRfcXWM8s9ZdVX0eEyPTph2rqQEBiiAHfKTsxiOlgetSyaYjZYO7thDPH/db5Tz7t0rvV7cyW+6cxwhuIIAR5IAPlG48Ul8VZ5dXhf26AVSFIAfqqeye3SourvP51c0srwmzzgFURJAD9dDQDUgkZpYD8A2CHKigbE/bHdtDefc/KEkK+/MChXx1yGflMLMcgC8Q5Ah45fboDgqSy+32fBZyYF+Det7GFSR3zzgV/vwatdyymXvbAHyOIEdAqzREXibE68O4XJ5lT11T71LGnD95Pstt0JUBoGoEOQJGVdt+urIyfVrGuRf+7ulpR0W1bpStPQEEFoIczZpn2PzQAbkqzCwPPuHdxiPVYSEWAE0BQY5moboJag2dWV4TFmIB0BQQ5LBO+CMzdNHLL0pFFyRJJjxcQbk/3oFu6AS1ivKmJKropwNYiAVAk0SQwypVraDmym3YNDLPEPnB/VJwsHSh5B8IxV1jlJv0Y6+b4AbQFBHksMpFq172+TUZIgdgs6DGrgAQmrxa7QcNVMfO7dV+0MCSncMqvB/VqY2iOrWRq6DA6+u6Y2KqfN/88OOOiVH2shcJcQBWo0eORlXxOW7P/W0f3OPOnfOYJDYZAdC8EeTwq4rPcvuSadFCMqZSYBPcAJozghx+44uNRkxIiAqvG6TQTf+o9Nm5pcsIbQABh3vk8Knq7ndLdXum24SGVvm+O7aHst9KVvayF1UUFy8TEqKiuHjudQMIWC5jjGnsSlQlnaUtHRUV1dpnbVx20xGXj75OeVMSKz1mJsmqwPZlG6NqtLF/0M7Oi4pqXe9zGVpHvYUmr1b4Y0kNXuq0lJHkjov33N9mERYAqB1Bjnqpz/3u7GUv1njOuQq97YJRtxHcAFALghx1EtWpTZ3PKYqL1+mULZKkbEnhjyUpqEwvvuIKagAA7xHkqFH4o39U2N+WNOgaeb//b8+f6WUDgG8R5AGmdGKaDh1QxxYtpIICKaSFZwOS4i5dFJya2uByTFCw3D16cl8bABxGkAeQive1Pcud/hDikmoN8fS07CqvVcrNMDkA+BVB3oxV3KPbdfZsna9RGtwVFYy6Tdli+VMAaGwEeTNT3TPdIQf21ek6JiREGalZNXYhiP4AAAkBSURBVB7D/W4AaHys7GaJmlZMK3tMm8Q7FHJgX4MXZnHH9mjQ+QAA/6BHboHqdggzd98p0669XOfOyVXmPrcvlJ1pDgBouuiRWyBs8V+qfN9ljIJOZ9UpxN0xMSqKi5eCg2VCW8m4XDIhLX7co7sre3QDgE3okVsg+PBBn10rd07JjPKoqNbKYO1kALAeQd6E1WcVtarwTDcANF8EeRPis+B2uaTgYB4JA4AAwD3yRtTq78sV1amN56cm2c+vLNl/Oyi41uvm3zlVGalZOp2yhRAHgGaOHrmPVVyEJe/+Bz1h6jqdpY7d/59X1zn9/ocqShhQ7r2CX/36xzJ+WIjFtGkjV/a5ktXZQlspf8JE5c5/2qe/EwCg6XIZ08AHjh1i4yb29dnas1ThNdfpbPJ6H9eoelFRra1sY5vQxs6jjf2DdnZeVFTrep/L0Hod1bQwS/i8pDpdKz0t2/PjzxAHADQfDK17KTR5tSJmPaSg0z8uW1q6MIu87IWnH02TWrVyqooAgABEkHuhIUPmUslCKxnVbD4CAEBDMLTuhYhZD3p1nGl1UZXvF8fE+LI6AAB4EORVaPHPD8s9FhZ0+nSNxxfFxSs9LVvnnn2uys9z5zzmRDUBAGBoXZJc6enq2OuKep9fusEIe3QDAPwtMIPcGHXo9RMFZaTXemjW/+1QyL491d4jz5uSWC6o2aMbAOBPzW5ovbrHw8KeeuLH4fLottWG+LmnF5d7LMwd272kp73sRbm7xvy4S1hMyS5hLL4CAGhM1i4IU9UKapLqPLu88Gc/19n3/rfe9bQVCzw4jzZ2Hm3sH7Sz8xqyIIyVQ+vhj8xQ2Mplntee57m9lP5tqhQR4UTVAADwK+uCPDR5dbkQ94YJDlbG9zXPPAcAwEZW3SMP/vZrRcy4v87nubv3dKA2AAA0Pr/0yLds2aKNGzeqQ4cOcrlcmj59ei21ClH72B7KS5ym4CNHFL74z16V4+4ao+ATxyu9X/p4GAAAzY3jQZ6fn6+5c+dq/fr1atmype69915t3bpVAwcOrP4kt7vkvvf9lQPfuFxyVTM/LzepZOEVnuMGAAQKx4P8iy++UJcuXdSyZUtJ0tVXX62UlJSag7yCvLvuVt79M2Sioqpd97zs89wENwAgUDge5JmZmQoPD/e8joiIUGZmpvcXCAlR2PLnFVb6eupkqc1F0pNPSvv3S3Fx0sMPK2zs2B+PgVca8rgDvEMbO4829g/auelyPMg7dOig3Nxcz+ucnBx16NCh5pNqe7R97NiSHwAAApzjs9b79u2r1NRUFRYWSpI+++wzDR482OliAQAICH5Z2W3z5s3asGGD2rdvrxYtWtQ+ax0AAHilyS7RCgAAamfVgjAAAKA8ghwAAIs12lrrta32VlBQoAULFig6OlpHjhzR1KlTddlllzVSbe1VWzsvX75cGRkZ6tixo/bt26f77rtPV1xxRSPV1k7erlz43nvvacaMGfrss8/KPZKJ2tXWxsYYrVq1SpJ04sQJZWdn68knn2yMqlqrtjY+duyYFi5cqKuuukoHDhzQLbfcohtuuKGRamun9PR0LV68WAcPHtSaNWsqfV7v3DONIC8vzwwdOtQUFBQYY4yZPn262bJlS7ljli1bZpYvX26MMebgwYNm3Lhxfq+n7bxp52eeecYUFxcbY4xZv369SUxM9Hs9beZNGxtjzNdff20WLVpkYmNjTU5Ojr+raTVv2jg5OdkkJyd7Xh84cMCvdbSdN22clJRkXnrpJWOMMfv27TM33nijv6tpvQ8++MD84x//MKNGjary8/rmXqMMrVe32ltZKSkp6tevnySpe/fuOnjwoHJycvxdVat5087333+/XC6XJKm4uFhhYSyrUxfetHF+fr5Wrlyp3/3ud41QQ/t508br1q3TmTNn9Oqrr2rRokWMeNSRN23csWNHZWVlSZKysrLUq1cvf1fTesOHD6/xu1nf3GuUIPdmtbcGrwiHOrVhYWGhkpOTdf/9dd9dLpB508bPPPOM7rnnHs//JFE33rRxamqqcnJydPvtt2vUqFGaMmWK3G63v6tqLW/aePLkydq9e7eefPJJPffccxo9erS/q9ns1Tf3GuUeuTervdVrRTiU420bFhYW6tFHH9UDDzygbt26+bOK1qutjb///ntlZ2frgw8+8Lz30ksvadCgQbrqqqv8WldbefM9joiIUJ8+fSRJl112mXJycvT9998rJibGr3W1lTdtPGvWLI0ZM0a33HKLsrKydNNNN+mjjz5Su3bt/F3dZqu+udcoPfLqVns7c+aMZxhh8ODB+vzzzyVJhw4dUo8ePRQREdEY1bWWN+18/vx5zZ07V5MnT1Z8fLw2bNjQmFW2Tm1t3LlzZz311FOaOnWqpk6dKqmkZ0OIe8+b7/HAgQN17NgxSSX/83O73YqKimq0OtvGmzb+/vvvPW3apk0bBQUFqbi4uNHq3Fz4IvcabUGYqlZ7W7hwodq1a6epU6fq/PnzWrBggaKionT06FElJiYya70eamvn6dOn66uvvlKnTp0kSXl5eVXOpkT1amtjqeSe4ptvvqlnn31W99xzj8aOHavo6OhGrrk9amvjc+fO6emnn1aXLl109OhRDRs2TIMGDWrsalultjbeuXOnXn31VcXFxen48ePq1auXxo0b19jVtsr27du1du1affLJJxo3bpzuuOMOLVmypMG5x8puAABYjAVhAACwGEEOAIDFCHIAACxGkAMAYDGCHAAAixHkAABYjCAHAMBiBDkQ4B5++GEtXbpUknTkyBENGzZM+/bta+RaAfAWC8IAAe7UqVMaPXq0VqxYoYceekiPPfaY+vfv39jVAuClRtk0BUDTER0drV/+8pcaP368lixZQogDlmFoHQhwmZmZ+te//qWLLrpInTt3buzqAKgjhtaBAJadna1JkyYpMTFRWVlZ+vjjj/XCCy80drUA1AE9ciBA5efnKzExUePGjdOwYcM0ZswYHTlyRJ9++mljVw1AHdAjBwDAYvTIAQCwGEEOAIDFCHIAACxGkAMAYDGCHAAAixHkAABYjCAHAMBiBDkAABb7/0nB8xwG062MAAAAAElFTkSuQmCC\n", + "image/png": 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\n", 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\n", 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\n", 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\n", + "image/png": 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\n", 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\n", 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\n", + "image/png": 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\n", 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\n", + "image/png": 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Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n", - "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/_multilayer_perceptron.py:585: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", - " % self.max_iter, ConvergenceWarning)\n" + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n", + "/Users/hjensen/opt/anaconda3/lib/python3.8/site-packages/sklearn/neural_network/_multilayer_perceptron.py:582: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n", + " warnings.warn(\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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"stream", "text": [ - "0.037875961483052376\n" + "0.03787596148305239\n" ] } ], @@ -1595,23 +1595,23 @@ "Mean squared error: 12.36\n", "Variance score: 1.00\n", "Mean absolute error: 2.83\n", - "[ 0. 618.32047562 -861.13519106 1404.91549644] -11.057088709963296\n", + "[ 0. 618.32047562 -861.13519106 1404.91549644] -11.057088709963637\n", "Mean squared error: 197.93\n", "Variance score: 1.00\n", "Mean absolute error: 11.69\n", - "[ 0. 28.18220995 282.79902342 842.30879705] 12.946893955209475\n" + "[ 0. 28.18220995 282.79902342 842.30879705] 12.946893955206974\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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\n", 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\n", + "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/src/LectureNotes/_build/jupyter_execute/regression_133_0.png" + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_133_0.png" } }, "output_type": "display_data" @@ -2170,8 +2170,8 @@ "\n", "The model performance for testing set\n", "--------------------------------------\n", - "RMSE is 5.137400784702911\n", - "R2 score is 0.6628996975186953\n" + "RMSE is 5.137400784702912\n", + "R2 score is 0.6628996975186952\n" ] } ], @@ -2216,14 +2216,14 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/src/LectureNotes/_build/jupyter_execute/regression_140_0.png" + "image/png": "/Users/hjensen/Teaching/FYS-STK4150/doc/src/LectureNotes/_build/jupyter_execute/regression_140_0.png" } }, "output_type": "display_data" @@ -2321,27 +2321,27 @@ "MSE before scaling: 0.00\n", "R2 score before scaling 0.99\n", "Feature min values before scaling:\n", - " [1.00000000e+00 2.87272654e-03 3.53889759e-04 8.25255780e-06\n", - " 1.01662850e-06 1.25237961e-07 2.37073419e-08 2.92049569e-09\n", - " 3.59774416e-10 4.43204320e-11 6.81047103e-11 8.38978549e-12\n", - " 1.03353352e-12 1.27320481e-13 1.56845470e-14 1.95646209e-13\n", - " 2.41015595e-14 2.96905916e-15 3.65756927e-16 4.50574144e-17\n", - " 5.55060055e-18]\n", + " [1.00000000e+00 2.70650053e-04 1.70425352e-03 7.32514510e-08\n", + " 4.61256305e-07 2.90448006e-06 1.98255091e-11 1.24839043e-10\n", + " 7.86097682e-10 4.94997037e-09 5.36577508e-15 3.37876937e-14\n", + " 2.12757379e-13 1.33970974e-12 8.43600443e-12 1.45224731e-18\n", + " 9.14464107e-18 5.75827959e-17 3.62592512e-16 2.28320505e-15\n", + " 1.43770903e-14]\n", "Feature max values before scaling:\n", - " [1. 0.99925912 0.99832942 0.9985188 0.99758978 0.99666162\n", - " 0.99777902 0.99685069 0.99592322 0.99499662 0.99703979 0.99611215\n", - " 0.99518537 0.99425945 0.99333439 0.99630111 0.99537415 0.99444806\n", - " 0.99352283 0.99259846 0.99167494]\n", + " [1. 0.99958956 0.99908436 0.99917929 0.9986743 0.99816955\n", + " 0.99876919 0.9982644 0.99775987 0.99725559 0.99835926 0.99785468\n", + " 0.99735035 0.99684628 0.99634246 0.9979495 0.99744512 0.996941\n", + " 0.99643713 0.99593352 0.99543016]\n", "Feature min values after scaling:\n", - " [ 0. -1.79114601 -1.81317122 -1.13657683 -1.14440538 -1.15246945\n", - " -0.8846243 -0.88839445 -0.89227535 -0.89626966 -0.74432686 -0.74630093\n", - " -0.74832308 -0.75039501 -0.75251847 -0.6518502 -0.652995 -0.65416038\n", - " -0.65534716 -0.6565562 -0.65778837]\n", + " [ 0. -1.76022296 -1.83404211 -1.14581009 -1.16015297 -1.17531975\n", + " -0.90221667 -0.9105284 -0.91876649 -0.92694434 -0.76295619 -0.76977308\n", + " -0.77649633 -0.78311771 -0.78962976 -0.66997319 -0.67600919 -0.68199208\n", + " -0.68791314 -0.69376357 -0.69953457]\n", "Feature max values after scaling:\n", - " [0. 1.7867041 1.75828655 2.31046377 2.29284732 2.27481524\n", - " 2.74261238 2.72572784 2.70867091 2.69143457 3.11466065 3.09717816\n", - " 3.07959555 3.0619116 3.0441249 3.4415776 3.42335567 3.40506051\n", - " 3.3866923 3.36825115 3.34973716]\n", + " [0. 1.73102381 1.68493089 2.26096593 2.20791419 2.15452546\n", + " 2.69341363 2.64475059 2.59522254 2.54488068 3.06558633 3.02242943\n", + " 2.97825315 2.93307898 2.88693235 3.394687 3.35696162 3.31817404\n", + " 3.27832771 3.23742905 3.19548764]\n", "MSE after scaling: 0.00\n", "R2 score for scaled data: 0.99\n" ] @@ -2771,16 +2771,16 @@ "[[ 4. 2. 2.]\n", " [ 2. 6. -4.]\n", " [ 2. -4. 6.]]\n", - "[[-1.96889890e-16 8.16496581e-01 -5.77350269e-01]\n", + "[[-9.57425734e-17 8.16496581e-01 -5.77350269e-01]\n", " [-7.07106781e-01 4.08248290e-01 5.77350269e-01]\n", " [ 7.07106781e-01 4.08248290e-01 5.77350269e-01]]\n", - "[1.00000000e+01 6.00000000e+00 2.38805416e-31]\n", - "[[-5.76324444e-17 -7.07106781e-01 7.07106781e-01]\n", + "[1.00000000e+01 6.00000000e+00 9.10898112e-32]\n", + "[[ 3.33066907e-17 -7.07106781e-01 7.07106781e-01]\n", " [ 8.16496581e-01 4.08248290e-01 4.08248290e-01]\n", - " [-5.77350269e-01 5.77350269e-01 5.77350269e-01]]\n", - "[[ 1.39583657e+30 -1.39583657e+30 -1.39583657e+30]\n", - " [-1.39583657e+30 1.39583657e+30 1.39583657e+30]\n", - " [-1.39583657e+30 1.39583657e+30 1.39583657e+30]]\n" + " [ 5.77350269e-01 -5.77350269e-01 -5.77350269e-01]]\n", + "[[-3.65939208e+30 3.65939208e+30 3.65939208e+30]\n", + " [ 3.65939208e+30 -3.65939208e+30 -3.65939208e+30]\n", + " [ 3.65939208e+30 -3.65939208e+30 -3.65939208e+30]]\n" ] } ], @@ -3578,10 +3578,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "-0.1366872399802231\n", - "3.6073404954504893\n", - "[[ 1.07916088 3.25530416]\n", - " [ 3.25530416 10.7545475 ]]\n" + "-0.03657945968920499\n", + "4.0843822059793204\n", + "[[ 1.07379261 3.24702637]\n", + " [ 3.24702637 10.84879359]]\n" ] } ], @@ -3620,10 +3620,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.07669023219579478\n", - "1.5824854012671488\n", - "[[1. 0.62520173]\n", - " [0.62520173 1. ]]\n" + "0.08730525680217946\n", + "1.6300895034092742\n", + "[[1. 0.67148001]\n", + " [0.67148001 1. ]]\n" ] } ], @@ -3675,30 +3675,30 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 1.20437373 3.4833127 ]\n", - " [ 0.02359134 0.12344538]\n", - " [-1.49200846 -3.86438835]\n", - " [-1.27249678 -4.49260513]\n", - " [ 0.65853763 1.6246682 ]\n", - " [ 0.42037118 2.93246581]\n", - " [ 0.10958353 -1.3601736 ]\n", - " [ 0.95445711 2.76475208]\n", - " [-0.12333742 0.61124865]\n", - " [-0.48307186 -1.82272573]]\n", + "[[-1.48148987 -4.42262915]\n", + " [ 1.83374146 3.45946449]\n", + " [-0.23090678 -0.72931901]\n", + " [-1.13123132 -3.0478547 ]\n", + " [-0.21545509 -0.5847631 ]\n", + " [ 2.42510042 7.54666425]\n", + " [-0.3841726 -0.06507766]\n", + " [-0.47611774 -0.92923474]\n", + " [ 1.09099713 3.18436382]\n", + " [-1.43046561 -4.4116142 ]]\n", " 0 1\n", - "0 1.204374 3.483313\n", - "1 0.023591 0.123445\n", - "2 -1.492008 -3.864388\n", - "3 -1.272497 -4.492605\n", - "4 0.658538 1.624668\n", - "5 0.420371 2.932466\n", - "6 0.109584 -1.360174\n", - "7 0.954457 2.764752\n", - "8 -0.123337 0.611249\n", - "9 -0.483072 -1.822726\n", + "0 -1.481490 -4.422629\n", + "1 1.833741 3.459464\n", + "2 -0.230907 -0.729319\n", + "3 -1.131231 -3.047855\n", + "4 -0.215455 -0.584763\n", + "5 2.425100 7.546664\n", + "6 -0.384173 -0.065078\n", + "7 -0.476118 -0.929235\n", + "8 1.090997 3.184364\n", + "9 -1.430466 -4.411614\n", " 0 1\n", - "0 1.000000 0.944551\n", - "1 0.944551 1.000000\n" + "0 1.000000 0.981231\n", + 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0.079590 \n", - "12 0.0 0.067543 0.066930 0.079165 0.077482 0.076037 0.079067 0.077253 \n", - "13 0.0 0.064670 0.064761 0.076214 0.075177 0.074287 0.076513 0.075262 \n", - "14 0.0 0.062196 0.062890 0.073685 0.073202 0.072789 0.074337 0.073567 \n", + "1 0.0 0.087277 0.086036 0.090334 0.089428 0.088628 0.082923 0.082097 \n", + "2 0.0 0.086036 0.085851 0.090718 0.090454 0.090258 0.084323 0.083962 \n", + "3 0.0 0.090334 0.090718 0.098733 0.098573 0.098477 0.093678 0.093287 \n", + "4 0.0 0.089428 0.090454 0.098573 0.098881 0.099227 0.094140 0.094116 \n", + "5 0.0 0.088628 0.090258 0.098477 0.099227 0.099993 0.094625 0.094948 \n", + "6 0.0 0.082923 0.084323 0.093678 0.094140 0.094625 0.090901 0.090954 \n", + "7 0.0 0.082097 0.083962 0.093287 0.094116 0.094948 0.090954 0.091305 \n", + "8 0.0 0.081413 0.083717 0.093019 0.094195 0.095358 0.091098 0.091731 \n", + "9 0.0 0.080864 0.083585 0.092870 0.094377 0.095856 0.091331 0.092235 \n", + "10 0.0 0.074520 0.076481 0.086093 0.086978 0.087856 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0.074208 0.072928 \n", - "9 0.078052 0.076848 0.077236 0.075714 0.074421 0.073326 0.072405 \n", - "10 0.079575 0.077236 0.080968 0.078074 0.075614 0.073526 0.071757 \n", - "11 0.077492 0.075714 0.078074 0.075837 0.073938 0.072331 0.070975 \n", - "12 0.075717 0.074421 0.075614 0.073938 0.072521 0.071327 0.070327 \n", - "13 0.074208 0.073326 0.073526 0.072331 0.071327 0.070489 0.069796 \n", - "14 0.072928 0.072405 0.071757 0.070975 0.070327 0.069796 0.069371 \n" + "1 0.081413 0.080864 0.074520 0.073878 0.073365 0.072973 0.072698 \n", + "2 0.083717 0.083585 0.076481 0.076197 0.076024 0.075959 0.075997 \n", + "3 0.093019 0.092870 0.086093 0.085738 0.085504 0.085386 0.085382 \n", + "4 0.094195 0.094377 0.086978 0.086916 0.086962 0.087113 0.087366 \n", + "5 0.095358 0.095856 0.087856 0.088073 0.088386 0.088793 0.089294 \n", + "6 0.091098 0.091331 0.084942 0.084912 0.084981 0.085145 0.085403 \n", + "7 0.091731 0.092235 0.085332 0.085545 0.085846 0.086233 0.086704 \n", + "8 0.092427 0.093188 0.085784 0.086229 0.086751 0.087351 0.088028 \n", + "9 0.093188 0.094197 0.086299 0.086966 0.087701 0.088506 0.089381 \n", + "10 0.085784 0.086299 0.080425 0.080656 0.080963 0.081344 0.081799 \n", + "11 0.086229 0.086966 0.080656 0.081089 0.081588 0.082154 0.082787 \n", + "12 0.086751 0.087701 0.080963 0.081588 0.082272 0.083016 0.083820 \n", + "13 0.087351 0.088506 0.081344 0.082154 0.083016 0.083931 0.084901 \n", + "14 0.088028 0.089381 0.081799 0.082787 0.083820 0.084901 0.086033 \n" ] } ], @@ -4352,10 +4352,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Runtime: 0.214823 sec\n", + "Runtime: 0.430137 sec\n", "Jackknife Statistics :\n", "original bias std. error\n", - " 100.073 100.063 0.149\n" + " 100.065 100.055 0.149964\n" ] } ], @@ -4504,10 +4504,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Runtime: 2.01087 sec\n", + "Runtime: 2.02866 sec\n", "Bootstrap Statistics :\n", "original bias std. error\n", - " 100.227 15.0424 100.231 0.150484\n" + " 100.052 15.0878 100.051 0.150313\n" ] }, { @@ -4518,25 +4518,25 @@ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbootstrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdatapoints\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[0;31m# the histogram of the bootstrapped data\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbinsboot\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpatches\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m50\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnormed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfacecolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'red'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.75\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 32\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 33\u001b[0m \u001b[0;31m# add a 'best fit' line\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mhist\u001b[0;34m(x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, data, **kwargs)\u001b[0m\n\u001b[1;32m 2608\u001b[0m \u001b[0malign\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0malign\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morientation\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrwidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrwidth\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2609\u001b[0m color=color, label=label, stacked=stacked, **({\"data\": data}\n\u001b[0;32m-> 2610\u001b[0;31m if data is not None else {}), **kwargs)\n\u001b[0m\u001b[1;32m 2611\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2612\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/matplotlib/__init__.py\u001b[0m in \u001b[0;36minner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1563\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0minner\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1564\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mdata\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1565\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msanitize_sequence\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1566\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1567\u001b[0m \u001b[0mbound\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_sig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbind\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mhist\u001b[0;34m(self, x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, **kwargs)\u001b[0m\n\u001b[1;32m 6806\u001b[0m \u001b[0;32mif\u001b[0m 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{!r}'\n\u001b[0m\u001b[1;32m 1002\u001b[0m .format(type(self).__name__, k))\n\u001b[1;32m 1003\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mAttributeError\u001b[0m: 'Rectangle' object has no property 'normed'" ] }, { "data": { - "image/png": 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\n", 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zOHiP1)6-!EoW&ploL#NgsR70V{3C%qpn^(U)SVW8$+^d)Q6O!an5$%cUXFU>&KW9h zQf)GpG`tfP73J&e`w&EVFgGqP#!;)}!ZfmzX+~zLMuvsB{^>p(c3cxCR`H$cq-_nQ$i1>Edxn1Pt0Sucs3L}HMKDqN#Od-xX)Ptyy&QU%2F?9bkVb4cD`~3IEaPR4r2$7^R9jU1K#V{Sr6d>gB MQ^yMab@|)>11Djz4FCWD diff --git a/doc/src/LectureNotes/_build/jupyter_execute/regression_70_0.png b/doc/src/LectureNotes/_build/jupyter_execute/regression_70_0.png index 1438c767eca33dbe07c8829705269b2b544b15ca..d26dc0e802b69108c34ec342aed640dc25e578c9 100644 GIT binary patch delta 20 ccmaDG@it;YE~C-JJPDR*@;#j!yB=!;0AL6R=>Px# delta 20 ccmaDG@it;YE~DYZJPDS?pR8_e?0T#X0A 2610 if data is not None else {}), **kwargs) - 2611  - 2612  +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/pyplot.py in hist(x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, data, **kwargs) + 2603 orientation='vertical', rwidth=None, log=False, color=None, + 2604 label=None, stacked=False, *, data=None, **kwargs): +-> 2605 return gca().hist( + 2606 x, bins=bins, range=range, density=density, weights=weights, + 2607 cumulative=cumulative, bottom=bottom, histtype=histtype, -~/anaconda3/lib/python3.6/site-packages/matplotlib/__init__.py in inner(ax, data, *args, **kwargs) +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/__init__.py in inner(ax, data, *args, **kwargs)  1563 def inner(ax, *args, data=None, **kwargs):  1564 if data is None: -> 1565 return func(ax, *map(sanitize_sequence, args), **kwargs)  1566   1567 bound = new_sig.bind(ax, *args, **kwargs) -~/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py in hist(self, x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, **kwargs) - 6806 if patch: - 6807 p = patch[0] --> 6808 p.update(kwargs) - 6809 if lbl is not None: - 6810 p.set_label(lbl) +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_axes.py in hist(self, x, bins, range, density, weights, cumulative, bottom, histtype, align, orientation, rwidth, log, color, label, stacked, **kwargs) + 6817 if patch: + 6818 p = patch[0] +-> 6819 p.update(kwargs) + 6820 if lbl is not None: + 6821 p.set_label(lbl) -~/anaconda3/lib/python3.6/site-packages/matplotlib/artist.py in update(self, props) +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py in update(self, props)  1004   1005 with cbook._setattr_cm(self, eventson=False): -> 1006 ret = [_update_property(self, k, v) for k, v in props.items()]  1007   1008 if len(ret): -~/anaconda3/lib/python3.6/site-packages/matplotlib/artist.py in (.0) +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py in (.0)  1004   1005 with cbook._setattr_cm(self, eventson=False): -> 1006 ret = [_update_property(self, k, v) for k, v in props.items()]  1007   1008 if len(ret): -~/anaconda3/lib/python3.6/site-packages/matplotlib/artist.py in _update_property(self, k, v) +~/opt/anaconda3/lib/python3.8/site-packages/matplotlib/artist.py in _update_property(self, k, v) + 999 func = getattr(self, 'set_' + k, None)  1000 if not callable(func): - 1001 raise AttributeError('{!r} object has no property {!r}' --> 1002 .format(type(self).__name__, k)) - 1003 return func(v) - 1004  +-> 1001 raise AttributeError('{!r} object has no property {!r}' + 1002 .format(type(self).__name__, k)) + 1003 return func(v) AttributeError: 'Rectangle' object has no property 'normed' AttributeError: 'Rectangle' object has no property 'normed' diff --git a/doc/src/LectureNotes/_toc.yml b/doc/src/LectureNotes/_toc.yml index 578da04ff..6e9ffe8f8 100644 --- a/doc/src/LectureNotes/_toc.yml +++ b/doc/src/LectureNotes/_toc.yml @@ -1,10 +1,4 @@ - file: introduction.ipynb - numbered: true -- part: Getting started #includes also linear algebra - chapters: - - file: gettingstarted.ipynb -- part: Linear and Logistic Regression - chapters: - - file: regression.ipynb - - file: logistic.ipynb -- part: Deep Learning and Neural Networks \ No newline at end of file +- file: gettingstarted.ipynb +- file: regression.ipynb +- file: logistic.ipynb diff --git a/doc/src/LectureNotes/introduction.md b/doc/src/LectureNotes/introduction.md deleted file mode 100644 index 5d5627872..000000000 --- a/doc/src/LectureNotes/introduction.md +++ /dev/null @@ -1,339 +0,0 @@ - -# Introduction to Applied Data Analysis and Machine Learning - - -**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University - -Date: **Nov 19, 2019** - -Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license - - - - - -## Introduction - -During the last two decades there has been a swift and amazing -development of Machine Learning techniques and algorithms that impact -many areas in not only Science and Technology but also the Humanities, -Social Sciences, Medicine, Law, indeed, almost all possible -disciplines. The applications are incredibly many, from self-driving -cars to solving high-dimensional differential equations or complicated -quantum mechanical many-body problems. Machine Learning is perceived -by many as one of the main disruptive techniques nowadays. - -Statistics, Data science and Machine Learning form important -fields of research in modern science. They describe how to learn and -make predictions from data, as well as allowing us to extract -important correlations about physical process and the underlying laws -of motion in large data sets. The latter, big data sets, appear -frequently in essentially all disciplines, from the traditional -Science, Technology, Mathematics and Engineering fields to Life -Science, Law, education research, the Humanities and the Social -Sciences. - -It has become more -and more common to see research projects on big data in for example -the Social Sciences where extracting patterns from complicated survey -data is one of many research directions. Having a solid grasp of data -analysis and machine learning is thus becoming central to scientific -computing in many fields, and competences and skills within the fields -of machine learning and scientific computing are nowadays strongly -requested by many potential employers. The latter cannot be -overstated, familiarity with machine learning has almost become a -prerequisite for many of the most exciting employment opportunities, -whether they are in bioinformatics, life science, physics or finance, -in the private or the public sector. This author has had several -students or met students who have been hired recently based on their -skills and competences in scientific computing and data science, often -with marginal knowledge of machine learning. - -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. Many of the methods we will study are also -strongly rooted in basic mathematics and physics research. - -Ideally, machine learning represents the science of giving computers -the ability to learn without being explicitly programmed. The idea is -that there exist generic algorithms which can be used to find patterns -in a broad class of data sets without having to write code -specifically for each problem. The algorithm will build its own logic -based on the data. You should however always keep in mind that -machines and algorithms are to a large extent developed by humans. The -insights and knowledge we have about a specific system, play a central -role when we develop a specific machine learning algorithm. - -Machine learning is an extremely rich field, in spite of its young -age. The increases we have seen during the last three decades in -computational capabilities have been followed by developments of -methods and techniques for analyzing and handling large date sets, -relying heavily on statistics, computer science and mathematics. The -field is rather new and developing rapidly. Popular software packages -written in Python for machine learning like -[Scikit-learn](http://scikit-learn.org/stable/), -[Tensorflow](https://www.tensorflow.org/), -[PyTorch](http://pytorch.org/) and [Keras](https://keras.io/), all -freely available at their respective GitHub sites, encompass -communities of developers in the thousands or more. And the number of -code developers and contributors keeps increasing. Not all the -algorithms and methods can be given a rigorous mathematical -justification, opening up thereby large rooms for experimenting and -trial and error and thereby exciting new developments. However, a -solid command of linear algebra, multivariate theory, probability -theory, statistical data analysis, understanding errors and Monte -Carlo methods are central elements in a proper understanding of many -of algorithms and methods we will discuss. - - - -## Learning outcomes - -These sets of lectures aim at giving you an overview of central aspects of -statistical data analysis as well as some of the central algorithms -used in machine learning. We will introduce a variety of central -algorithms and methods essential for studies of data analysis and -machine learning. - -Hands-on projects and experimenting with data and algorithms plays a central role in -these lectures, and our hope is, through the various -projects and exercises, to expose you to fundamental -research problems in these fields, with the aim to reproduce state of -the art scientific results. You will learn to develop and -structure codes for studying these systems, get acquainted with -computing facilities and learn to handle large scientific projects. A -good scientific and ethical conduct is emphasized throughout the -course. More specifically, you will - -1. Learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning; - -2. Be capable of extending the acquired knowledge to other systems and cases; - -3. Have an understanding of central algorithms used in data analysis and machine learning; - -4. Gain knowledge of central aspects of Monte Carlo methods, Markov chains, Gibbs samplers and their possible applications, from numerical integration to simulation of stock markets; - -5. Understand methods for regression and classification; - -6. Learn about neural network, genetic algorithms and Boltzmann machines; - -7. Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++, in addition to a basic knowledge of linear algebra (typically taught during the first one or two years of undergraduate studies). - -There are several topics we will cover here, spanning from -statistical data analysis and its basic concepts such as expectation -values, variance, covariance, correlation functions and errors, via -well-known probability distribution functions like the uniform -distribution, the binomial distribution, the Poisson distribution and -simple and multivariate normal distributions to central elements of -Bayesian statistics and modeling. We will also remind the reader about -central elements from linear algebra and standard methods based on -linear algebra used to optimize (minimize) functions (the family of gradient descent methods) -and the Singular-value decomposition and -least square methods for parameterizing data. - -We will also cover Monte Carlo methods, Markov chains, well-known -algorithms for sampling stochastic events like the Metropolis-Hastings -and Gibbs sampling methods. An important aspect of all our -calculations is a proper estimation of errors. Here we will also -discuss famous resampling techniques like the blocking, the bootstrapping -and the jackknife methods and the infamous bias-variance tradeoff. - -The second part of the material covers several algorithms used in -machine learning. - - - - - - -## Types of Machine Learning - - -The approaches to machine learning are many, but are often split into -two main categories. In *supervised learning* we know the answer to a -problem, and let the computer deduce the logic behind it. On the other -hand, *unsupervised learning* is a method for finding patterns and -relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely -*reinforcement learning*. This is a paradigm of learning inspired by -behavioral psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. - -Another way to categorize machine learning tasks is to consider the -desired output of a system. Some of the most common tasks are: - - * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. - - * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. - - * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. - -The methods we cover have three main topics in common, irrespective of -whether we deal with supervised or unsupervised learning. The first -ingredient is normally our data set (which can be subdivided into -training and test data), the second item is a model which is normally -a function of some parameters. The model reflects our knowledge of -the system (or lack thereof). As an example, if we know that our data -show a behavior similar to what would be predicted by a polynomial, -fitting our data to a polynomial of some degree would then determin -our model. - -The last ingredient is a so-called **cost** -function which allows us to present an estimate on how good our model -is in reproducing the data it is supposed to train. - -Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms - -1. Linear regression and its variants - -2. Decision tree algorithms, from single trees to random forests - -3. Bayesian statistics and regression - -4. Support vector machines and finally various variants of - -5. Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks - -6. Networks for unsupervised learning using for example reduced Boltzmann machines. - -## Choice of programming language - -Python plays nowadays a central role in the development of machine -learning techniques and tools for data analysis. In particular, seen -the wealth of machine learning and data analysis libraries written in -Python, easy to use libraries with immediate visualization(and not the -least impressive galleries of existing examples), the popularity of the -Jupyter notebook framework with the possibility to run **R** codes or -compiled programs written in C++, and much more made our choice of -programming language for this series of lectures easy. However, -since the focus here is not only on using existing Python libraries such -as **Scikit-Learn** or **Tensorflow**, but also on developing your own -algorithms and codes, we will as far as possible present many of these -algorithms either as a Python codes or C++ or Fortran (or other languages) codes. - -The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -[Lapack](http://www.netlib.org/lapack/) or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like [Numba](https://numba.pydata.org/) -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. - -Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. - -## Data handling, machine learning and ethical aspects - -In most of the cases we will study, we will either generate the data -to analyze ourselves (both for supervised learning and unsupervised -learning) or we will recur again and again to data present in say -**Scikit-Learn** or **Tensorflow**. Many of the examples we end up -dealing with are from a privacy and data protection point of view, -rather inoccuous and boring results of numerical -calculations. However, this does not hinder us from developing a sound -ethical attitude to the data we use, how we analyze the data and how -we handle the data. - -The most immediate and simplest possible ethical aspects deal with our -approach to the scientific process. Nowadays, with version control -software like [Git](https://git-scm.com/) and various online -repositories like [Github](https://github.com/), -[Gitlab](https://about.gitlab.com/) etc, we can easily make our codes -and data sets we have used, freely and easily accessible to a wider -community. This helps us almost automagically in making our science -reproducible. The large open-source development communities involved -in say [Scikit-Learn](http://scikit-learn.org/stable/), -[Tensorflow](https://www.tensorflow.org/), -[PyTorch](http://pytorch.org/) and [Keras](https://keras.io/), are -all excellent examples of this. The codes can be tested and improved -upon continuosly, helping thereby our scientific community at large in -developing data analysis and machine learning tools. It is much -easier today to gain traction and acceptance for making your science -reproducible. From a societal stand, this is an important element -since many of the developers are employees of large public institutions like -universities and research labs. Our fellow taxpayers do deserve to get -something back for their bucks. - -However, this more mechanical aspect of the ethics of science (in -particular the reproducibility of scientific results) is something -which is obvious and everybody should do so as part of the dialectics of -science. The fact that many scientists are not willing to share their codes or -data is detrimental to the scientific discourse. - -Before we proceed, we should add a disclaimer. Even though -we may dream of computers developing some kind of higher learning -capabilities, at the end (even if the artificial intelligence -community keeps touting our ears full of fancy futuristic avenues), it is we, yes you reading these lines, -who end up constructing and instructing, via various algorithms, the -machine learning approaches. Self-driving cars for example, rely on sofisticated -programs which take into account all possible situations a car can -encounter. In addition, extensive usage of training data from GPS -information, maps etc, are typically fed into the software for -self-driving cars. Adding to this various sensors and cameras that -feed information to the programs, there are zillions of ethical issues -which arise from this. - -For self-driving cars, where basically many of the standard machine -learning algorithms discussed here enter into the codes, at a certain -stage we have to make choices. Yes, we , the lads and lasses who wrote -a program for a specific brand of a self-driving car. As an example, -all carmakers have as their utmost priority the security of the -driver and the accompanying passengers. A famous European carmaker, which is -one of the leaders in the market of self-driving cars, had **if** -statements of the following type: suppose there are two obstacles in -front of you and you cannot avoid to collide with one of them. One of -the obstacles is a monstertruck while the other one is a kindergarten -class trying to cross the road. The self-driving car algo would then -opt for the hitting the small folks instead of the monstertruck, since -the likelihood of surving a collision with our future citizens, is -much higher. - -This leads to serious ethical aspects. Why should we opt for such an -option? Who decides and who is entitled to make such choices? Keep in -mind that many of the algorithms you will encounter in this series of -lectures or hear about later, are indeed based on simple programming -instructions. And you are very likely to be one of the people who may -end up writing such a code. Thus, developing a sound ethical attitude -to what we do, an approach well beyond the simple mechanistic one of -making our science available and reproducible, is much needed. The -example of the self-driving cars is just one of infinitely many cases -where we have to make choices. When you analyze data on economic -inequalities, who guarantees that you are not weighting some data in a -particular way, perhaps because you dearly want a specific conclusion -which may support your political views? Or what about the recent -claims that a famous IT company like Apple has a sexist bias on the -their recently [launched credit card](https://qz.com/1748321/the-role-of-goldman-sachs-algorithms-in-the-apple-credit-card-scandal/)? - -We do not have the answers here, nor will we venture into a deeper -discussions of these aspects, but we want you think over these topics -in a more overarching way. A statistical data analysis with its dry -numbers and graphs meant to guide the eye, does not necessarily -reflect the truth, whatever that is. As a scientist, and after a -university education, you are supposedly a better citizen, with an -improved critical view and understanding of the scientific method, and -perhaps some deeper understanding of the ethics of science at -large. Use these insights. Be a critical citizen. You owe it to our -society.