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Morten Hjorth-Jensen
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@@ -0,0 +1,912 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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||||
"# Logistic Regression\n",
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"\n",
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||||
"\n",
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"\n",
|
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"## Logistic Regression\n",
|
||||
"\n",
|
||||
"In linear regression our main interest was centered on learning the\n",
|
||||
"coefficients of a functional fit (say a polynomial) in order to be\n",
|
||||
"able to predict the response of a continuous variable on some unseen\n",
|
||||
"data. The fit to the continuous variable $y_i$ is based on some\n",
|
||||
"independent variables $x_i$. Linear regression resulted in\n",
|
||||
"analytical expressions for standard ordinary Least Squares or Ridge\n",
|
||||
"regression (in terms of matrices to invert) for several quantities,\n",
|
||||
"ranging from the variance and thereby the confidence intervals of the\n",
|
||||
"optimal parameters $\\hat{\\beta}$ to the mean squared error. If we can invert\n",
|
||||
"the product of the design matrices, linear regression gives then a\n",
|
||||
"simple recipe for fitting our data.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Classification problems, however, are concerned with outcomes taking\n",
|
||||
"the form of discrete variables (i.e. categories). We may for example,\n",
|
||||
"on the basis of DNA sequencing for a number of patients, like to find\n",
|
||||
"out which mutations are important for a certain disease; or based on\n",
|
||||
"scans of various patients' brains, figure out if there is a tumor or\n",
|
||||
"not; or given a specific physical system, we'd like to identify its\n",
|
||||
"state, say whether it is an ordered or disordered system (typical\n",
|
||||
"situation in solid state physics); or classify the status of a\n",
|
||||
"patient, whether she/he has a stroke or not and many other similar\n",
|
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"situations.\n",
|
||||
"\n",
|
||||
"The most common situation we encounter when we apply logistic\n",
|
||||
"regression is that of two possible outcomes, normally denoted as a\n",
|
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"binary outcome, true or false, positive or negative, success or\n",
|
||||
"failure etc.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Logistic regression will also serve as our stepping stone towards\n",
|
||||
"neural network algorithms and supervised deep learning. For logistic\n",
|
||||
"learning, the minimization of the cost function leads to a non-linear\n",
|
||||
"equation in the parameters $\\hat{\\beta}$. The optimization of the\n",
|
||||
"problem calls therefore for minimization algorithms. This forms the\n",
|
||||
"bottle neck of all machine learning algorithms, namely how to find\n",
|
||||
"reliable minima of a multi-variable function. This leads us to the\n",
|
||||
"family of gradient descent methods. The latter are the working horses\n",
|
||||
"of basically all modern machine learning algorithms.\n",
|
||||
"\n",
|
||||
"We note also that many of the topics discussed here on logistic \n",
|
||||
"regression are also commonly used in modern supervised Deep Learning\n",
|
||||
"models, as we will see later.\n",
|
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"\n",
|
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"\n",
|
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"\n",
|
||||
"## Basics\n",
|
||||
"\n",
|
||||
"We consider the case where the dependent variables, also called the\n",
|
||||
"responses or the outcomes, $y_i$ are discrete and only take values\n",
|
||||
"from $k=0,\\dots,K-1$ (i.e. $K$ classes).\n",
|
||||
"\n",
|
||||
"The goal is to predict the\n",
|
||||
"output classes from the design matrix $\\boldsymbol{X}\\in\\mathbb{R}^{n\\times p}$\n",
|
||||
"made of $n$ samples, each of which carries $p$ features or predictors. The\n",
|
||||
"primary goal is to identify the classes to which new unseen samples\n",
|
||||
"belong.\n",
|
||||
"\n",
|
||||
"Let us specialize to the case of two classes only, with outputs\n",
|
||||
"$y_i=0$ and $y_i=1$. Our outcomes could represent the status of a\n",
|
||||
"credit card user that could default or not on her/his credit card\n",
|
||||
"debt. That is"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"y_i = \\begin{bmatrix} 0 & \\mathrm{no}\\\\ 1 & \\mathrm{yes} \\end{bmatrix}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Before moving to the logistic model, let us try to use our linear\n",
|
||||
"regression model to classify these two outcomes. We could for example\n",
|
||||
"fit a linear model to the default case if $y_i > 0.5$ and the no\n",
|
||||
"default case $y_i \\leq 0.5$.\n",
|
||||
"\n",
|
||||
"We would then have our \n",
|
||||
"weighted linear combination, namely"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto1\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation}\n",
|
||||
"\\boldsymbol{y} = \\boldsymbol{X}^T\\boldsymbol{\\beta} + \\boldsymbol{\\epsilon},\n",
|
||||
"\\label{_auto1} \\tag{1}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"where $\\boldsymbol{y}$ is a vector representing the possible outcomes, $\\boldsymbol{X}$ is our\n",
|
||||
"$n\\times p$ design matrix and $\\boldsymbol{\\beta}$ represents our estimators/predictors.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"The main problem with our function is that it takes values on the\n",
|
||||
"entire real axis. In the case of logistic regression, however, the\n",
|
||||
"labels $y_i$ are discrete variables. A typical example is the credit\n",
|
||||
"card data discussed below here, where we can set the state of\n",
|
||||
"defaulting the debt to $y_i=1$ and not to $y_i=0$ for one the persons\n",
|
||||
"in the data set (see the full example below).\n",
|
||||
"\n",
|
||||
"One simple way to get a discrete output is to have sign\n",
|
||||
"functions that map the output of a linear regressor to values $\\{0,1\\}$,\n",
|
||||
"$f(s_i)=sign(s_i)=1$ if $s_i\\ge 0$ and 0 if otherwise. \n",
|
||||
"We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron\" model in the machine learning\n",
|
||||
"literature. This model is extremely simple. However, in many cases it is more\n",
|
||||
"favorable to use a ``soft\" classifier that outputs\n",
|
||||
"the probability of a given category. This leads us to the logistic function.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%matplotlib inline\n",
|
||||
"\n",
|
||||
"# Common imports\n",
|
||||
"import os\n",
|
||||
"import numpy as np\n",
|
||||
"import pandas as pd\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"from sklearn.linear_model import LinearRegression, Ridge, Lasso\n",
|
||||
"from sklearn.model_selection import train_test_split\n",
|
||||
"from sklearn.utils import resample\n",
|
||||
"from sklearn.metrics import mean_squared_error\n",
|
||||
"from IPython.display import display\n",
|
||||
"from pylab import plt, mpl\n",
|
||||
"plt.style.use('seaborn')\n",
|
||||
"mpl.rcParams['font.family'] = 'serif'\n",
|
||||
"\n",
|
||||
"# Where to save the figures and data files\n",
|
||||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||||
"DATA_ID = \"DataFiles/\"\n",
|
||||
"\n",
|
||||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||||
"\n",
|
||||
"if not os.path.exists(FIGURE_ID):\n",
|
||||
" os.makedirs(FIGURE_ID)\n",
|
||||
"\n",
|
||||
"if not os.path.exists(DATA_ID):\n",
|
||||
" os.makedirs(DATA_ID)\n",
|
||||
"\n",
|
||||
"def image_path(fig_id):\n",
|
||||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||||
"\n",
|
||||
"def data_path(dat_id):\n",
|
||||
" return os.path.join(DATA_ID, dat_id)\n",
|
||||
"\n",
|
||||
"def save_fig(fig_id):\n",
|
||||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||||
"\n",
|
||||
"infile = open(data_path(\"chddata.csv\"),'r')\n",
|
||||
"\n",
|
||||
"# Read the chd data as csv file and organize the data into arrays with age group, age, and chd\n",
|
||||
"chd = pd.read_csv(infile, names=('ID', 'Age', 'Agegroup', 'CHD'))\n",
|
||||
"chd.columns = ['ID', 'Age', 'Agegroup', 'CHD']\n",
|
||||
"output = chd['CHD']\n",
|
||||
"age = chd['Age']\n",
|
||||
"agegroup = chd['Agegroup']\n",
|
||||
"numberID = chd['ID'] \n",
|
||||
"display(chd)\n",
|
||||
"\n",
|
||||
"plt.scatter(age, output, marker='o')\n",
|
||||
"plt.axis([18,70.0,-0.1, 1.2])\n",
|
||||
"plt.xlabel(r'Age')\n",
|
||||
"plt.ylabel(r'CHD')\n",
|
||||
"plt.title(r'Age distribution and Coronary heart disease')\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"What we could attempt however is to plot the mean value for each group."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n",
|
||||
"group = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
|
||||
"plt.plot(group, agegroupmean, \"r-\")\n",
|
||||
"plt.axis([0,9,0, 1.0])\n",
|
||||
"plt.xlabel(r'Age group')\n",
|
||||
"plt.ylabel(r'CHD mean values')\n",
|
||||
"plt.title(r'Mean values for each age group')\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We are now trying to find a function $f(y\\vert x)$, that is a function which gives us an expected value for the output $y$ with a given input $x$.\n",
|
||||
"In standard linear regression with a linear dependence on $x$, we would write this in terms of our model"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"f(y_i\\vert x_i)=\\beta_0+\\beta_1 x_i.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This expression implies however that $f(y_i\\vert x_i)$ could take any\n",
|
||||
"value from minus infinity to plus infinity. If we however let\n",
|
||||
"$f(y\\vert y)$ be represented by the mean value, the above example\n",
|
||||
"shows us that we can constrain the function to take values between\n",
|
||||
"zero and one, that is we have $0 \\le f(y_i\\vert x_i) \\le 1$. Looking\n",
|
||||
"at our last curve we see also that it has an S-shaped form. This leads\n",
|
||||
"us to a very popular model for the function $f$, namely the so-called\n",
|
||||
"Sigmoid function or logistic model. We will consider this function as\n",
|
||||
"representing the probability for finding a value of $y_i$ with a given\n",
|
||||
"$x_i$.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## The logistic function\n",
|
||||
"\n",
|
||||
"Another widely studied model, is the so-called \n",
|
||||
"perceptron model, which is an example of a \"hard classification\" model. We\n",
|
||||
"will encounter this model when we discuss neural networks as\n",
|
||||
"well. Each datapoint is deterministically assigned to a category (i.e\n",
|
||||
"$y_i=0$ or $y_i=1$). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a \"soft\"\n",
|
||||
"classifier that outputs the probability of a given category rather\n",
|
||||
"than a single value. For example, given $x_i$, the classifier\n",
|
||||
"outputs the probability of being in a category $k$. Logistic regression\n",
|
||||
"is the most common example of a so-called soft classifier. In logistic\n",
|
||||
"regression, the probability that a data point $x_i$\n",
|
||||
"belongs to a category $y_i=\\{0,1\\}$ is given by the so-called logit function (or Sigmoid) which is meant to represent the likelihood for a given event,"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"p(t) = \\frac{1}{1+\\mathrm \\exp{-t}}=\\frac{\\exp{t}}{1+\\mathrm \\exp{t}}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Note that $1-p(t)= p(-t)$.\n",
|
||||
"\n",
|
||||
"## Examples of likelihood functions used in logistic regression and nueral networks\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"The following code plots the logistic function, the step function and other functions we will encounter from here and on."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"\"\"\"The sigmoid function (or the logistic curve) is a\n",
|
||||
"function that takes any real number, z, and outputs a number (0,1).\n",
|
||||
"It is useful in neural networks for assigning weights on a relative scale.\n",
|
||||
"The value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\n",
|
||||
"\n",
|
||||
"import numpy\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"import math as mt\n",
|
||||
"\n",
|
||||
"z = numpy.arange(-5, 5, .1)\n",
|
||||
"sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))\n",
|
||||
"sigma = sigma_fn(z)\n",
|
||||
"\n",
|
||||
"fig = plt.figure()\n",
|
||||
"ax = fig.add_subplot(111)\n",
|
||||
"ax.plot(z, sigma)\n",
|
||||
"ax.set_ylim([-0.1, 1.1])\n",
|
||||
"ax.set_xlim([-5,5])\n",
|
||||
"ax.grid(True)\n",
|
||||
"ax.set_xlabel('z')\n",
|
||||
"ax.set_title('sigmoid function')\n",
|
||||
"\n",
|
||||
"plt.show()\n",
|
||||
"\n",
|
||||
"\"\"\"Step Function\"\"\"\n",
|
||||
"z = numpy.arange(-5, 5, .02)\n",
|
||||
"step_fn = numpy.vectorize(lambda z: 1.0 if z >= 0.0 else 0.0)\n",
|
||||
"step = step_fn(z)\n",
|
||||
"\n",
|
||||
"fig = plt.figure()\n",
|
||||
"ax = fig.add_subplot(111)\n",
|
||||
"ax.plot(z, step)\n",
|
||||
"ax.set_ylim([-0.5, 1.5])\n",
|
||||
"ax.set_xlim([-5,5])\n",
|
||||
"ax.grid(True)\n",
|
||||
"ax.set_xlabel('z')\n",
|
||||
"ax.set_title('step function')\n",
|
||||
"\n",
|
||||
"plt.show()\n",
|
||||
"\n",
|
||||
"\"\"\"tanh Function\"\"\"\n",
|
||||
"z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n",
|
||||
"t = numpy.tanh(z)\n",
|
||||
"\n",
|
||||
"fig = plt.figure()\n",
|
||||
"ax = fig.add_subplot(111)\n",
|
||||
"ax.plot(z, t)\n",
|
||||
"ax.set_ylim([-1.0, 1.0])\n",
|
||||
"ax.set_xlim([-2*mt.pi,2*mt.pi])\n",
|
||||
"ax.grid(True)\n",
|
||||
"ax.set_xlabel('z')\n",
|
||||
"ax.set_title('tanh function')\n",
|
||||
"\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We assume now that we have two classes with $y_i$ either $0$ or $1$. Furthermore we assume also that we have only two parameters $\\beta$ in our fitting of the Sigmoid function, that is we define probabilities"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\begin{align*}\n",
|
||||
"p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
|
||||
"p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
|
||||
"\\end{align*}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n",
|
||||
"\n",
|
||||
"Note that we used"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"p(y_i=0\\vert x_i, \\boldsymbol{\\beta}) = 1-p(y_i=1\\vert x_i, \\boldsymbol{\\beta}).\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"In order to define the total likelihood for all possible outcomes from a \n",
|
||||
"dataset $\\mathcal{D}=\\{(y_i,x_i)\\}$, with the binary labels\n",
|
||||
"$y_i\\in\\{0,1\\}$ and where the data points are drawn independently, we use the so-called [Maximum Likelihood Estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) (MLE) principle. \n",
|
||||
"We aim thus at maximizing \n",
|
||||
"the probability of seeing the observed data. We can then approximate the \n",
|
||||
"likelihood in terms of the product of the individual probabilities of a specific outcome $y_i$, that is"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\begin{align*}\n",
|
||||
"P(\\mathcal{D}|\\boldsymbol{\\beta})& = \\prod_{i=1}^n \\left[p(y_i=1|x_i,\\boldsymbol{\\beta})\\right]^{y_i}\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]^{1-y_i}\\nonumber \\\\\n",
|
||||
"\\end{align*}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"from which we obtain the log-likelihood and our **cost/loss** function"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left( y_i\\log{p(y_i=1|x_i,\\boldsymbol{\\beta})} + (1-y_i)\\log\\left[1-p(y_i=1|x_i,\\boldsymbol{\\beta}))\\right]\\right).\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Reordering the logarithms, we can rewrite the **cost/loss** function as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\mathcal{C}(\\boldsymbol{\\beta}) = \\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The maximum likelihood estimator is defined as the set of parameters that maximize the log-likelihood where we maximize with respect to $\\beta$.\n",
|
||||
"Since the cost (error) function is just the negative log-likelihood, for logistic regression we have that"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\mathcal{C}(\\boldsymbol{\\beta})=-\\sum_{i=1}^n \\left(y_i(\\beta_0+\\beta_1x_i) -\\log{(1+\\exp{(\\beta_0+\\beta_1x_i)})}\\right).\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"This equation is known in statistics as the **cross entropy**. Finally, we note that just as in linear regression, \n",
|
||||
"in practice we often supplement the cross-entropy with additional regularization terms, usually $L_1$ and $L_2$ regularization as we did for Ridge and Lasso regression.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"The cross entropy is a convex function of the weights $\\boldsymbol{\\beta}$ and,\n",
|
||||
"therefore, any local minimizer is a global minimizer. \n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Minimizing this\n",
|
||||
"cost function with respect to the two parameters $\\beta_0$ and $\\beta_1$ we obtain"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_0} = -\\sum_{i=1}^n \\left(y_i -\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right),\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\beta_1} = -\\sum_{i=1}^n \\left(y_ix_i -x_i\\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}}\\right).\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Let us now define a vector $\\boldsymbol{y}$ with $n$ elements $y_i$, an\n",
|
||||
"$n\\times p$ matrix $\\boldsymbol{X}$ which contains the $x_i$ values and a\n",
|
||||
"vector $\\boldsymbol{p}$ of fitted probabilities $p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We can rewrite in a more compact form the first\n",
|
||||
"derivative of cost function as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
|
||||
"$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with $p$ predictors"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\log{ \\frac{p(\\boldsymbol{\\beta}\\boldsymbol{x})}{1-p(\\boldsymbol{\\beta}\\boldsymbol{x})}} = \\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Here we defined $\\boldsymbol{x}=[1,x_1,x_2,\\dots,x_p]$ and $\\boldsymbol{\\beta}=[\\beta_0, \\beta_1, \\dots, \\beta_p]$ leading to"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"p(\\boldsymbol{\\beta}\\boldsymbol{x})=\\frac{ \\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}{1+\\exp{(\\beta_0+\\beta_1x_1+\\beta_2x_2+\\dots+\\beta_px_p)}}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Till now we have mainly focused on two classes, the so-called binary\n",
|
||||
"system. Suppose we wish to extend to $K$ classes. Let us for the sake\n",
|
||||
"of simplicity assume we have only two predictors. We have then following model"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\log{\\frac{p(C=1\\vert x)}{p(K\\vert x)}} = \\beta_{10}+\\beta_{11}x_1,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\log{\\frac{p(C=2\\vert x)}{p(K\\vert x)}} = \\beta_{20}+\\beta_{21}x_1,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and so on till the class $C=K-1$ class"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"\\log{\\frac{p(C=K-1\\vert x)}{p(K\\vert x)}} = \\beta_{(K-1)0}+\\beta_{(K-1)1}x_1,\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and the model is specified in term of $K-1$ so-called log-odds or\n",
|
||||
"**logit** transformations.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"In our discussion of neural networks we will encounter the above again\n",
|
||||
"in terms of a slightly modified function, the so-called **Softmax** function.\n",
|
||||
"\n",
|
||||
"The softmax function is used in various multiclass classification\n",
|
||||
"methods, such as multinomial logistic regression (also known as\n",
|
||||
"softmax regression), multiclass linear discriminant analysis, naive\n",
|
||||
"Bayes classifiers, and artificial neural networks. Specifically, in\n",
|
||||
"multinomial logistic regression and linear discriminant analysis, the\n",
|
||||
"input to the function is the result of $K$ distinct linear functions,\n",
|
||||
"and the predicted probability for the $k$-th class given a sample\n",
|
||||
"vector $\\boldsymbol{x}$ and a weighting vector $\\boldsymbol{\\beta}$ is (with two\n",
|
||||
"predictors):"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"p(C=k\\vert \\mathbf {x} )=\\frac{\\exp{(\\beta_{k0}+\\beta_{k1}x_1)}}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}}.\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"It is easy to extend to more predictors. The final class is"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"$$\n",
|
||||
"p(C=K\\vert \\mathbf {x} )=\\frac{1}{1+\\sum_{l=1}^{K-1}\\exp{(\\beta_{l0}+\\beta_{l1}x_1)}},\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and they sum to one. Our earlier discussions were all specialized to\n",
|
||||
"the case with two classes only. It is easy to see from the above that\n",
|
||||
"what we derived earlier is compatible with these equations.\n",
|
||||
"\n",
|
||||
"To find the optimal parameters we would typically use a gradient\n",
|
||||
"descent method. Newton's method and gradient descent methods are\n",
|
||||
"discussed in the material on [optimization\n",
|
||||
"methods](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n",
|
||||
"\n",
|
||||
"## Wisconsin Cancer Data\n",
|
||||
"\n",
|
||||
"We show here how we can use a simple regression case on the breast\n",
|
||||
"cancer data using Logistic regression as our algorithm for\n",
|
||||
"classification."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"import numpy as np\n",
|
||||
"from sklearn.model_selection import train_test_split \n",
|
||||
"from sklearn.datasets import load_breast_cancer\n",
|
||||
"from sklearn.linear_model import LogisticRegression\n",
|
||||
"\n",
|
||||
"# Load the data\n",
|
||||
"cancer = load_breast_cancer()\n",
|
||||
"\n",
|
||||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||||
"print(X_train.shape)\n",
|
||||
"print(X_test.shape)\n",
|
||||
"# Logistic Regression\n",
|
||||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||||
"logreg.fit(X_train, y_train)\n",
|
||||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||||
"#now scale the data\n",
|
||||
"from sklearn.preprocessing import StandardScaler\n",
|
||||
"scaler = StandardScaler()\n",
|
||||
"scaler.fit(X_train)\n",
|
||||
"X_train_scaled = scaler.transform(X_train)\n",
|
||||
"X_test_scaled = scaler.transform(X_test)\n",
|
||||
"# Logistic Regression\n",
|
||||
"logreg.fit(X_train_scaled, y_train)\n",
|
||||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"In addition to the above scores, we could also study the covariance (and the correlation matrix).\n",
|
||||
"We use **Pandas** to compute the correlation matrix."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"import numpy as np\n",
|
||||
"from sklearn.model_selection import train_test_split \n",
|
||||
"from sklearn.datasets import load_breast_cancer\n",
|
||||
"from sklearn.linear_model import LogisticRegression\n",
|
||||
"cancer = load_breast_cancer()\n",
|
||||
"import pandas as pd\n",
|
||||
"# Making a data frame\n",
|
||||
"cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||||
"\n",
|
||||
"fig, axes = plt.subplots(15,2,figsize=(10,20))\n",
|
||||
"malignant = cancer.data[cancer.target == 0]\n",
|
||||
"benign = cancer.data[cancer.target == 1]\n",
|
||||
"ax = axes.ravel()\n",
|
||||
"\n",
|
||||
"for i in range(30):\n",
|
||||
" _, bins = np.histogram(cancer.data[:,i], bins =50)\n",
|
||||
" ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)\n",
|
||||
" ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)\n",
|
||||
" ax[i].set_title(cancer.feature_names[i])\n",
|
||||
" ax[i].set_yticks(())\n",
|
||||
"ax[0].set_xlabel(\"Feature magnitude\")\n",
|
||||
"ax[0].set_ylabel(\"Frequency\")\n",
|
||||
"ax[0].legend([\"Malignant\", \"Benign\"], loc =\"best\")\n",
|
||||
"fig.tight_layout()\n",
|
||||
"plt.show()\n",
|
||||
"\n",
|
||||
"import seaborn as sns\n",
|
||||
"correlation_matrix = cancerpd.corr().round(1)\n",
|
||||
"# use the heatmap function from seaborn to plot the correlation matrix\n",
|
||||
"# annot = True to print the values inside the square\n",
|
||||
"plt.figure(figsize=(15,8))\n",
|
||||
"sns.heatmap(data=correlation_matrix, annot=True)\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"In the above example we note two things. In the first plot we display\n",
|
||||
"the overlap of benign and malignant tumors as functions of the various\n",
|
||||
"features in the Wisconsing breast cancer data set. We see that for\n",
|
||||
"some of the features we can distinguish clearly the benign and\n",
|
||||
"malignant cases while for other features we cannot. This can point to\n",
|
||||
"us which features may be of greater interest when we wish to classify\n",
|
||||
"a benign or not benign tumour.\n",
|
||||
"\n",
|
||||
"In the second figure we have computed the so-called correlation\n",
|
||||
"matrix, which in our case with thirty features becomes a $30\\times 30$\n",
|
||||
"matrix.\n",
|
||||
"\n",
|
||||
"We constructed this matrix using **pandas** via the statements"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and then"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"correlation_matrix = cancerpd.corr().round(1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Diagonalizing this matrix we can in turn say something about which\n",
|
||||
"features are of relevance and which are not. This leads us to\n",
|
||||
"the classical Principal Component Analysis (PCA) theorem with\n",
|
||||
"applications. This will be discussed later this semester ([week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html))."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"editable": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"import numpy as np\n",
|
||||
"from sklearn.model_selection import train_test_split \n",
|
||||
"from sklearn.datasets import load_breast_cancer\n",
|
||||
"from sklearn.linear_model import LogisticRegression\n",
|
||||
"\n",
|
||||
"# Load the data\n",
|
||||
"cancer = load_breast_cancer()\n",
|
||||
"\n",
|
||||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||||
"print(X_train.shape)\n",
|
||||
"print(X_test.shape)\n",
|
||||
"# Logistic Regression\n",
|
||||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||||
"logreg.fit(X_train, y_train)\n",
|
||||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||||
"#now scale the data\n",
|
||||
"from sklearn.preprocessing import StandardScaler\n",
|
||||
"scaler = StandardScaler()\n",
|
||||
"scaler.fit(X_train)\n",
|
||||
"X_train_scaled = scaler.transform(X_train)\n",
|
||||
"X_test_scaled = scaler.transform(X_test)\n",
|
||||
"# Logistic Regression\n",
|
||||
"logreg.fit(X_train_scaled, y_train)\n",
|
||||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"from sklearn.preprocessing import LabelEncoder\n",
|
||||
"from sklearn.model_selection import cross_validate\n",
|
||||
"#Cross validation\n",
|
||||
"accuracy = cross_validate(logreg,X_test_scaled,y_test,cv=10)['test_score']\n",
|
||||
"print(accuracy)\n",
|
||||
"print(\"Test set accuracy with Logistic Regression and scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"import scikitplot as skplt\n",
|
||||
"y_pred = logreg.predict(X_test_scaled)\n",
|
||||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||||
"plt.show()\n",
|
||||
"y_probas = logreg.predict_proba(X_test_scaled)\n",
|
||||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||||
"plt.show()\n",
|
||||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||||
"plt.show()"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 4
|
||||
}
|
||||
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|
||||
# Applied Data Analysis and Machine Learning, FYS-STK3155/4155 at the University of Oslo, Norway
|
||||
|
||||
## Introduction
|
||||
|
||||
Probability theory and statistical methods play a central role in Science. Nowadays we are
|
||||
surrounded by huge amounts of data. For example, there are more than one trillion web pages; more than one
|
||||
hour of video is uploaded to YouTube every second, amounting to years of content every
|
||||
day; the genomes of 1000s of people, each of which has a length of more than a billion base pairs, have
|
||||
been sequenced by various labs and so on. This deluge of data calls for automated methods of data analysis,
|
||||
which is exactly what machine learning aims at providing.
|
||||
|
||||
## Learning outcomes
|
||||
|
||||
This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects and weekly exercises you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach with an emphasis on predictions and correaltions. However, we will try, where appropriate, to link our machine learning models with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, 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, after this course you will
|
||||
|
||||
- Learn about basic data analysis, statistical analysis, Bayesian statistics, Monte Carlo sampling, data optimization and machine learning;
|
||||
- Be capable of extending the acquired knowledge to other systems and cases;
|
||||
- Have an understanding of central algorithms used in data analysis and machine learning;
|
||||
- Understand linear methods for regression and classification, from ordinary least squares, via Lasso and Ridge to Logistic regression and Kernel regression;
|
||||
- Learn about neural networks and deep learning methods for supervised and unsupervised learning. Emphasis on feed forward neural networks, convolutional and recurrent neural networks;
|
||||
- Learn about about decision trees, random forests, bagging and boosting methods;
|
||||
- Learn about support vector machines and kernel transformations;
|
||||
- Reduction of data sets and unsupervised learning, from PCA to clustering;
|
||||
- Autoencoders and Reinforcement Learning;
|
||||
- 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++ and/or Fortran (Fortran2003 or later).
|
||||
|
||||
## Prerequisites and background
|
||||
|
||||
Basic knowledge in programming and mathematics, with an emphasis on linear algebra. Knowledge of Python or/and C++ as programming languages is strongly recommended and experience with Jupyter notebooks is recommended. Required courses are the equivalents to the University of Oslo mathematics courses MAT1100, MAT1110, MAT1120 and at least one of the corresponding computing and programming courses INF1000/INF1110 or MAT-INF1100/MAT-INF1100L/BIOS1100/KJM-INF1100. Most universities offer nowadays a basic programming course (often compulsory) where Python is the recurring programming language.
|
||||
We recommend also refreshing your knowledge on Statistics and Probability theory. The lecture notes at https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html offer a review of Statistics and Probability theory.
|
||||
|
||||
## The course has two central parts
|
||||
|
||||
1. Statistical analysis and optimization of data
|
||||
2. Machine learning
|
||||
|
||||
|
||||
### Statistical analysis and optimization of data
|
||||
|
||||
The following topics will be covered
|
||||
- Basic concepts, expectation values, variance, covariance, correlation functions and errors;
|
||||
- Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
|
||||
- Central elements of Bayesian statistics and modeling;
|
||||
- Gradient methods for data optimization,
|
||||
- Monte Carlo methods, Markov chains, Gibbs sampling and Metropolis-Hastings sampling;
|
||||
- Estimation of errors and resampling techniques such as the cross-validation, blocking, bootstrapping and jackknife methods;
|
||||
- Principal Component Analysis (PCA) and its mathematical foundation
|
||||
|
||||
### Machine learning
|
||||
|
||||
The following topics will be covered:
|
||||
- Linear Regression and Logistic Regression;
|
||||
- Neural networks and deep learning, including convolutional and recurrent neural networks
|
||||
- Decisions trees, Random Forests, Bagging and Boosting
|
||||
- Support vector machines
|
||||
- Bayesian linear and logistic regression
|
||||
- Boltzmann Machines
|
||||
- Unsupervised learning Dimensionality reduction, PCA, k-means and clustering
|
||||
- Autoenconders
|
||||
|
||||
Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics.
|
||||
|
||||
Computational aspects play a central role and you are
|
||||
expected to work on numerical examples and projects which illustrate
|
||||
the theory and various algorithms discussed during the lectures. We recommend strongly to form small project groups of 2-3 participants, if possible.
|
||||
|
||||
|
||||
|
||||
## Required Technologies
|
||||
|
||||
Course participants are expected to have their own laptops/PCs. We use _Git_ as version control software and the usage of providers like _GitHub_, _GitLab_ or similar are strongly recommended. If you are not familiar with Git as version control software, the following video may be of interest, see https://www.youtube.com/watch?v=RGOj5yH7evk&ab_channel=freeCodeCamp.org
|
||||
|
||||
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 and you feel
|
||||
pretty familiar with installing different packages, we recommend that
|
||||
you install the following Python packages via _pip_ as
|
||||
|
||||
* pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow
|
||||
|
||||
For OSX users we recommend, after having installed Xcode, to
|
||||
install _brew_. Brew allows for a seamless installation of additional
|
||||
software via for example
|
||||
|
||||
* 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
|
||||
|
||||
* sudo apt-get install python3
|
||||
|
||||
### 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
|
||||
|
||||
|
||||
|
||||
|
||||
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@@ -0,0 +1,185 @@
|
||||
# Teaching schedule with links to material
|
||||
|
||||
|
||||
This course will be delivered in a hybrid mode, with online lectures and on site or online laboratory sessions.
|
||||
|
||||
1. Four lectures per week, Fall semester, 10 ECTS. The lectures are in person but will be recorded and linked to this site and the official University of Oslo website for the course;
|
||||
2. Two hours of laboratory sessions for work on computational projects and exercises for each group. There will also be fully digital laboratory sessions for those who cannot attend;
|
||||
3. Three projects which are graded and count 1/3 each of the final grade. The deadlines for the projects are October 11 for project 1, November 15 for project 2 and December 13 for project 3.
|
||||
4. A selected number of weekly assignments;
|
||||
5. The course is part of the CS Master of Science program, but is open to other bachelor and Master of Science students at the University of Oslo;
|
||||
6. The course is offered as a FYS-MAT4155 (Master of Science level) and a FYS-MAT3155 (senior undergraduate) course;
|
||||
7. Videos of teaching material are available via the links at https://compphysics.github.io/MachineLearning/doc/web/course.html;
|
||||
8. Weekly emails with summary of activities will be mailed to all participants;
|
||||
|
||||
|
||||
|
||||
## Weekly Schedule
|
||||
|
||||
For the reading assignments we use the following abbreviations:
|
||||
- GBC: Goodfellow, Bengio, and Courville, Deep Learning
|
||||
- CMB: Christopher M. Bishop, Pattern Recognition and Machine Learning
|
||||
- HTF: Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning
|
||||
- AG: Aurelien Geron, Hands‑On Machine Learning with Scikit‑Learn and TensorFlow
|
||||
|
||||
### Week 34 August 23-27
|
||||
- Lab Wednesday: Introduction to software and repetition of Python Programming
|
||||
- Lecture Thursday: Introduction to the course, what is Machine Learning and introduction to Linear Regression.
|
||||
- Video of Lecture August 26, 2021 at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureThursdayAugust26.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Basics of Linear Regression
|
||||
- Video of Lecture August 27, 2021 at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureThursdayAugust27.mp4?vrtx=view-as-webpage
|
||||
|
||||
- Reading recommendations:
|
||||
- Refresh linear algebra, GBC chapters 1 and 2.
|
||||
- CMB sections 1.1 and 3.1.
|
||||
- HTF chapters 2 and 3.
|
||||
- See lecture notes for week 34 at https://compphysics.github.io/MachineLearning/doc/web/course.html
|
||||
|
||||
### Week 35 August 30-September 3
|
||||
- Lab Wednesday: Work on exercises 1-3 for week 35
|
||||
- Thursday: Review of ordinary Least Squares with applications and discussion of Ridge Regression and Singular Value Decomposition
|
||||
- Video of lecture Thursday at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember2.mp4?vrtx=view-as-webpage.
|
||||
- Friday: Analysis of Ridge and Lasso Regression and links with Singular Value Decomposition
|
||||
- Video of lecture Friday at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember3.mp4?vrtx=view-as-webpage
|
||||
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 35 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- HTF chapter 3. GBC chapters 1 and and sections 3.1-3.11 and 5.1
|
||||
- CMB sections 1.1 and 3.1
|
||||
|
||||
|
||||
### Week 36 September 6-10
|
||||
- Lab Wednesday: Exercises 1 and 2 from week 36
|
||||
- Lecture Thursday: Summary from last week on SVD, Statistics, probability theory and linear regression
|
||||
- Video of Lecture https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember9.mp4?vrtx=view-as-webpage
|
||||
- Friday: Linear Regression and links with Statistics, Resampling methods and presentation of first project.
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureSeptember10.mp4?vrtx=view-as-webpage
|
||||
|
||||
- Reading recommendations:
|
||||
- Lectures on Regression for week 36 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Bishop 1.1, 1.2, 2.1, 2.2, 2.3 and 3.1
|
||||
- Hastie et al chapter 3
|
||||
|
||||
### Week 37 September 13-17
|
||||
- Lab Wednesday: Work on Project 1
|
||||
- Lecture Thursday: Resampling methods, cross-validation and Bootstrap
|
||||
- Thursday September 16: Summary of Ridge and Lasso with examples and start resampling techniques
|
||||
- Video of Lecture, first part at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember16Firstpart.mp4?vrtx=view-as-webpage"
|
||||
- Video of Lecture, second part at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember16SecondPart.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: More on Resampling methods and summary of linear regression
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember17.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- Lectures on Resampling methods for week 37 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Bishop 1.3 (cross-validation) and 3.2 (bias-variance tradeoff)
|
||||
- Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation) and 7.11 (bootstrap)
|
||||
- Goodfellow et al discuss some of these topics in sections 5.2-5.5.
|
||||
|
||||
|
||||
### Week 38 September 20-24
|
||||
- Lab Wednesday: Work on Project 1
|
||||
- Lecture Thursday: Classification problems and Logistic Regression, from binary cases to several categories
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureSeptember23.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Logistic Regression and gradient optimization
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember24.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 38 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Bishop 4.1, 4.2 and 4.3. Not all the material is relevant or will be covered. Section 4.3 is the most relevant, but 4.1 and 4.2 give interesting background readings for logistic regression
|
||||
- Hastie et al 4.1, 4.2 and 4.3 on logistic regression
|
||||
- For a good discussion on gradient methods, see Goodfellow et al section 4.3-4.5 and chapter 8. We will come back to the latter chapter in our discussion of Neural networks as well.
|
||||
|
||||
### Week 39 September 27- October 1
|
||||
- Lab Wednesday: Work on Project 1
|
||||
- Lecture Thursday: Gradient Optimization methods
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureSeptember30.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Gradient methods
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober1.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 39 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- For a good discussion on gradient methods, see Goodfellow et al section 4.3-4.5 and chapter 8. We will come back to the latter chapter in our discussion of Neural networks as well.
|
||||
|
||||
|
||||
|
||||
### Week 40 October 4-8
|
||||
- Lab Wednesday: Wrap up project 1
|
||||
- Lecture Thursday: Stochastic gradient descent, automatic differentiation and start discussion of feed-forward Neural Network code for regression and classification
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober7.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Deep Learning and Neural Networks: the back propagation algorithm
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober8.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 40 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- For neural networks we recommend Goodfellow et al chapters 6 and 7 and Bishop 5.1-5.4
|
||||
- For stochastic gradient descent we recommend Goodfellow et al chapter 8
|
||||
|
||||
### Week 41 October 11-15
|
||||
- Lab Wednesday: Work on project 2
|
||||
- Lecture Thursday: Deep learning and Neural Networks, developing a code for Neural Networks
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober14.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Tensorflow and the mathematics of neural network
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureOctober15.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 41 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- For neural networks we recommend Goodfellow et al chapters 6 and 7. For CNNs, see Goodfellow et al chapter 9. chapter 11 and 12 on practicalities and applications
|
||||
|
||||
|
||||
### Week 42 October 18-22
|
||||
- Lab Wednesday: Work on project 2
|
||||
- Lecture Thursday: Solving differential equations with neural networks and start Convolutional Neural Networks and classification problems
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober21.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Convolutional Neural Networks and classification problems
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 42 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- For neural networks we recommend Goodfellow et al chapters 6 and 7. For CNNs, see Goodfellow et al chapter 9. See also chapter 11 and 12 on practicalities and applications
|
||||
|
||||
### Week 43 October 25-29
|
||||
- Lab Wednesday: Work on project 2
|
||||
- Lecture Thursday: Recurrent Neural Networks
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober28.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Recurrent Neural Networks and time series and principal component analysis (PCA)
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureOctober29.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 43 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- For RNNs, see Goodfellow et al chapter 10 and discussions in chapter 11 and 12 on practicalities and applications
|
||||
- For PCA, see lecture notes chapter 11 and Geron's text chapter 8
|
||||
### Week 44 November 1-5
|
||||
- Lab Wednesday: Work on project 2
|
||||
- Lecture Thursday: Summary on PCA and discussion of Clustering for unsupervised learning. Decision trees, classification and regression
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureNovember4.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Decision trees, basic algorithms
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureNovember5.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 44 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Hastie et al sections 9.1 and 9.2. Geron's text chapter 6 (Decision trees) and chapter 8 on PCA and Clustering
|
||||
|
||||
### Week 45 November 8-12
|
||||
- Lab Wednesday: Work on project 2, project 3 available. Deadline project 2 is November 15.
|
||||
- Lecture Thursday: Ensemble methods, bagging and random forests
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureNovember11.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Boosting and gradient boosting
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureNovember12.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 45 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Hastie et al chapter 10
|
||||
|
||||
### Week 46 November 15-19
|
||||
- Lab Wednesday: Work on project 3
|
||||
- Lecture Thursday: Support Vector machines
|
||||
- Lecture Friday: Workshop on project 3
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureNovember19.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 46 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Hastie et al chapter 12
|
||||
|
||||
### Week 47 November 22-26
|
||||
- Lab Wednesday: Work on project 3
|
||||
- Lecture Thursday: Support Vector Machines
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureNovember25.mp4?vrtx=view-as-webpage
|
||||
- Lecture Friday: Support Vector Machines and Summary of course
|
||||
- Video of Lecture at https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h21/forelesningsvideoer/LectureNovember26.mp4?vrtx=view-as-webpage
|
||||
- Reading recommendations:
|
||||
- See lecture notes for week 47 at https://compphysics.github.io/MachineLearning/doc/web/course.html.
|
||||
- Geron's chapter 5.
|
||||
- Hastie et al Chapter 12 (sections 12.1-12.3 are the most relevant ones)
|
||||
- Bishop chapter 7, with sections 7.1 and 7.2 as the essential ones
|
||||
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,36 @@
|
||||
# Teachers and Grading
|
||||
|
||||
|
||||
## Instructor information
|
||||
* _Name_: Morten Hjorth-Jensen
|
||||
* _Email_: morten.hjorth-jensen@fys.uio.no
|
||||
* _Phone_: +47-48257387
|
||||
* _Office_: Department of Physics, University of Oslo, Eastern wing, room FØ470
|
||||
* _Office hours_: *Anytime*! Feel free to send an email for planning. Both in person meetings or digital meetings are possible.
|
||||
|
||||
## Teaching Assistants Fall semester 2021
|
||||
* Øyvind Sigmundson Schøyen, oyvinssc@student.matnat.uio.no
|
||||
* Stian Bilek, stian.bilek@fys.uio.no
|
||||
* Linus Ekstrøm, linueks@gmail.com, linus.ekstrom@fys.uio.no
|
||||
* Nicholas Karlsen, nicholaskarlsen1102@gmail.com, nicholas.karlsen@fys.uio.no
|
||||
* Bendik Steinsvåg Dalen, b.s.dalen@fys.uio.no
|
||||
* Philip Karim Sørli Niane, p.k.s.niane@fys.uio.no
|
||||
|
||||
|
||||
|
||||
## Grading
|
||||
Grading scale: Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. There are three projects which are graded and each project counts 1/3 of the final grade. The total score is thus the average from all three projects.
|
||||
|
||||
The final number of points is based on the average of all projects (including eventual additional points) and the grade follows the following table:
|
||||
|
||||
* 92-100 points: A
|
||||
* 77-91 points: B
|
||||
* 58-76 points: C
|
||||
* 46-57 points: D
|
||||
* 40-45 points: E
|
||||
* 0-39 points: F-failed
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -0,0 +1,44 @@
|
||||
|
||||
## Textbooks
|
||||
|
||||
_Recommended textbooks_:
|
||||
The lecture notes are collected as a jupyter-book at https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html. In addition to the electure notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts.
|
||||
- Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, https://www.springer.com/gp/book/9780387310732. This is the main textbook and this course covers chapters 1-7, 11 and 12. You can download for free the textbook in PDF format at https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf
|
||||
- Ian Goodfellow, Yoshua Bengio, and Aaron Courville. The different chapters are available for free at https://www.deeplearningbook.org/. Chapters 2-14 are highly recommended. The lectures follow to a larg extent this text.
|
||||
The weekly plans will include reading suggestions from these two textbooks.
|
||||
_Additional textbooks_:
|
||||
- Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer, https://www.springer.com/gp/book/9780387848570. This is a well-known text and serves as additional literature.
|
||||
- Aurelien Geron, Hands‑On Machine Learning with Scikit‑Learn and TensorFlow, O'Reilly, https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/. This text is very useful since it contains many code examples and hands-on applications of all algorithms discussed in this course.
|
||||
|
||||
|
||||
|
||||
|
||||
_General learning book on statistical analysis_:
|
||||
- Christian Robert and George Casella, Monte Carlo Statistical Methods, Springer
|
||||
- Peter Hoff, A first course in Bayesian statistical models, Springer
|
||||
|
||||
_General Machine Learning Books_:
|
||||
- Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press
|
||||
- David J.C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press
|
||||
- David Barber, Bayesian Reasoning and Machine Learning, Cambridge University Press
|
||||
|
||||
|
||||
|
||||
## Links to relevant courses at the University of Oslo
|
||||
The link here https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/ gives an excellent overview of courses on Machine learning at UiO.
|
||||
|
||||
- _STK2100 Machine learning and statistical methods for prediction and classification_ http://www.uio.no/studier/emner/matnat/math/STK2100/index-eng.html.
|
||||
- _IN3050 Introduction to Artificial Intelligence and Machine Learning_ https://www.uio.no/studier/emner/matnat/ifi/IN3050/index-eng.html. Introductory course in machine learning and AI with an algorithmic approach.
|
||||
- _STK-INF3000/4000 Selected Topics in Data Science_ http://www.uio.no/studier/emner/matnat/math/STK-INF3000/index-eng.html. The course provides insight into selected contemporary relevant topics within Data Science.
|
||||
- _IN4080 Natural Language Processing_ https://www.uio.no/studier/emner/matnat/ifi/IN4080/index.html. Probabilistic and machine learning techniques applied to natural language processing.
|
||||
- _STK-IN4300 Statistical learning methods in Data Science_ https://www.uio.no/studier/emner/matnat/math/STK-IN4300/index-eng.html. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.
|
||||
- _INF4490 Biologically Inspired Computing_ http://www.uio.no/studier/emner/matnat/ifi/INF4490/. An introduction to self-adapting methods also called artificial intelligence or machine learning.
|
||||
- _IN-STK5000 Adaptive Methods for Data-Based Decision Making_ https://www.uio.no/studier/emner/matnat/ifi/IN-STK5000/index-eng.html. Methods for adaptive collection and processing of data based on machine learning techniques.
|
||||
- _IN5400/INF5860 Machine Learning for Image Analysis_ https://www.uio.no/studier/emner/matnat/ifi/IN5400/. An introduction to deep learning with particular emphasis on applications within Image analysis, but useful for other application areas too.
|
||||
- _TEK5040 Deep learning for autonomous systems_ https://www.uio.no/studier/emner/matnat/its/TEK5040/. The course addresses advanced algorithms and architectures for deep learning with neural networks. The course provides an introduction to how deep-learning techniques can be used in the construction of key parts of advanced autonomous systems that exist in physical environments and cyber environments.
|
||||
- _STK4051 Computational Statistics_ https://www.uio.no/studier/emner/matnat/math/STK4051/index-eng.html
|
||||
- _STK4021 Applied Bayesian Analysis and Numerical Methods_ https://www.uio.no/studier/emner/matnat/math/STK4021/
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -0,0 +1,904 @@
|
||||
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|
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|
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|
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|
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*
|
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* :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
|
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|
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|
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|
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|
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||||
}
|
||||
|
||||
ul.keywordmatches li.goodmatch a {
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
/* -- index page ------------------------------------------------------------ */
|
||||
|
||||
table.contentstable {
|
||||
width: 90%;
|
||||
margin-left: auto;
|
||||
margin-right: auto;
|
||||
}
|
||||
|
||||
table.contentstable p.biglink {
|
||||
line-height: 150%;
|
||||
}
|
||||
|
||||
a.biglink {
|
||||
font-size: 1.3em;
|
||||
}
|
||||
|
||||
span.linkdescr {
|
||||
font-style: italic;
|
||||
padding-top: 5px;
|
||||
font-size: 90%;
|
||||
}
|
||||
|
||||
/* -- general index --------------------------------------------------------- */
|
||||
|
||||
table.indextable {
|
||||
width: 100%;
|
||||
}
|
||||
|
||||
table.indextable td {
|
||||
text-align: left;
|
||||
vertical-align: top;
|
||||
}
|
||||
|
||||
table.indextable ul {
|
||||
margin-top: 0;
|
||||
margin-bottom: 0;
|
||||
list-style-type: none;
|
||||
}
|
||||
|
||||
table.indextable > tbody > tr > td > ul {
|
||||
padding-left: 0em;
|
||||
}
|
||||
|
||||
table.indextable tr.pcap {
|
||||
height: 10px;
|
||||
}
|
||||
|
||||
table.indextable tr.cap {
|
||||
margin-top: 10px;
|
||||
background-color: #f2f2f2;
|
||||
}
|
||||
|
||||
img.toggler {
|
||||
margin-right: 3px;
|
||||
margin-top: 3px;
|
||||
cursor: pointer;
|
||||
}
|
||||
|
||||
div.modindex-jumpbox {
|
||||
border-top: 1px solid #ddd;
|
||||
border-bottom: 1px solid #ddd;
|
||||
margin: 1em 0 1em 0;
|
||||
padding: 0.4em;
|
||||
}
|
||||
|
||||
div.genindex-jumpbox {
|
||||
border-top: 1px solid #ddd;
|
||||
border-bottom: 1px solid #ddd;
|
||||
margin: 1em 0 1em 0;
|
||||
padding: 0.4em;
|
||||
}
|
||||
|
||||
/* -- domain module index --------------------------------------------------- */
|
||||
|
||||
table.modindextable td {
|
||||
padding: 2px;
|
||||
border-collapse: collapse;
|
||||
}
|
||||
|
||||
/* -- general body styles --------------------------------------------------- */
|
||||
|
||||
div.body {
|
||||
min-width: 450px;
|
||||
max-width: 800px;
|
||||
}
|
||||
|
||||
div.body p, div.body dd, div.body li, div.body blockquote {
|
||||
-moz-hyphens: auto;
|
||||
-ms-hyphens: auto;
|
||||
-webkit-hyphens: auto;
|
||||
hyphens: auto;
|
||||
}
|
||||
|
||||
a.headerlink {
|
||||
visibility: hidden;
|
||||
}
|
||||
|
||||
a.brackets:before,
|
||||
span.brackets > a:before{
|
||||
content: "[";
|
||||
}
|
||||
|
||||
a.brackets:after,
|
||||
span.brackets > a:after {
|
||||
content: "]";
|
||||
}
|
||||
|
||||
h1:hover > a.headerlink,
|
||||
h2:hover > a.headerlink,
|
||||
h3:hover > a.headerlink,
|
||||
h4:hover > a.headerlink,
|
||||
h5:hover > a.headerlink,
|
||||
h6:hover > a.headerlink,
|
||||
dt:hover > a.headerlink,
|
||||
caption:hover > a.headerlink,
|
||||
p.caption:hover > a.headerlink,
|
||||
div.code-block-caption:hover > a.headerlink {
|
||||
visibility: visible;
|
||||
}
|
||||
|
||||
div.body p.caption {
|
||||
text-align: inherit;
|
||||
}
|
||||
|
||||
div.body td {
|
||||
text-align: left;
|
||||
}
|
||||
|
||||
.first {
|
||||
margin-top: 0 !important;
|
||||
}
|
||||
|
||||
p.rubric {
|
||||
margin-top: 30px;
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
img.align-left, figure.align-left, .figure.align-left, object.align-left {
|
||||
clear: left;
|
||||
float: left;
|
||||
margin-right: 1em;
|
||||
}
|
||||
|
||||
img.align-right, figure.align-right, .figure.align-right, object.align-right {
|
||||
clear: right;
|
||||
float: right;
|
||||
margin-left: 1em;
|
||||
}
|
||||
|
||||
img.align-center, figure.align-center, .figure.align-center, object.align-center {
|
||||
display: block;
|
||||
margin-left: auto;
|
||||
margin-right: auto;
|
||||
}
|
||||
|
||||
img.align-default, figure.align-default, .figure.align-default {
|
||||
display: block;
|
||||
margin-left: auto;
|
||||
margin-right: auto;
|
||||
}
|
||||
|
||||
.align-left {
|
||||
text-align: left;
|
||||
}
|
||||
|
||||
.align-center {
|
||||
text-align: center;
|
||||
}
|
||||
|
||||
.align-default {
|
||||
text-align: center;
|
||||
}
|
||||
|
||||
.align-right {
|
||||
text-align: right;
|
||||
}
|
||||
|
||||
/* -- sidebars -------------------------------------------------------------- */
|
||||
|
||||
div.sidebar,
|
||||
aside.sidebar {
|
||||
margin: 0 0 0.5em 1em;
|
||||
border: 1px solid #ddb;
|
||||
padding: 7px;
|
||||
background-color: #ffe;
|
||||
width: 40%;
|
||||
float: right;
|
||||
clear: right;
|
||||
overflow-x: auto;
|
||||
}
|
||||
|
||||
p.sidebar-title {
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
div.admonition, div.topic, blockquote {
|
||||
clear: left;
|
||||
}
|
||||
|
||||
/* -- topics ---------------------------------------------------------------- */
|
||||
|
||||
div.topic {
|
||||
border: 1px solid #ccc;
|
||||
padding: 7px;
|
||||
margin: 10px 0 10px 0;
|
||||
}
|
||||
|
||||
p.topic-title {
|
||||
font-size: 1.1em;
|
||||
font-weight: bold;
|
||||
margin-top: 10px;
|
||||
}
|
||||
|
||||
/* -- admonitions ----------------------------------------------------------- */
|
||||
|
||||
div.admonition {
|
||||
margin-top: 10px;
|
||||
margin-bottom: 10px;
|
||||
padding: 7px;
|
||||
}
|
||||
|
||||
div.admonition dt {
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
p.admonition-title {
|
||||
margin: 0px 10px 5px 0px;
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
div.body p.centered {
|
||||
text-align: center;
|
||||
margin-top: 25px;
|
||||
}
|
||||
|
||||
/* -- content of sidebars/topics/admonitions -------------------------------- */
|
||||
|
||||
div.sidebar > :last-child,
|
||||
aside.sidebar > :last-child,
|
||||
div.topic > :last-child,
|
||||
div.admonition > :last-child {
|
||||
margin-bottom: 0;
|
||||
}
|
||||
|
||||
div.sidebar::after,
|
||||
aside.sidebar::after,
|
||||
div.topic::after,
|
||||
div.admonition::after,
|
||||
blockquote::after {
|
||||
display: block;
|
||||
content: '';
|
||||
clear: both;
|
||||
}
|
||||
|
||||
/* -- tables ---------------------------------------------------------------- */
|
||||
|
||||
table.docutils {
|
||||
margin-top: 10px;
|
||||
margin-bottom: 10px;
|
||||
border: 0;
|
||||
border-collapse: collapse;
|
||||
}
|
||||
|
||||
table.align-center {
|
||||
margin-left: auto;
|
||||
margin-right: auto;
|
||||
}
|
||||
|
||||
table.align-default {
|
||||
margin-left: auto;
|
||||
margin-right: auto;
|
||||
}
|
||||
|
||||
table caption span.caption-number {
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
table caption span.caption-text {
|
||||
}
|
||||
|
||||
table.docutils td, table.docutils th {
|
||||
padding: 1px 8px 1px 5px;
|
||||
border-top: 0;
|
||||
border-left: 0;
|
||||
border-right: 0;
|
||||
border-bottom: 1px solid #aaa;
|
||||
}
|
||||
|
||||
table.footnote td, table.footnote th {
|
||||
border: 0 !important;
|
||||
}
|
||||
|
||||
th {
|
||||
text-align: left;
|
||||
padding-right: 5px;
|
||||
}
|
||||
|
||||
table.citation {
|
||||
border-left: solid 1px gray;
|
||||
margin-left: 1px;
|
||||
}
|
||||
|
||||
table.citation td {
|
||||
border-bottom: none;
|
||||
}
|
||||
|
||||
th > :first-child,
|
||||
td > :first-child {
|
||||
margin-top: 0px;
|
||||
}
|
||||
|
||||
th > :last-child,
|
||||
td > :last-child {
|
||||
margin-bottom: 0px;
|
||||
}
|
||||
|
||||
/* -- figures --------------------------------------------------------------- */
|
||||
|
||||
div.figure, figure {
|
||||
margin: 0.5em;
|
||||
padding: 0.5em;
|
||||
}
|
||||
|
||||
div.figure p.caption, figcaption {
|
||||
padding: 0.3em;
|
||||
}
|
||||
|
||||
div.figure p.caption span.caption-number,
|
||||
figcaption span.caption-number {
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
div.figure p.caption span.caption-text,
|
||||
figcaption span.caption-text {
|
||||
}
|
||||
|
||||
/* -- field list styles ----------------------------------------------------- */
|
||||
|
||||
table.field-list td, table.field-list th {
|
||||
border: 0 !important;
|
||||
}
|
||||
|
||||
.field-list ul {
|
||||
margin: 0;
|
||||
padding-left: 1em;
|
||||
}
|
||||
|
||||
.field-list p {
|
||||
margin: 0;
|
||||
}
|
||||
|
||||
.field-name {
|
||||
-moz-hyphens: manual;
|
||||
-ms-hyphens: manual;
|
||||
-webkit-hyphens: manual;
|
||||
hyphens: manual;
|
||||
}
|
||||
|
||||
/* -- hlist styles ---------------------------------------------------------- */
|
||||
|
||||
table.hlist {
|
||||
margin: 1em 0;
|
||||
}
|
||||
|
||||
table.hlist td {
|
||||
vertical-align: top;
|
||||
}
|
||||
|
||||
/* -- object description styles --------------------------------------------- */
|
||||
|
||||
.sig {
|
||||
font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
|
||||
}
|
||||
|
||||
.sig-name, code.descname {
|
||||
background-color: transparent;
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
.sig-name {
|
||||
font-size: 1.1em;
|
||||
}
|
||||
|
||||
code.descname {
|
||||
font-size: 1.2em;
|
||||
}
|
||||
|
||||
.sig-prename, code.descclassname {
|
||||
background-color: transparent;
|
||||
}
|
||||
|
||||
.optional {
|
||||
font-size: 1.3em;
|
||||
}
|
||||
|
||||
.sig-paren {
|
||||
font-size: larger;
|
||||
}
|
||||
|
||||
.sig-param.n {
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
/* C++ specific styling */
|
||||
|
||||
.sig-inline.c-texpr,
|
||||
.sig-inline.cpp-texpr {
|
||||
font-family: unset;
|
||||
}
|
||||
|
||||
.sig.c .k, .sig.c .kt,
|
||||
.sig.cpp .k, .sig.cpp .kt {
|
||||
color: #0033B3;
|
||||
}
|
||||
|
||||
.sig.c .m,
|
||||
.sig.cpp .m {
|
||||
color: #1750EB;
|
||||
}
|
||||
|
||||
.sig.c .s, .sig.c .sc,
|
||||
.sig.cpp .s, .sig.cpp .sc {
|
||||
color: #067D17;
|
||||
}
|
||||
|
||||
|
||||
/* -- other body styles ----------------------------------------------------- */
|
||||
|
||||
ol.arabic {
|
||||
list-style: decimal;
|
||||
}
|
||||
|
||||
ol.loweralpha {
|
||||
list-style: lower-alpha;
|
||||
}
|
||||
|
||||
ol.upperalpha {
|
||||
list-style: upper-alpha;
|
||||
}
|
||||
|
||||
ol.lowerroman {
|
||||
list-style: lower-roman;
|
||||
}
|
||||
|
||||
ol.upperroman {
|
||||
list-style: upper-roman;
|
||||
}
|
||||
|
||||
:not(li) > ol > li:first-child > :first-child,
|
||||
:not(li) > ul > li:first-child > :first-child {
|
||||
margin-top: 0px;
|
||||
}
|
||||
|
||||
:not(li) > ol > li:last-child > :last-child,
|
||||
:not(li) > ul > li:last-child > :last-child {
|
||||
margin-bottom: 0px;
|
||||
}
|
||||
|
||||
ol.simple ol p,
|
||||
ol.simple ul p,
|
||||
ul.simple ol p,
|
||||
ul.simple ul p {
|
||||
margin-top: 0;
|
||||
}
|
||||
|
||||
ol.simple > li:not(:first-child) > p,
|
||||
ul.simple > li:not(:first-child) > p {
|
||||
margin-top: 0;
|
||||
}
|
||||
|
||||
ol.simple p,
|
||||
ul.simple p {
|
||||
margin-bottom: 0;
|
||||
}
|
||||
|
||||
dl.footnote > dt,
|
||||
dl.citation > dt {
|
||||
float: left;
|
||||
margin-right: 0.5em;
|
||||
}
|
||||
|
||||
dl.footnote > dd,
|
||||
dl.citation > dd {
|
||||
margin-bottom: 0em;
|
||||
}
|
||||
|
||||
dl.footnote > dd:after,
|
||||
dl.citation > dd:after {
|
||||
content: "";
|
||||
clear: both;
|
||||
}
|
||||
|
||||
dl.field-list {
|
||||
display: grid;
|
||||
grid-template-columns: fit-content(30%) auto;
|
||||
}
|
||||
|
||||
dl.field-list > dt {
|
||||
font-weight: bold;
|
||||
word-break: break-word;
|
||||
padding-left: 0.5em;
|
||||
padding-right: 5px;
|
||||
}
|
||||
|
||||
dl.field-list > dt:after {
|
||||
content: ":";
|
||||
}
|
||||
|
||||
dl.field-list > dd {
|
||||
padding-left: 0.5em;
|
||||
margin-top: 0em;
|
||||
margin-left: 0em;
|
||||
margin-bottom: 0em;
|
||||
}
|
||||
|
||||
dl {
|
||||
margin-bottom: 15px;
|
||||
}
|
||||
|
||||
dd > :first-child {
|
||||
margin-top: 0px;
|
||||
}
|
||||
|
||||
dd ul, dd table {
|
||||
margin-bottom: 10px;
|
||||
}
|
||||
|
||||
dd {
|
||||
margin-top: 3px;
|
||||
margin-bottom: 10px;
|
||||
margin-left: 30px;
|
||||
}
|
||||
|
||||
dl > dd:last-child,
|
||||
dl > dd:last-child > :last-child {
|
||||
margin-bottom: 0;
|
||||
}
|
||||
|
||||
dt:target, span.highlighted {
|
||||
background-color: #fbe54e;
|
||||
}
|
||||
|
||||
rect.highlighted {
|
||||
fill: #fbe54e;
|
||||
}
|
||||
|
||||
dl.glossary dt {
|
||||
font-weight: bold;
|
||||
font-size: 1.1em;
|
||||
}
|
||||
|
||||
.versionmodified {
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
.system-message {
|
||||
background-color: #fda;
|
||||
padding: 5px;
|
||||
border: 3px solid red;
|
||||
}
|
||||
|
||||
.footnote:target {
|
||||
background-color: #ffa;
|
||||
}
|
||||
|
||||
.line-block {
|
||||
display: block;
|
||||
margin-top: 1em;
|
||||
margin-bottom: 1em;
|
||||
}
|
||||
|
||||
.line-block .line-block {
|
||||
margin-top: 0;
|
||||
margin-bottom: 0;
|
||||
margin-left: 1.5em;
|
||||
}
|
||||
|
||||
.guilabel, .menuselection {
|
||||
font-family: sans-serif;
|
||||
}
|
||||
|
||||
.accelerator {
|
||||
text-decoration: underline;
|
||||
}
|
||||
|
||||
.classifier {
|
||||
font-style: oblique;
|
||||
}
|
||||
|
||||
.classifier:before {
|
||||
font-style: normal;
|
||||
margin: 0.5em;
|
||||
content: ":";
|
||||
}
|
||||
|
||||
abbr, acronym {
|
||||
border-bottom: dotted 1px;
|
||||
cursor: help;
|
||||
}
|
||||
|
||||
/* -- code displays --------------------------------------------------------- */
|
||||
|
||||
pre {
|
||||
overflow: auto;
|
||||
overflow-y: hidden; /* fixes display issues on Chrome browsers */
|
||||
}
|
||||
|
||||
pre, div[class*="highlight-"] {
|
||||
clear: both;
|
||||
}
|
||||
|
||||
span.pre {
|
||||
-moz-hyphens: none;
|
||||
-ms-hyphens: none;
|
||||
-webkit-hyphens: none;
|
||||
hyphens: none;
|
||||
}
|
||||
|
||||
div[class*="highlight-"] {
|
||||
margin: 1em 0;
|
||||
}
|
||||
|
||||
td.linenos pre {
|
||||
border: 0;
|
||||
background-color: transparent;
|
||||
color: #aaa;
|
||||
}
|
||||
|
||||
table.highlighttable {
|
||||
display: block;
|
||||
}
|
||||
|
||||
table.highlighttable tbody {
|
||||
display: block;
|
||||
}
|
||||
|
||||
table.highlighttable tr {
|
||||
display: flex;
|
||||
}
|
||||
|
||||
table.highlighttable td {
|
||||
margin: 0;
|
||||
padding: 0;
|
||||
}
|
||||
|
||||
table.highlighttable td.linenos {
|
||||
padding-right: 0.5em;
|
||||
}
|
||||
|
||||
table.highlighttable td.code {
|
||||
flex: 1;
|
||||
overflow: hidden;
|
||||
}
|
||||
|
||||
.highlight .hll {
|
||||
display: block;
|
||||
}
|
||||
|
||||
div.highlight pre,
|
||||
table.highlighttable pre {
|
||||
margin: 0;
|
||||
}
|
||||
|
||||
div.code-block-caption + div {
|
||||
margin-top: 0;
|
||||
}
|
||||
|
||||
div.code-block-caption {
|
||||
margin-top: 1em;
|
||||
padding: 2px 5px;
|
||||
font-size: small;
|
||||
}
|
||||
|
||||
div.code-block-caption code {
|
||||
background-color: transparent;
|
||||
}
|
||||
|
||||
table.highlighttable td.linenos,
|
||||
span.linenos,
|
||||
div.highlight span.gp { /* gp: Generic.Prompt */
|
||||
user-select: none;
|
||||
-webkit-user-select: text; /* Safari fallback only */
|
||||
-webkit-user-select: none; /* Chrome/Safari */
|
||||
-moz-user-select: none; /* Firefox */
|
||||
-ms-user-select: none; /* IE10+ */
|
||||
}
|
||||
|
||||
div.code-block-caption span.caption-number {
|
||||
padding: 0.1em 0.3em;
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
div.code-block-caption span.caption-text {
|
||||
}
|
||||
|
||||
div.literal-block-wrapper {
|
||||
margin: 1em 0;
|
||||
}
|
||||
|
||||
code.xref, a code {
|
||||
background-color: transparent;
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
|
||||
background-color: transparent;
|
||||
}
|
||||
|
||||
.viewcode-link {
|
||||
float: right;
|
||||
}
|
||||
|
||||
.viewcode-back {
|
||||
float: right;
|
||||
font-family: sans-serif;
|
||||
}
|
||||
|
||||
div.viewcode-block:target {
|
||||
margin: -1px -10px;
|
||||
padding: 0 10px;
|
||||
}
|
||||
|
||||
/* -- math display ---------------------------------------------------------- */
|
||||
|
||||
img.math {
|
||||
vertical-align: middle;
|
||||
}
|
||||
|
||||
div.body div.math p {
|
||||
text-align: center;
|
||||
}
|
||||
|
||||
span.eqno {
|
||||
float: right;
|
||||
}
|
||||
|
||||
span.eqno a.headerlink {
|
||||
position: absolute;
|
||||
z-index: 1;
|
||||
}
|
||||
|
||||
div.math:hover a.headerlink {
|
||||
visibility: visible;
|
||||
}
|
||||
|
||||
/* -- printout stylesheet --------------------------------------------------- */
|
||||
|
||||
@media print {
|
||||
div.document,
|
||||
div.documentwrapper,
|
||||
div.bodywrapper {
|
||||
margin: 0 !important;
|
||||
width: 100%;
|
||||
}
|
||||
|
||||
div.sphinxsidebar,
|
||||
div.related,
|
||||
div.footer,
|
||||
#top-link {
|
||||
display: none;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,4 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-check" width="44" height="44" viewBox="0 0 24 24" stroke-width="2" stroke="#22863a" fill="none" stroke-linecap="round" stroke-linejoin="round">
|
||||
<path stroke="none" d="M0 0h24v24H0z" fill="none"/>
|
||||
<path d="M5 12l5 5l10 -10" />
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 313 B |
File diff suppressed because one or more lines are too long
@@ -0,0 +1,5 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-clipboard" width="44" height="44" viewBox="0 0 24 24" stroke-width="1.5" stroke="#2c3e50" fill="none" stroke-linecap="round" stroke-linejoin="round">
|
||||
<path stroke="none" d="M0 0h24v24H0z" fill="none"/>
|
||||
<path d="M9 5h-2a2 2 0 0 0 -2 2v12a2 2 0 0 0 2 2h10a2 2 0 0 0 2 -2v-12a2 2 0 0 0 -2 -2h-2" />
|
||||
<rect x="9" y="3" width="6" height="4" rx="2" />
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 434 B |
@@ -0,0 +1,81 @@
|
||||
/* Copy buttons */
|
||||
button.copybtn {
|
||||
position: absolute;
|
||||
display: flex;
|
||||
top: .3em;
|
||||
right: .5em;
|
||||
width: 1.7em;
|
||||
height: 1.7em;
|
||||
opacity: 0;
|
||||
transition: opacity 0.3s, border .3s, background-color .3s;
|
||||
user-select: none;
|
||||
padding: 0;
|
||||
border: none;
|
||||
outline: none;
|
||||
border-radius: 0.4em;
|
||||
border: #e1e1e1 1px solid;
|
||||
background-color: rgb(245, 245, 245);
|
||||
}
|
||||
|
||||
button.copybtn.success {
|
||||
border-color: #22863a;
|
||||
}
|
||||
|
||||
button.copybtn img {
|
||||
width: 100%;
|
||||
padding: .2em;
|
||||
}
|
||||
|
||||
div.highlight {
|
||||
position: relative;
|
||||
}
|
||||
|
||||
.highlight:hover button.copybtn {
|
||||
opacity: 1;
|
||||
}
|
||||
|
||||
.highlight button.copybtn:hover {
|
||||
background-color: rgb(235, 235, 235);
|
||||
}
|
||||
|
||||
.highlight button.copybtn:active {
|
||||
background-color: rgb(187, 187, 187);
|
||||
}
|
||||
|
||||
/**
|
||||
* A minimal CSS-only tooltip copied from:
|
||||
* https://codepen.io/mildrenben/pen/rVBrpK
|
||||
*
|
||||
* To use, write HTML like the following:
|
||||
*
|
||||
* <p class="o-tooltip--left" data-tooltip="Hey">Short</p>
|
||||
*/
|
||||
.o-tooltip--left {
|
||||
position: relative;
|
||||
}
|
||||
|
||||
.o-tooltip--left:after {
|
||||
opacity: 0;
|
||||
visibility: hidden;
|
||||
position: absolute;
|
||||
content: attr(data-tooltip);
|
||||
padding: .2em;
|
||||
font-size: .8em;
|
||||
left: -.2em;
|
||||
background: grey;
|
||||
color: white;
|
||||
white-space: nowrap;
|
||||
z-index: 2;
|
||||
border-radius: 2px;
|
||||
transform: translateX(-102%) translateY(0);
|
||||
transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
|
||||
}
|
||||
|
||||
.o-tooltip--left:hover:after {
|
||||
display: block;
|
||||
opacity: 1;
|
||||
visibility: visible;
|
||||
transform: translateX(-100%) translateY(0);
|
||||
transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
|
||||
transition-delay: .5s;
|
||||
}
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user