Classification and Regression, from linear and logistic regression to neural networks
+
+
+The main aim of this project is to study both classification and
+regression problems, starting with the regression algortihms studied
+in project 1. We will include logistic regresion for classification
+problems and write our own multilayer perceptron code for studying
+both regression and classification problems. The codes developed in
+project 1, including bootstrap and/or cross-validation as well as the
+computation of the mean-squared error and the R2 score function can
+also be utilized (and included in logistic regression and the neural
+network codes) in the present analysis.
+
+
+We will use the Ising model to generate our training data and will
+focus mainly on supervised training. We will follow closely the recent
+article of Mehta et al, arXiv
+1803.08823. This article stands
+out as an excellent review on machine learning (ML) algorithms applied
+to typical physics problems. The added benefit is that each figure and
+model presented in this article is accompanied by its jupyter
+notebook. This
+means that we can start using these and compare with our own
+results. In case you wish to use their data for the Ising model, their
+data can be downloaded from the same link which lists to the jupyter
+notebooks. See also at the end of the project description for more
+information on how to install various Python packages.
+
+
+With the abovementioned configurations we will determine, using first
+various regression methods, the value of the coupling constant for the
+energy of the one-dimensional Ising model. Thereafter, we will use the
+two-dimensional data, but now computed at different temperatures, in
+order to classify the phase of the Ising model. Below the critical
+temperature, the system will be in a so-called ferromagnetic
+phase. Close to the critical temperature, the final magnetization
+becomes smaller and smaller in absolute value while above the critical
+temperature, the net magnetization is zero. This classification case,
+that is the two-dimensional Ising model, will be studied using
+logistic regression and deep neural networks. The aim is to develop
+your own logistic regression code for the classification of the phases
+(this is a binary model) and your multilayer perceptron code for the
+classification and regression case.
+
+
+Feel free to use the notebooks to benchmark your code. If you wish to
+write your own C++ or Fortran program for say a simple neural network
+model and a logistic regression model, please feel free to do so. You can then benchmark your results
+against the above jupyter notebooks.
+
+
Part a): Producing the data
+
+
+You can use the Ising model data from the article of Mehta et al.,
+or generate your own data. If you opt for using your own Ising model
+code, you need to generate \( 10000 \) energy configurations with their
+spin orientations after the system has reached its most likely
+state. These energies and their corresponding spin orientations
+represent then your data. We will use a fixed lattice of \( L\times L =
+40 \times 40 \) spins in two dimensions and \( L=40 \) spins in one
+dimension. Make sure the calculations have been equilibrated. For the
+two-dimensional system, compute the configurations for three values of
+the temperature, namely \( T=0.75 \) (ordered phase), \( T=2.3 \) (near the
+critical point) and \( T=4.0 \) (disordered phase). For the
+one-dimensional system it suffices to compute the various
+configurations for one temperature only, say \( T=2.0 \). These are the
+data you will use to study different ML algorithms. We generate our
+data with \( J=1 \).
+
+
Part b): Estimating the coupling constant of the one-dimensional Ising model
+
+
+We start with the one-dimensional Ising model and use the data we have
+generated with \( J=1 \). Use linear regression, Lasso and Ridge
+regression as described section 6 and in Notebook 4 of Mehta *et
+al.*. Discuss
+the methods and how they perform in computing the coupling constant
+\( J \). Give a critical analysis and discuss how to evaluate the cost
+function. You should feel free to write your own code, see also the
+lecture notes of
+FYS-STK4155,
+in particular te material on least square methods. You can use
+scikit-learn to perform these analyses. See below for instruction on
+how to install scikit-learn.
+
+
Part c): Determine the phase of the two-dimensional Ising model
+
+
+We switch now to binary classification methods and use logistic
+regression to define the phases of the Ising model. Use described
+section 7 and in Notebook 6 of Mehta *et
+al.*. Discuss
+the methods and how they perform. Give a critical analysis and discuss
+how to evaluate the cost function. You should feel free to write
+your own code.
+
+
Part d): Classifying the Ising model phase using neural networks
+
+
+We end the classification problem of the phases of the Ising model by
+employing the algorithm for so-called feed-forward deep neural
+networks (see section 9 of Mehta et al.). The method is described in
+notebook
+12.
+
+
+You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
+
+
+Here follows a brief recipe and recommendation on how to write a report for each
+project.
+
+
+
Give a short description of the nature of the problem and the eventual numerical methods you have used.
+
Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.
+
Include the source code of your program. Comment your program properly.
+
If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.
+
Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.
+
Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.
+
Try to give an interpretation of you results in your answers to the problems.
+
Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.
+
Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.
+
+
+
Format for electronic delivery of report and programs
+
+
+The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file. As programming language we prefer that you choose between C/C++, Fortran2008 or Python. The following prescription should be followed when preparing the report:
+
+
+
Use Devilry to hand in your projects, log in at http://devilry.ifi.uio.no with your normal UiO username and password and choose either 'fysstk3155' or 'fysstk4155'. There you can load up the files within the deadline.
+
Upload only the report file! For the source code file(s) you have developed please provide us with your link to your github domain. The report file should include all of your discussions and a list of the codes you have developed. Do not include library files which are available at the course homepage, unless you have made specific changes to them.
+
In your git repository, please include a folder which contains selected results. These can be in the form of output from your code for a selected set of runs and input parameters.
+
In this and all later projects, you should include tests (for example unit tests) of your code(s).
+
Comments from us on your projects, approval or not, corrections to be made etc can be found under your Devilry domain and are only visible to you and the teachers of the course.
+
+
+Finally,
+we encourage you to collaborate. Optimal working groups consist of
+2-3 students. You can then hand in a common report.
+
+
Software and needed installations
+
+
+If you have Python installed (we recommend Python3) and you feel pretty familiar with installing different packages,
+we recommend that you install the following Python packages via pip as
+
+
+See below for a discussion of tensorflow and scikit-learn.
+
+
+For OSX users we recommend also, 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 (or python for python2.7)
+
+
+etc etc.
+
+
+If you don't want to install various Python packages with their dependencies separately, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely
+
+
+
Anaconda 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
+
Enthought canopy is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.
+
+
+Popular software packages written in Python for ML are
+
+
+
+These are all freely available at their respective GitHub sites. They
+encompass communities of developers in the thousands or more. And the number
+of code developers and contributors keeps increasing.
+
+
Classification and Regression, from linear and logistic regression to neural networks
+
+
+The main aim of this project is to study both classification and
+regression problems, starting with the regression algortihms studied
+in project 1. We will include logistic regresion for classification
+problems and write our own multilayer perceptron code for studying
+both regression and classification problems. The codes developed in
+project 1, including bootstrap and/or cross-validation as well as the
+computation of the mean-squared error and the R2 score function can
+also be utilized (and included in logistic regression and the neural
+network codes) in the present analysis.
+
+
+We will use the Ising model to generate our training data and will
+focus mainly on supervised training. We will follow closely the recent
+article of Mehta et al, arXiv
+1803.08823. This article stands
+out as an excellent review on machine learning (ML) algorithms applied
+to typical physics problems. The added benefit is that each figure and
+model presented in this article is accompanied by its jupyter
+notebook. This
+means that we can start using these and compare with our own
+results. In case you wish to use their data for the Ising model, their
+data can be downloaded from the same link which lists to the jupyter
+notebooks. See also at the end of the project description for more
+information on how to install various Python packages.
+
+
+With the abovementioned configurations we will determine, using first
+various regression methods, the value of the coupling constant for the
+energy of the one-dimensional Ising model. Thereafter, we will use the
+two-dimensional data, but now computed at different temperatures, in
+order to classify the phase of the Ising model. Below the critical
+temperature, the system will be in a so-called ferromagnetic
+phase. Close to the critical temperature, the final magnetization
+becomes smaller and smaller in absolute value while above the critical
+temperature, the net magnetization is zero. This classification case,
+that is the two-dimensional Ising model, will be studied using
+logistic regression and deep neural networks. The aim is to develop
+your own logistic regression code for the classification of the phases
+(this is a binary model) and your multilayer perceptron code for the
+classification and regression case.
+
+
+Feel free to use the notebooks to benchmark your code. If you wish to
+write your own C++ or Fortran program for say a simple neural network
+model and a logistic regression model, please feel free to do so. You can then benchmark your results
+against the above jupyter notebooks.
+
+
Part a): Producing the data
+
+
+You can use the Ising model data from the article of Mehta et al.,
+or generate your own data. If you opt for using your own Ising model
+code, you need to generate \( 10000 \) energy configurations with their
+spin orientations after the system has reached its most likely
+state. These energies and their corresponding spin orientations
+represent then your data. We will use a fixed lattice of \( L\times L =
+40 \times 40 \) spins in two dimensions and \( L=40 \) spins in one
+dimension. Make sure the calculations have been equilibrated. For the
+two-dimensional system, compute the configurations for three values of
+the temperature, namely \( T=0.75 \) (ordered phase), \( T=2.3 \) (near the
+critical point) and \( T=4.0 \) (disordered phase). For the
+one-dimensional system it suffices to compute the various
+configurations for one temperature only, say \( T=2.0 \). These are the
+data you will use to study different ML algorithms. We generate our
+data with \( J=1 \).
+
+
Part b): Estimating the coupling constant of the one-dimensional Ising model
+
+
+We start with the one-dimensional Ising model and use the data we have
+generated with \( J=1 \). Use linear regression, Lasso and Ridge
+regression as described section 6 and in Notebook 4 of Mehta *et
+al.*. Discuss
+the methods and how they perform in computing the coupling constant
+\( J \). Give a critical analysis and discuss how to evaluate the cost
+function. You should feel free to write your own code, see also the
+lecture notes of
+FYS-STK4155,
+in particular te material on least square methods. You can use
+scikit-learn to perform these analyses. See below for instruction on
+how to install scikit-learn.
+
+
Part c): Determine the phase of the two-dimensional Ising model
+
+
+We switch now to binary classification methods and use logistic
+regression to define the phases of the Ising model. Use described
+section 7 and in Notebook 6 of Mehta *et
+al.*. Discuss
+the methods and how they perform. Give a critical analysis and discuss
+how to evaluate the cost function. You should feel free to write
+your own code.
+
+
Part d): Classifying the Ising model phase using neural networks
+
+
+We end the classification problem of the phases of the Ising model by
+employing the algorithm for so-called feed-forward deep neural
+networks (see section 9 of Mehta et al.). The method is described in
+notebook
+12.
+
+
+You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
+
+
+Here follows a brief recipe and recommendation on how to write a report for each
+project.
+
+
+
Give a short description of the nature of the problem and the eventual numerical methods you have used.
+
Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.
+
Include the source code of your program. Comment your program properly.
+
If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.
+
Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.
+
Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.
+
Try to give an interpretation of you results in your answers to the problems.
+
Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.
+
Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.
+
+
+
Format for electronic delivery of report and programs
+
+
+The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file. As programming language we prefer that you choose between C/C++, Fortran2008 or Python. The following prescription should be followed when preparing the report:
+
+
+
Use Devilry to hand in your projects, log in at http://devilry.ifi.uio.no with your normal UiO username and password and choose either 'fysstk3155' or 'fysstk4155'. There you can load up the files within the deadline.
+
Upload only the report file! For the source code file(s) you have developed please provide us with your link to your github domain. The report file should include all of your discussions and a list of the codes you have developed. Do not include library files which are available at the course homepage, unless you have made specific changes to them.
+
In your git repository, please include a folder which contains selected results. These can be in the form of output from your code for a selected set of runs and input parameters.
+
In this and all later projects, you should include tests (for example unit tests) of your code(s).
+
Comments from us on your projects, approval or not, corrections to be made etc can be found under your Devilry domain and are only visible to you and the teachers of the course.
+
+
+Finally,
+we encourage you to collaborate. Optimal working groups consist of
+2-3 students. You can then hand in a common report.
+
+
Software and needed installations
+
+
+If you have Python installed (we recommend Python3) and you feel pretty familiar with installing different packages,
+we recommend that you install the following Python packages via pip as
+
+
+See below for a discussion of tensorflow and scikit-learn.
+
+
+For OSX users we recommend also, 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 (or python for python2.7)
+
+
+etc etc.
+
+
+If you don't want to install various Python packages with their dependencies separately, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely
+
+
+
Anaconda 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
+
Enthought canopy is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.
+
+
+Popular software packages written in Python for ML are
+
+
+
+These are all freely available at their respective GitHub sites. They
+encompass communities of developers in the thousands or more. And the number
+of code developers and contributors keeps increasing.
+
+
+
+
+
+
+
+
diff --git a/doc/Projects/2018/Project2/ipynb/ipynb-Project2-src.tar.gz b/doc/Projects/2018/Project2/ipynb/ipynb-Project2-src.tar.gz
new file mode 100644
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new file mode 100644
index 000000000..6f41ac3de
--- /dev/null
+++ b/doc/Projects/2018/Project2/pdf/Project2.p.tex
@@ -0,0 +1,406 @@
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+%% ptex2tex: http://code.google.com/p/ptex2tex/
+%%
+%% Run
+%% ptex2tex myfile
+%% or
+%% doconce ptex2tex myfile
+%%
+%% to turn myfile.p.tex into an ordinary LaTeX file myfile.tex.
+%% (The ptex2tex program: http://code.google.com/p/ptex2tex)
+%% Many preprocess options can be added to ptex2tex or doconce ptex2tex
+%%
+%% ptex2tex -DMINTED myfile
+%% doconce ptex2tex myfile envir=minted
+%%
+%% ptex2tex will typeset code environments according to a global or local
+%% .ptex2tex.cfg configure file. doconce ptex2tex will typeset code
+%% according to options on the command line (just type doconce ptex2tex to
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+% #define PREAMBLE
+
+% #ifdef PREAMBLE
+%-------------------- begin preamble ----------------------
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+\listfiles % print all files needed to compile this document
+
+\usepackage{relsize,makeidx,color,setspace,amsmath,amsfonts,amssymb}
+\usepackage[table]{xcolor}
+\usepackage{bm,ltablex,microtype}
+
+\usepackage[pdftex]{graphicx}
+
+\usepackage[T1]{fontenc}
+%\usepackage[latin1]{inputenc}
+\usepackage{ucs}
+\usepackage[utf8x]{inputenc}
+
+\usepackage{lmodern} % Latin Modern fonts derived from Computer Modern
+
+% Hyperlinks in PDF:
+\definecolor{linkcolor}{rgb}{0,0,0.4}
+\usepackage{hyperref}
+\hypersetup{
+ breaklinks=true,
+ colorlinks=true,
+ linkcolor=linkcolor,
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+ citecolor=black,
+ filecolor=black,
+ %filecolor=blue,
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+ pdftoolbar=true,
+ bookmarksdepth=3 % Uncomment (and tweak) for PDF bookmarks with more levels than the TOC
+ }
+%\hyperbaseurl{} % hyperlinks are relative to this root
+
+\setcounter{tocdepth}{2} % levels in table of contents
+
+% --- fancyhdr package for fancy headers ---
+\usepackage{fancyhdr}
+\fancyhf{} % sets both header and footer to nothing
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+\fancyfoot[LE,RO]{\thepage}
+% Ensure copyright on titlepage (article style) and chapter pages (book style)
+\fancypagestyle{plain}{
+ \fancyhf{}
+ \fancyfoot[C]{{\footnotesize \copyright\ 1999-2018, "Data Analysis and Machine Learning FYS-STK3155/FYS4155":"http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html". Released under CC Attribution-NonCommercial 4.0 license}}
+% \renewcommand{\footrulewidth}{0mm}
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+}
+% Ensure copyright on titlepages with \thispagestyle{empty}
+\fancypagestyle{empty}{
+ \fancyhf{}
+ \fancyfoot[C]{{\footnotesize \copyright\ 1999-2018, "Data Analysis and Machine Learning FYS-STK3155/FYS4155":"http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html". Released under CC Attribution-NonCommercial 4.0 license}}
+ \renewcommand{\footrulewidth}{0mm}
+ \renewcommand{\headrulewidth}{0mm}
+}
+
+\pagestyle{fancy}
+
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+\widowpenalty = 10000
+
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+
+
+% insert custom LaTeX commands...
+
+\raggedbottom
+\makeindex
+\usepackage[totoc]{idxlayout} % for index in the toc
+\usepackage[nottoc]{tocbibind} % for references/bibliography in the toc
+
+%-------------------- end preamble ----------------------
+
+\begin{document}
+
+% matching end for #ifdef PREAMBLE
+% #endif
+
+\newcommand{\exercisesection}[1]{\subsection*{#1}}
+
+
+% ------------------- main content ----------------------
+
+
+
+% ----------------- title -------------------------
+
+\thispagestyle{empty}
+
+\begin{center}
+{\LARGE\bf
+\begin{spacing}{1.25}
+Project 2 on Machine Learning, deadline November 5
+\end{spacing}
+}
+\end{center}
+
+% ----------------- author(s) -------------------------
+
+\begin{center}
+{\bf \href{{http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html}}{Data Analysis and Machine Learning FYS-STK3155/FYS4155}}
+\end{center}
+
+ \begin{center}
+% List of all institutions:
+\centerline{{\small Department of Physics, University of Oslo, Norway}}
+\end{center}
+
+% ----------------- end author(s) -------------------------
+
+% --- begin date ---
+\begin{center}
+Oct 8, 2018
+\end{center}
+% --- end date ---
+
+\vspace{1cm}
+
+
+\begin{enumerate}
+\item add about ising model
+
+\item link to where we have the data
+
+\item explain how to fit the model
+
+\item link to mehta's article
+\end{enumerate}
+
+\noindent
+\subsection{Classification and Regression, from linear and logistic regression to neural networks}
+
+The main aim of this project is to study both classification and
+regression problems, starting with the regression algortihms studied
+in project 1. We will include logistic regresion for classification
+problems and write our own multilayer perceptron code for studying
+both regression and classification problems. The codes developed in
+project 1, including bootstrap and/or cross-validation as well as the
+computation of the mean-squared error and the R2 score function can
+also be utilized (and included in logistic regression and the neural
+network codes) in the present analysis.
+
+We will use the Ising model to generate our training data and will
+focus mainly on supervised training. We will follow closely the recent
+article of \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv
+1803.08823}. This article stands
+out as an excellent review on machine learning (ML) algorithms applied
+to typical physics problems. The added benefit is that each figure and
+model presented in \href{{https://physics.bu.edu/~pankajm/MLnotebooks.html}}{this article is accompanied by its jupyter
+notebook}. This
+means that we can start using these and compare with our own
+results. In case you wish to use their data for the Ising model, their
+data can be downloaded from the same link which lists to the jupyter
+notebooks. See also at the end of the project description for more
+information on how to install various Python packages.
+
+
+
+With the abovementioned configurations we will determine, using first
+various regression methods, the value of the coupling constant for the
+energy of the one-dimensional Ising model. Thereafter, we will use the
+two-dimensional data, but now computed at different temperatures, in
+order to classify the phase of the Ising model. Below the critical
+temperature, the system will be in a so-called ferromagnetic
+phase. Close to the critical temperature, the final magnetization
+becomes smaller and smaller in absolute value while above the critical
+temperature, the net magnetization is zero. This classification case,
+that is the two-dimensional Ising model, will be studied using
+logistic regression and deep neural networks. The aim is to develop
+your own logistic regression code for the classification of the phases
+(this is a binary model) and your multilayer perceptron code for the
+classification and regression case.
+
+
+Feel free to use the notebooks to benchmark your code. If you wish to
+write your own C++ or Fortran program for say a simple neural network
+model and a logistic regression model, please feel free to do so. You can then benchmark your results
+against the above jupyter notebooks.
+
+
+\paragraph{Part a): Producing the data.}
+You can use the Ising model data from the article of Mehta \emph{et al.},
+or generate your own data. If you opt for using your own Ising model
+code, you need to generate $10000$ energy configurations with their
+spin orientations after the system has reached its most likely
+state. These energies and their corresponding spin orientations
+represent then your data. We will use a fixed lattice of $L\times L =
+40 \times 40$ spins in two dimensions and $L=40$ spins in one
+dimension. Make sure the calculations have been equilibrated. For the
+two-dimensional system, compute the configurations for three values of
+the temperature, namely $T=0.75$ (ordered phase), $T=2.3$ (near the
+critical point) and $T=4.0$ (disordered phase). For the
+one-dimensional system it suffices to compute the various
+configurations for one temperature only, say $T=2.0$. These are the
+data you will use to study different ML algorithms. We generate our
+data with $J=1$.
+
+\paragraph{Part b): Estimating the coupling constant of the one-dimensional Ising model.}
+We start with the one-dimensional Ising model and use the data we have
+generated with $J=1$. Use linear regression, Lasso and Ridge
+regression as described section 6 and in Notebook 4 of \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CVI-linreg_ising.html}}{Mehta *et
+al.*}. Discuss
+the methods and how they perform in computing the coupling constant
+$J$. Give a critical analysis and discuss how to evaluate the \emph{cost
+function}. You should feel free to write your own code, see also the
+lecture notes of
+\href{{https://compphysics.github.io/MachineLearning/doc/web/course.html}}{FYS-STK4155},
+in particular te material on least square methods. You can use
+scikit-learn to perform these analyses. See below for instruction on
+how to install scikit-learn.
+
+\paragraph{Part c): Determine the phase of the two-dimensional Ising model.}
+We switch now to binary classification methods and use logistic
+regression to define the phases of the Ising model. Use described
+section 7 and in Notebook 6 of \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CVII-logreg_ising.html}}{Mehta *et
+al.*}. Discuss
+the methods and how they perform. Give a critical analysis and discuss
+how to evaluate the \emph{cost function}. You should feel free to write
+your own code.
+
+
+\paragraph{Part d): Classifying the Ising model phase using neural networks.}
+We end the classification problem of the phases of the Ising model by
+employing the algorithm for so-called feed-forward deep neural
+networks (see section 9 of Mehta \emph{et al.}). The method is described in
+\href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html}}{notebook
+12}.
+
+You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
+
+\subsection{Background literature}
+
+
+\begin{enumerate}
+\item The textbook of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}, chapters 3 and 7 are the most relevant ones for the analysis here.
+
+\item \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv 1803.08823}, \emph{A high-bias, low-variance introduction to Machine Learning for physicists}, ArXiv:1803.08823.
+\end{enumerate}
+
+\noindent
+If you wish to read more about the Ising model and statistical physics here are three suggestions.
+
+\begin{enumerate}
+\item \href{{http://www.worldscientific.com/worldscibooks/10.1142/5660}}{M. Plischke and B. Bergersen}, \emph{Equilibrium Statistical Physics}, World Scientific, see chapters 5 and 6.
+
+\item \href{{http://www.cambridge.org/no/academic/subjects/physics/computational-science-and-modelling/guide-monte-carlo-simulations-statistical-physics-4th-edition?format=HB}}{D. P. Landau and K. Binder}, \emph{A Guide to Monte Carlo Simulations in Statistical Physics}, Cambridge, see chapters 2,3 and 4.
+
+\item \href{{https://global.oup.com/academic/product/monte-carlo-methods-in-statistical-physics-9780198517979?cc=no&lang=en&}}{M. E. J. Newman and T. Barkema}, \emph{Monte Carlo Methods in Statistical Physics}, Oxford, see chapters 3 and 4.
+\end{enumerate}
+
+\noindent
+\subsection{Introduction to numerical projects}
+
+Here follows a brief recipe and recommendation on how to write a report for each
+project.
+
+\begin{itemize}
+ \item Give a short description of the nature of the problem and the eventual numerical methods you have used.
+
+ \item Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.
+
+ \item Include the source code of your program. Comment your program properly.
+
+ \item If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.
+
+ \item Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.
+
+ \item Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.
+
+ \item Try to give an interpretation of you results in your answers to the problems.
+
+ \item Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.
+
+ \item Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.
+\end{itemize}
+
+\noindent
+\subsection{Format for electronic delivery of report and programs}
+
+The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file. As programming language we prefer that you choose between C/C++, Fortran2008 or Python. The following prescription should be followed when preparing the report:
+
+\begin{itemize}
+ \item Use Devilry to hand in your projects, log in at \href{{http://devilry.ifi.uio.no}}{\nolinkurl{http://devilry.ifi.uio.no}} with your normal UiO username and password and choose either 'fysstk3155' or 'fysstk4155'. There you can load up the files within the deadline.
+
+ \item Upload \textbf{only} the report file! For the source code file(s) you have developed please provide us with your link to your github domain. The report file should include all of your discussions and a list of the codes you have developed. Do not include library files which are available at the course homepage, unless you have made specific changes to them.
+
+ \item In your git repository, please include a folder which contains selected results. These can be in the form of output from your code for a selected set of runs and input parameters.
+
+ \item In this and all later projects, you should include tests (for example unit tests) of your code(s).
+
+ \item Comments from us on your projects, approval or not, corrections to be made etc can be found under your Devilry domain and are only visible to you and the teachers of the course.
+\end{itemize}
+
+\noindent
+Finally,
+we encourage you to collaborate. Optimal working groups consist of
+2-3 students. You can then hand in a common report.
+
+
+
+\subsection{Software and needed installations}
+
+If you have Python installed (we recommend Python3) and you feel pretty familiar with installing different packages,
+we recommend that you install the following Python packages via \textbf{pip} as
+\begin{enumerate}
+\item pip install numpy scipy matplotlib ipython scikit-learn tensorflow sympy pandas pillow
+\end{enumerate}
+
+\noindent
+For Python3, replace \textbf{pip} with \textbf{pip3}.
+
+See below for a discussion of \textbf{tensorflow} and \textbf{scikit-learn}.
+
+For OSX users we recommend also, after having installed Xcode, to install \textbf{brew}. Brew allows
+for a seamless installation of additional software via for example
+\begin{enumerate}
+\item brew install python3
+\end{enumerate}
+
+\noindent
+For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution
+you can use \textbf{pip} as well and simply install Python as
+\begin{enumerate}
+\item sudo apt-get install python3 (or python for python2.7)
+\end{enumerate}
+
+\noindent
+etc etc.
+
+If you don't want to install various Python packages with their dependencies separately, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely
+\begin{enumerate}
+\item \href{{https://docs.anaconda.com/}}{Anaconda} 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 \textbf{conda}
+
+\item \href{{https://www.enthought.com/product/canopy/}}{Enthought canopy} is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.
+\end{enumerate}
+
+\noindent
+Popular software packages written in Python for ML are
+
+\begin{itemize}
+\item \href{{http://scikit-learn.org/stable/}}{Scikit-learn},
+
+\item \href{{https://www.tensorflow.org/}}{Tensorflow},
+
+\item \href{{http://pytorch.org/}}{PyTorch} and
+
+\item \href{{https://keras.io/}}{Keras}.
+\end{itemize}
+
+\noindent
+These are all freely available at their respective GitHub sites. They
+encompass communities of developers in the thousands or more. And the number
+of code developers and contributors keeps increasing.
+
+
+
+
+
+
+
+
+% ------------------- end of main content ---------------
+
+% #ifdef PREAMBLE
+\end{document}
+% #endif
+
diff --git a/doc/Projects/2018/Project2/pdf/Project2.pdf b/doc/Projects/2018/Project2/pdf/Project2.pdf
new file mode 100644
index 000000000..95bc1a5d5
Binary files /dev/null and b/doc/Projects/2018/Project2/pdf/Project2.pdf differ
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new file mode 100644
index 000000000..1de756aa3
--- /dev/null
+++ b/doc/Projects/2018/Project2/pdf/Project2.tex
@@ -0,0 +1,378 @@
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+% insert custom LaTeX commands...
+
+\raggedbottom
+\makeindex
+\usepackage[totoc]{idxlayout} % for index in the toc
+\usepackage[nottoc]{tocbibind} % for references/bibliography in the toc
+
+%-------------------- end preamble ----------------------
+
+\begin{document}
+
+% matching end for #ifdef PREAMBLE
+
+\newcommand{\exercisesection}[1]{\subsection*{#1}}
+
+
+% ------------------- main content ----------------------
+
+
+
+% ----------------- title -------------------------
+
+\thispagestyle{empty}
+
+\begin{center}
+{\LARGE\bf
+\begin{spacing}{1.25}
+Project 2 on Machine Learning, deadline November 5
+\end{spacing}
+}
+\end{center}
+
+% ----------------- author(s) -------------------------
+
+\begin{center}
+{\bf \href{{http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html}}{Data Analysis and Machine Learning FYS-STK3155/FYS4155}}
+\end{center}
+
+ \begin{center}
+% List of all institutions:
+\centerline{{\small Department of Physics, University of Oslo, Norway}}
+\end{center}
+
+% ----------------- end author(s) -------------------------
+
+% --- begin date ---
+\begin{center}
+Oct 8, 2018
+\end{center}
+% --- end date ---
+
+\vspace{1cm}
+
+
+\begin{enumerate}
+\item add about ising model
+
+\item link to where we have the data
+
+\item explain how to fit the model
+
+\item link to mehta's article
+\end{enumerate}
+
+\noindent
+\subsection*{Classification and Regression, from linear and logistic regression to neural networks}
+
+The main aim of this project is to study both classification and
+regression problems, starting with the regression algortihms studied
+in project 1. We will include logistic regresion for classification
+problems and write our own multilayer perceptron code for studying
+both regression and classification problems. The codes developed in
+project 1, including bootstrap and/or cross-validation as well as the
+computation of the mean-squared error and the R2 score function can
+also be utilized (and included in logistic regression and the neural
+network codes) in the present analysis.
+
+We will use the Ising model to generate our training data and will
+focus mainly on supervised training. We will follow closely the recent
+article of \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv
+1803.08823}. This article stands
+out as an excellent review on machine learning (ML) algorithms applied
+to typical physics problems. The added benefit is that each figure and
+model presented in \href{{https://physics.bu.edu/~pankajm/MLnotebooks.html}}{this article is accompanied by its jupyter
+notebook}. This
+means that we can start using these and compare with our own
+results. In case you wish to use their data for the Ising model, their
+data can be downloaded from the same link which lists to the jupyter
+notebooks. See also at the end of the project description for more
+information on how to install various Python packages.
+
+
+
+With the abovementioned configurations we will determine, using first
+various regression methods, the value of the coupling constant for the
+energy of the one-dimensional Ising model. Thereafter, we will use the
+two-dimensional data, but now computed at different temperatures, in
+order to classify the phase of the Ising model. Below the critical
+temperature, the system will be in a so-called ferromagnetic
+phase. Close to the critical temperature, the final magnetization
+becomes smaller and smaller in absolute value while above the critical
+temperature, the net magnetization is zero. This classification case,
+that is the two-dimensional Ising model, will be studied using
+logistic regression and deep neural networks. The aim is to develop
+your own logistic regression code for the classification of the phases
+(this is a binary model) and your multilayer perceptron code for the
+classification and regression case.
+
+
+Feel free to use the notebooks to benchmark your code. If you wish to
+write your own C++ or Fortran program for say a simple neural network
+model and a logistic regression model, please feel free to do so. You can then benchmark your results
+against the above jupyter notebooks.
+
+
+\paragraph{Part a): Producing the data.}
+You can use the Ising model data from the article of Mehta \emph{et al.},
+or generate your own data. If you opt for using your own Ising model
+code, you need to generate $10000$ energy configurations with their
+spin orientations after the system has reached its most likely
+state. These energies and their corresponding spin orientations
+represent then your data. We will use a fixed lattice of $L\times L =
+40 \times 40$ spins in two dimensions and $L=40$ spins in one
+dimension. Make sure the calculations have been equilibrated. For the
+two-dimensional system, compute the configurations for three values of
+the temperature, namely $T=0.75$ (ordered phase), $T=2.3$ (near the
+critical point) and $T=4.0$ (disordered phase). For the
+one-dimensional system it suffices to compute the various
+configurations for one temperature only, say $T=2.0$. These are the
+data you will use to study different ML algorithms. We generate our
+data with $J=1$.
+
+\paragraph{Part b): Estimating the coupling constant of the one-dimensional Ising model.}
+We start with the one-dimensional Ising model and use the data we have
+generated with $J=1$. Use linear regression, Lasso and Ridge
+regression as described section 6 and in Notebook 4 of \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CVI-linreg_ising.html}}{Mehta *et
+al.*}. Discuss
+the methods and how they perform in computing the coupling constant
+$J$. Give a critical analysis and discuss how to evaluate the \emph{cost
+function}. You should feel free to write your own code, see also the
+lecture notes of
+\href{{https://compphysics.github.io/MachineLearning/doc/web/course.html}}{FYS-STK4155},
+in particular te material on least square methods. You can use
+scikit-learn to perform these analyses. See below for instruction on
+how to install scikit-learn.
+
+\paragraph{Part c): Determine the phase of the two-dimensional Ising model.}
+We switch now to binary classification methods and use logistic
+regression to define the phases of the Ising model. Use described
+section 7 and in Notebook 6 of \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CVII-logreg_ising.html}}{Mehta *et
+al.*}. Discuss
+the methods and how they perform. Give a critical analysis and discuss
+how to evaluate the \emph{cost function}. You should feel free to write
+your own code.
+
+
+\paragraph{Part d): Classifying the Ising model phase using neural networks.}
+We end the classification problem of the phases of the Ising model by
+employing the algorithm for so-called feed-forward deep neural
+networks (see section 9 of Mehta \emph{et al.}). The method is described in
+\href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html}}{notebook
+12}.
+
+You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
+
+\subsection*{Background literature}
+
+
+\begin{enumerate}
+\item The textbook of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}, chapters 3 and 7 are the most relevant ones for the analysis here.
+
+\item \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv 1803.08823}, \emph{A high-bias, low-variance introduction to Machine Learning for physicists}, ArXiv:1803.08823.
+\end{enumerate}
+
+\noindent
+If you wish to read more about the Ising model and statistical physics here are three suggestions.
+
+\begin{enumerate}
+\item \href{{http://www.worldscientific.com/worldscibooks/10.1142/5660}}{M. Plischke and B. Bergersen}, \emph{Equilibrium Statistical Physics}, World Scientific, see chapters 5 and 6.
+
+\item \href{{http://www.cambridge.org/no/academic/subjects/physics/computational-science-and-modelling/guide-monte-carlo-simulations-statistical-physics-4th-edition?format=HB}}{D. P. Landau and K. Binder}, \emph{A Guide to Monte Carlo Simulations in Statistical Physics}, Cambridge, see chapters 2,3 and 4.
+
+\item \href{{https://global.oup.com/academic/product/monte-carlo-methods-in-statistical-physics-9780198517979?cc=no&lang=en&}}{M. E. J. Newman and T. Barkema}, \emph{Monte Carlo Methods in Statistical Physics}, Oxford, see chapters 3 and 4.
+\end{enumerate}
+
+\noindent
+\subsection*{Introduction to numerical projects}
+
+Here follows a brief recipe and recommendation on how to write a report for each
+project.
+
+\begin{itemize}
+ \item Give a short description of the nature of the problem and the eventual numerical methods you have used.
+
+ \item Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.
+
+ \item Include the source code of your program. Comment your program properly.
+
+ \item If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.
+
+ \item Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.
+
+ \item Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.
+
+ \item Try to give an interpretation of you results in your answers to the problems.
+
+ \item Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.
+
+ \item Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.
+\end{itemize}
+
+\noindent
+\subsection*{Format for electronic delivery of report and programs}
+
+The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file. As programming language we prefer that you choose between C/C++, Fortran2008 or Python. The following prescription should be followed when preparing the report:
+
+\begin{itemize}
+ \item Use Devilry to hand in your projects, log in at \href{{http://devilry.ifi.uio.no}}{\nolinkurl{http://devilry.ifi.uio.no}} with your normal UiO username and password and choose either 'fysstk3155' or 'fysstk4155'. There you can load up the files within the deadline.
+
+ \item Upload \textbf{only} the report file! For the source code file(s) you have developed please provide us with your link to your github domain. The report file should include all of your discussions and a list of the codes you have developed. Do not include library files which are available at the course homepage, unless you have made specific changes to them.
+
+ \item In your git repository, please include a folder which contains selected results. These can be in the form of output from your code for a selected set of runs and input parameters.
+
+ \item In this and all later projects, you should include tests (for example unit tests) of your code(s).
+
+ \item Comments from us on your projects, approval or not, corrections to be made etc can be found under your Devilry domain and are only visible to you and the teachers of the course.
+\end{itemize}
+
+\noindent
+Finally,
+we encourage you to collaborate. Optimal working groups consist of
+2-3 students. You can then hand in a common report.
+
+
+
+\subsection*{Software and needed installations}
+
+If you have Python installed (we recommend Python3) and you feel pretty familiar with installing different packages,
+we recommend that you install the following Python packages via \textbf{pip} as
+\begin{enumerate}
+\item pip install numpy scipy matplotlib ipython scikit-learn tensorflow sympy pandas pillow
+\end{enumerate}
+
+\noindent
+For Python3, replace \textbf{pip} with \textbf{pip3}.
+
+See below for a discussion of \textbf{tensorflow} and \textbf{scikit-learn}.
+
+For OSX users we recommend also, after having installed Xcode, to install \textbf{brew}. Brew allows
+for a seamless installation of additional software via for example
+\begin{enumerate}
+\item brew install python3
+\end{enumerate}
+
+\noindent
+For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution
+you can use \textbf{pip} as well and simply install Python as
+\begin{enumerate}
+\item sudo apt-get install python3 (or python for python2.7)
+\end{enumerate}
+
+\noindent
+etc etc.
+
+If you don't want to install various Python packages with their dependencies separately, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely
+\begin{enumerate}
+\item \href{{https://docs.anaconda.com/}}{Anaconda} 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 \textbf{conda}
+
+\item \href{{https://www.enthought.com/product/canopy/}}{Enthought canopy} is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.
+\end{enumerate}
+
+\noindent
+Popular software packages written in Python for ML are
+
+\begin{itemize}
+\item \href{{http://scikit-learn.org/stable/}}{Scikit-learn},
+
+\item \href{{https://www.tensorflow.org/}}{Tensorflow},
+
+\item \href{{http://pytorch.org/}}{PyTorch} and
+
+\item \href{{https://keras.io/}}{Keras}.
+\end{itemize}
+
+\noindent
+These are all freely available at their respective GitHub sites. They
+encompass communities of developers in the thousands or more. And the number
+of code developers and contributors keeps increasing.
+
+
+
+
+
+
+
+
+% ------------------- end of main content ---------------
+
+\end{document}
+
diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
deleted file mode 100644
index 968509243..000000000
--- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
+++ /dev/null
@@ -1,3234 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "# Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep 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: **Oct 4, 2018**\n",
- "\n",
- "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
- "\n",
- "\n",
- "\n",
- "\n",
- "## Neural networks\n",
- "\n",
- "Artificial neural networks are computational systems that can learn to\n",
- "perform tasks by considering examples, generally without being\n",
- "programmed with any task-specific rules. It is supposed to mimic a\n",
- "biological system, wherein neurons interact by sending signals in the\n",
- "form of mathematical functions between layers. All layers can contain\n",
- "an arbitrary number of neurons, and each connection is represented by\n",
- "a weight variable.\n",
- "\n",
- "\n",
- "## Artificial neurons\n",
- "\n",
- "The field of artificial neural networks has a long history of\n",
- "development, and is closely connected with the advancement of computer\n",
- "science and computers in general. A model of artificial neurons was\n",
- "first developed by McCulloch and Pitts in 1943 to study signal\n",
- "processing in the brain and has later been refined by others. The\n",
- "general idea is to mimic neural networks in the human brain, which is\n",
- "composed of billions of neurons that communicate with each other by\n",
- "sending electrical signals. Each neuron accumulates its incoming\n",
- "signals, which must exceed an activation threshold to yield an\n",
- "output. If the threshold is not overcome, the neuron remains inactive,\n",
- "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",
- "$$\n",
- "\\begin{equation}\n",
- " y = f\\left(\\sum_{i=1}^n w_ix_i\\right) = f(u)\n",
- "\\label{artificialNeuron} \\tag{1}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "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",
- "Conceptually, it is helpful to divide neural networks into four\n",
- "categories:\n",
- "1. general purpose neural networks for supervised learning,\n",
- "\n",
- "2. neural networks designed specifically for image processing, the most prominent example of this class being Convolutional Neural Networks (CNNs),\n",
- "\n",
- "3. neural networks for sequential data such as Recurrent Neural Networks (RNNs), and\n",
- "\n",
- "4. neural networks for unsupervised learning such as Deep Boltzmann Machines.\n",
- "\n",
- "In natural science, DNNs and CNNs have already found numerous\n",
- "applications. In statistical physics, they have been applied to detect\n",
- "phase transitions in 2D Ising and Potts models, lattice gauge\n",
- "theories, and different phases of polymers, or solving the\n",
- "Navier-Stokes equation in weather forecasting. Deep learning has also\n",
- "found interesting applications in quantum physics. Various quantum\n",
- "phase transitions can be detected and studied using DNNs and CNNs,\n",
- "topological phases, and even non-equilibrium many-body\n",
- "localization. Representing quantum states as DNNs quantum state\n",
- "tomography are among some of the impressive achievements to reveal the\n",
- "potential of DNNs to facilitate the study of quantum systems.\n",
- "\n",
- "In quantum information theory, it has been shown that one can perform\n",
- "gate decompositions with the help of neural. \n",
- "\n",
- "The applications are not limited to the natural sciences. There is a\n",
- "plethora of applications in essentially all disciplines, from the\n",
- "humanities to life science and medicine.\n",
- "\n",
- "## Neural network types\n",
- "\n",
- "An artificial neural network (ANN), is a computational model that\n",
- "consists of layers of connected neurons, or nodes or units. We will\n",
- "refer to these interchangeably as units or nodes, and sometimes as\n",
- "neurons.\n",
- "\n",
- "It is supposed to mimic a biological nervous system by letting each\n",
- "neuron interact with other neurons by sending signals in the form of\n",
- "mathematical functions between layers. A wide variety of different\n",
- "ANNs have been developed, but most of them consist of an input layer,\n",
- "an output layer and eventual layers in-between, called *hidden\n",
- "layers*. All layers can contain an arbitrary number of nodes, and each\n",
- "connection between two nodes is associated with a weight variable.\n",
- "\n",
- "Neural networks (also called neural nets) are neural-inspired\n",
- "nonlinear models for supervised learning. As we will see, neural nets\n",
- "can be viewed as natural, more powerful extensions of supervised\n",
- "learning methods such as linear and logistic regression and soft-max\n",
- "methods we discussed earlier.\n",
- "\n",
- "\n",
- "## Feed-forward neural networks\n",
- "\n",
- "The feed-forward neural network (FFNN) was the first and simplest type\n",
- "of ANNs that were devised. In this network, the information moves in\n",
- "only one direction: forward through the layers.\n",
- "\n",
- "Nodes are represented by circles, while the arrows display the\n",
- "connections between the nodes, including the direction of information\n",
- "flow. Additionally, each arrow corresponds to a weight variable\n",
- "(figure to come). We observe that each node in a layer is connected\n",
- "to *all* nodes in the subsequent layer, making this a so-called\n",
- "*fully-connected* FFNN.\n",
- "\n",
- "\n",
- "\n",
- "## Convolutional Neural Network\n",
- "\n",
- "A different variant of FFNNs are *convolutional neural networks*\n",
- "(CNNs), which have a connectivity pattern inspired by the animal\n",
- "visual cortex. Individual neurons in the visual cortex only respond to\n",
- "stimuli from small sub-regions of the visual field, called a receptive\n",
- "field. This makes the neurons well-suited to exploit the strong\n",
- "spatially local correlation present in natural images. The response of\n",
- "each neuron can be approximated mathematically as a convolution\n",
- "operation. (figure to come)\n",
- "\n",
- "Convolutional neural networks emulate the behaviour of neurons in the\n",
- "visual cortex by enforcing a *local* connectivity pattern between\n",
- "nodes of adjacent layers: Each node in a convolutional layer is\n",
- "connected only to a subset of the nodes in the previous layer, in\n",
- "contrast to the fully-connected FFNN. Often, CNNs consist of several\n",
- "convolutional layers that learn local features of the input, with a\n",
- "fully-connected layer at the end, which gathers all the local data and\n",
- "produces the outputs. They have wide applications in image and video\n",
- "recognition.\n",
- "\n",
- "## Recurrent neural networks\n",
- "\n",
- "So far we have only mentioned ANNs where information flows in one\n",
- "direction: forward. *Recurrent neural networks* on the other hand,\n",
- "have connections between nodes that form directed *cycles*. This\n",
- "creates a form of internal memory which are able to capture\n",
- "information on what has been calculated before; the output is\n",
- "dependent on the previous computations. Recurrent NNs make use of\n",
- "sequential information by performing the same task for every element\n",
- "in a sequence, where each element depends on previous elements. An\n",
- "example of such information is sentences, making recurrent NNs\n",
- "especially well-suited for handwriting and speech recognition.\n",
- "\n",
- "## Other types of networks\n",
- "\n",
- "There are many other kinds of ANNs that have been developed. One type\n",
- "that is specifically designed for interpolation in multidimensional\n",
- "space is the radial basis function (RBF) network. RBFs are typically\n",
- "made up of three layers: an input layer, a hidden layer with\n",
- "non-linear radial symmetric activation functions and a linear output\n",
- "layer (''linear'' here means that each node in the output layer has a\n",
- "linear activation function). The layers are normally fully-connected\n",
- "and there are no cycles, thus RBFs can be viewed as a type of\n",
- "fully-connected FFNN. They are however usually treated as a separate\n",
- "type of NN due the unusual activation functions.\n",
- "\n",
- "## Multilayer perceptrons\n",
- "\n",
- "One uses often so-called fully-connected feed-forward neural networks\n",
- "with three or more layers (an input layer, one or more hidden layers\n",
- "and an output layer) consisting of neurons that have non-linear\n",
- "activation functions.\n",
- "\n",
- "Such networks are often called *multilayer perceptrons* (MLPs).\n",
- "\n",
- "## Why multilayer perceptrons?\n",
- "\n",
- "According to the *Universal approximation theorem*, a feed-forward\n",
- "neural network with just a single hidden layer containing a finite\n",
- "number of neurons can approximate a continuous multidimensional\n",
- "function to arbitrary accuracy, assuming the activation function for\n",
- "the hidden layer is a **non-constant, bounded and\n",
- "monotonically-increasing continuous function**.\n",
- "\n",
- "Note that the requirements on the activation function only applies to\n",
- "the hidden layer, the output nodes are always assumed to be linear, so\n",
- "as to not restrict the range of output values.\n",
- "\n",
- "\n",
- "## Mathematical model\n",
- "\n",
- "The output $y$ is produced via the activation function $f$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "y = f\\left(\\sum_{i=1}^n w_ix_i + b_i\\right) = f(z),\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This function receives $x_i$ as inputs.\n",
- "Here the activation $z=(\\sum_{i=1}^n w_ix_i+b_i)$. \n",
- "In an FFNN of such neurons, the *inputs* $x_i$ are the *outputs* of\n",
- "the neurons in the preceding layer. Furthermore, an MLP is\n",
- "fully-connected, which means that each neuron receives a weighted sum\n",
- "of the outputs of *all* neurons in the previous layer.\n",
- "\n",
- "## Mathematical model\n",
- "\n",
- "First, for each node $i$ in the first hidden layer, we calculate a weighted sum $z_i^1$ of the input coordinates $x_j$,"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation} z_i^1 = \\sum_{j=1}^{M} w_{ij}^1 x_j + b_i^1\n",
- "\\label{_auto1} \\tag{2}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here $b_i$ is the so-called bias which is normally needed in\n",
- "case of zero activation weights or inputs. How to fix the biases and\n",
- "the weights will be discussed below. The value of $z_i^1$ is the\n",
- "argument to the activation function $f_i$ of each node $i$, The\n",
- "variable $M$ stands for all possible inputs to a given node $i$ in the\n",
- "first layer. We define the output $y_i^1$ of all neurons in layer 1 as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- " y_i^1 = f(z_i^1) = f\\left(\\sum_{j=1}^M w_{ij}^1 x_j + b_i^1\\right)\n",
- "\\label{outputLayer1} \\tag{3}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where we assume that all nodes in the same layer have identical\n",
- "activation functions, hence the notation $f$. In general, we could assume in the more general case that different layers have different activation functions.\n",
- "In this case we would identify these functions with a superscript $l$ for the $l$-th layer,"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- " y_i^l = f^l(u_i^l) = f^l\\left(\\sum_{j=1}^{N_{l-1}} w_{ij}^l y_j^{l-1} + b_i^l\\right)\n",
- "\\label{generalLayer} \\tag{4}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where $N_l$ is the number of nodes in layer $l$. When the output of\n",
- "all the nodes in the first hidden layer are computed, the values of\n",
- "the subsequent layer can be calculated and so forth until the output\n",
- "is obtained.\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",
- "$$\n",
- "\\begin{equation}\n",
- " y_i^2 = f^2\\left(\\sum_{j=1}^N w_{ij}^2 y_j^1 + b_i^2\\right) \n",
- "\\label{_auto2} \\tag{5}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation} \n",
- " = f^2\\left[\\sum_{j=1}^N w_{ij}^2f^1\\left(\\sum_{k=1}^M w_{jk}^1 x_k + b_j^1\\right) + b_i^2\\right]\n",
- "\\label{outputLayer2} \\tag{6}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where we have substituted $y_k^1$ with the inputs $x_k$. Finally, the ANN output reads"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- " y_i^3 = f^3\\left(\\sum_{j=1}^N w_{ij}^3 y_j^2 + b_i^3\\right) \n",
- "\\label{_auto3} \\tag{7}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation} \n",
- " = f_3\\left[\\sum_{j} w_{ij}^3 f^2\\left(\\sum_{k} w_{jk}^2 f^1\\left(\\sum_{m} w_{km}^1 x_m + b_k^1\\right) + b_j^2\\right)\n",
- " + b_1^3\\right]\n",
- "\\label{_auto4} \\tag{8}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Mathematical model\n",
- "\n",
- "We can generalize this expression to an MLP with $l$ hidden\n",
- "layers. The complete functional form is,"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- "y^{l+1}_i = f^{l+1}\\left[\\!\\sum_{j=1}^{N_l} w_{ij}^3 f^l\\left(\\sum_{k=1}^{N_{l-1}}w_{jk}^{l-1}\\left(\\dots f^1\\left(\\sum_{n=1}^{N_0} w_{mn}^1 x_n+ b_m^1\\right)\\dots\\right)+b_k^2\\right)+b_1^3\\right] \n",
- "\\label{completeNN} \\tag{9}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "which illustrates a basic property of MLPs: The only independent\n",
- "variables are the input values $x_n$.\n",
- "\n",
- "## Mathematical model\n",
- "\n",
- "This confirms that an MLP, despite its quite convoluted mathematical\n",
- "form, is nothing more than an analytic function, specifically a\n",
- "mapping of real-valued vectors $\\hat{x} \\in \\mathbb{R}^n \\rightarrow\n",
- "\\hat{y} \\in \\mathbb{R}^m$.\n",
- "\n",
- "Furthermore, the flexibility and universality of an MLP can be\n",
- "illustrated by realizing that the expression is essentially a nested\n",
- "sum of scaled activation functions of the form"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- " f(x) = c_1 f(c_2 x + c_3) + c_4\n",
- "\\label{_auto5} \\tag{10}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where the parameters $c_i$ are weights and biases. By adjusting these\n",
- "parameters, the activation functions can be shifted up and down or\n",
- "left and right, change slope or be rescaled which is the key to the\n",
- "flexibility of a neural network.\n",
- "\n",
- "### Matrix-vector notation\n",
- "\n",
- "We can introduce a more convenient notation for the activations in an A NN. \n",
- "\n",
- "Additionally, we can represent the biases and activations\n",
- "as layer-wise column vectors $\\hat{b}_l$ and $\\hat{y}_l$, 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 an $N_{l-1} \\times N_l$ matrix, while $\\hat{b}_l$ and $\\hat{y}_l$ are $N_l \\times 1$ column vectors. \n",
- "With this notation, the sum becomes a matrix-vector multiplication, and we can write\n",
- "the equation for the activations of hidden layer 2 (assuming three nodes for simplicity) as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- " \\hat{y}_2 = f_2(\\mathrm{W}_2 \\hat{y}_{1} + \\hat{b}_{2}) = \n",
- " f_2\\left(\\left[\\begin{array}{ccc}\n",
- " w^2_{11} &w^2_{12} &w^2_{13} \\\\\n",
- " w^2_{21} &w^2_{22} &w^2_{23} \\\\\n",
- " w^2_{31} &w^2_{32} &w^2_{33} \\\\\n",
- " \\end{array} \\right] \\cdot\n",
- " \\left[\\begin{array}{c}\n",
- " y^1_1 \\\\\n",
- " y^1_2 \\\\\n",
- " y^1_3 \\\\\n",
- " \\end{array}\\right] + \n",
- " \\left[\\begin{array}{c}\n",
- " b^2_1 \\\\\n",
- " b^2_2 \\\\\n",
- " b^2_3 \\\\\n",
- " \\end{array}\\right]\\right).\n",
- "\\label{_auto6} \\tag{11}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "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",
- "$$\n",
- "\\begin{equation}\n",
- " y^2_i = f_2\\Bigr(w^2_{i1}y^1_1 + w^2_{i2}y^1_2 + w^2_{i3}y^1_3 + b^2_i\\Bigr) = \n",
- " f_2\\left(\\sum_{j=1}^3 w^2_{ij} y_j^1 + b^2_i\\right).\n",
- "\\label{_auto7} \\tag{12}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This is not just a convenient and compact notation, but also a useful\n",
- "and intuitive way to think about MLPs: The output is calculated by a\n",
- "series of matrix-vector multiplications and vector additions that are\n",
- "used as input to the activation functions. For each operation\n",
- "$\\mathrm{W}_l \\hat{y}_{l-1}$ we move forward one layer.\n",
- "\n",
- "\n",
- "### Activation functions\n",
- "\n",
- "A property that characterizes a neural network, other than its\n",
- "connectivity, is the choice of activation function(s). As described\n",
- "in, the following restrictions are imposed on an activation function\n",
- "for a FFNN 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\n",
- "a MLP with only linear activation functions, each layer simply\n",
- "performs a linear transformation of its inputs.\n",
- "\n",
- "Regardless of the number of layers, the output of the NN will be\n",
- "nothing but a linear function of the inputs. Thus we need to introduce\n",
- "some kind of non-linearity to the NN to be able to fit non-linear\n",
- "functions Typical examples are the logistic *Sigmoid*"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "f(x) = \\frac{1}{1 + e^{-x}},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and the *hyperbolic tangent* function"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "f(x) = \\tanh(x)\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Relevance\n",
- "\n",
- "The *sigmoid* function are more biologically plausible because the\n",
- "output of inactive neurons are zero. Such activation function are\n",
- "called *one-sided*. However, it has been shown that the hyperbolic\n",
- "tangent performs better than the sigmoid for training MLPs. has\n",
- "become the most popular for *deep neural networks*"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
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\n",
- "text/plain": [
- ""
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- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
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\n",
- "text/plain": [
- ""
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- "metadata": {},
- "output_type": "display_data"
- },
- {
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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "%matplotlib inline\n",
- "\n",
- "\"\"\"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",
- "\"\"\"Sine Function\"\"\"\n",
- "z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n",
- "t = numpy.sin(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('sine function')\n",
- "\n",
- "plt.show()\n",
- "\n",
- "\"\"\"Plots a graph of the squashing function used by a rectified linear\n",
- "unit\"\"\"\n",
- "z = numpy.arange(-2, 2, .1)\n",
- "zero = numpy.zeros(len(z))\n",
- "y = numpy.max([zero, z], axis=0)\n",
- "\n",
- "fig = plt.figure()\n",
- "ax = fig.add_subplot(111)\n",
- "ax.plot(z, y)\n",
- "ax.set_ylim([-2.0, 2.0])\n",
- "ax.set_xlim([-2.0, 2.0])\n",
- "ax.grid(True)\n",
- "ax.set_xlabel('z')\n",
- "ax.set_title('Rectified linear unit')\n",
- "\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## The multilayer perceptron (MLP)\n",
- "\n",
- "The multilayer perceptron is a very popular, and easy to implement approach, to deep learning. It consists of\n",
- "1. A neural network with one or more layers of nodes between the input and the output nodes.\n",
- "\n",
- "2. The multilayer network structure, or architecture, or topology, consists of an input layer, one or more hidden layers, and one output layer.\n",
- "\n",
- "3. The input nodes pass values to the first hidden layer, its nodes pass the information on to the second and so on till we reach the output layer.\n",
- "\n",
- "As a convention it is normal to call a network with one layer of input units, one layer of hidden\n",
- "units and one layer of output units as a two-layer network. A network with two layers of hidden units is called a three-layer network etc etc.\n",
- "\n",
- "For an MLP network there is no direct connection between the output nodes/neurons/units and the input nodes/neurons/units.\n",
- "Hereafter we will call the various entities of a layer for nodes.\n",
- "There are also no connections within a single layer.\n",
- "\n",
- "The number of input nodes does not need to equal the number of output\n",
- "nodes. This applies also to the hidden layers. Each layer may have its\n",
- "own number of nodes and activation functions.\n",
- "\n",
- "The hidden layers have their name from the fact that they are not\n",
- "linked to observables and as we will see below when we define the\n",
- "so-called activation $\\hat{z}$, we can think of this as a basis\n",
- "expansion of the original inputs $\\hat{x}$. The difference however\n",
- "between neural networks and say linear regression is that now these\n",
- "basis functions (which will correspond to the weights in the network)\n",
- "are learned from data. This results in an important difference between\n",
- "neural networks and deep learning approaches on one side and methods\n",
- "like logistic regression or linear regression and their modifications on the other side.\n",
- "\n",
- "\n",
- "## From one to many layers, the universal approximation theorem\n",
- "\n",
- "\n",
- "A neural network with only one layer, what we called the simple\n",
- "perceptron, is best suited if we have a standard binary model with\n",
- "clear (linear) boundaries between the outcomes. As such it could\n",
- "equally well be replaced by standard linear regression or logistic\n",
- "regression. Networks with one or more hidden layers approximate\n",
- "systems with more complex boundaries.\n",
- "\n",
- "As stated earlier, \n",
- "an important theorem in studies of neural networks, restated without\n",
- "proof here, is the [universal approximation\n",
- "theorem](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.441.7873&rep=rep1&type=pdf).\n",
- "\n",
- "It states that a feed-forward network with a single hidden layer\n",
- "containing a finite number of neurons can approximate continuous\n",
- "functions on compact subsets of real functions. The theorem thus\n",
- "states that simple neural networks can represent a wide variety of\n",
- "interesting functions when given appropriate parameters. It is the\n",
- "multilayer feedforward architecture itself which gives neural networks\n",
- "the potential of being universal approximators.\n",
- "\n",
- "\n",
- "## Deriving the back propagation code for a multilayer perceptron model\n",
- "\n",
- "\n",
- "**Note: figures will be inserted later!**\n",
- "\n",
- "As we have seen now in a feed forward network, we can express the final output of our network in terms of basic matrix-vector multiplications.\n",
- "The unknowwn quantities are our weights $w_{ij}$ and we need to find an algorithm for changing them so that our errors are as small as possible.\n",
- "This leads us to the famous [back propagation algorithm](https://www.nature.com/articles/323533a0).\n",
- "\n",
- "The questions we want to ask are how do changes in the biases and the\n",
- "weights in our network change the cost function and how can we use the\n",
- "final output to modify the weights?\n",
- "\n",
- "To derive these equations let us start with a plain regression problem\n",
- "and define our cost function as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "{\\cal C}(\\hat{W}) = \\frac{1}{2}\\sum_{i=1}^n\\left(y_i - t_i\\right)^2,\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where the $t_i$s are our $n$ targets (the values we want to\n",
- "reproduce), while the outputs of the network after having propagated\n",
- "all inputs $\\hat{x}$ are given by $y_i$. Below we will demonstrate\n",
- "how the basic equations arising from the back propagation algorithm\n",
- "can be modified in order to study classification problems with $K$\n",
- "classes.\n",
- "\n",
- "## Definitions\n",
- "\n",
- "With our definition of the targets $\\hat{t}$, the outputs of the\n",
- "network $\\hat{y}$ and the inputs $\\hat{x}$ we\n",
- "define now the activation $z_j^l$ of node/neuron/unit $j$ of the\n",
- "$l$-th layer as a function of the bias, the weights which add up from\n",
- "the previous layer $l-1$ and the forward passes/outputs\n",
- "$\\hat{a}^{l-1}$ from the previous layer as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "z_j^l = \\sum_{i=1}^{M_{l-1}}w_{ij}^la_j^{l-1}+b_j^l,\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where $b_k^l$ are the biases from layer $l$. Here $M_{l-1}$\n",
- "represents the total number of nodes/neurons/units of layer $l-1$. The\n",
- "figure here illustrates this equation. We can rewrite this in a more\n",
- "compact form as the matrix-vector products we discussed earlier,"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\hat{z}^l = \\left(\\hat{W}^l\\right)^T\\hat{a}^{l-1}+\\hat{b}^l.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "With the activation values $\\hat{z}^l$ we can in turn define the\n",
- "output of layer $l$ as $\\hat{a}^l = f(\\hat{z}^l)$ where $f$ is our\n",
- "activation function. In the examples here we will use the sigmoid\n",
- "function discussed in our logistic regression lectures. We will also use the same activation function $f$ for all layers\n",
- "and their nodes. It means we have"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "a_j^l = f(z_j^l) = \\frac{1}{1+\\exp{-(z_j^l)}}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Derivatives and the chain rule\n",
- "\n",
- "From the definition of the activation $z_j^l$ we have"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial z_j^l}{\\partial w_{ji}^l} = a_i^{l-1},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial z_j^l}{\\partial a_i^{l-1}} = w_{ji}^l.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "With our definition of the activation function we have that (note that this function depends only on $z_j^l$)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial a_j^l}{\\partial z_j^{l}} = a_j^l(1-a_j^l)=f(z_j^l)(1-f(z_j^l)).\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Derivative of the cost function\n",
- "\n",
- "With these definitions we can now compute the derivative of the cost function in terms of the weights.\n",
- "\n",
- "Let us specialize to the output layer $l=L$. Our cost function is"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "{\\cal C}(\\hat{W^L}) = \\frac{1}{2}\\sum_{i=1}^n\\left(y_i - t_i\\right)^2=\\frac{1}{2}\\sum_{i=1}^n\\left(a_i^L - t_i\\right)^2,\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The derivative of this function with respect to the weights is"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial{\\cal C}(\\hat{W^L})}{\\partial w_{jk}^L} = \\left(a_j^L - t_j\\right)\\frac{\\partial a_j^L}{\\partial w_{jk}^{L}},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The last partial derivative can easily be computed and reads (by applying the chain rule)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial a_j^L}{\\partial w_{jk}^{L}} = \\frac{\\partial a_j^L}{\\partial z_{j}^{L}}\\frac{\\partial z_j^L}{\\partial w_{jk}^{L}}=a_j^L(1-a_j^L)a_k^{L-1},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Bringing it together, first back propagation equation\n",
- "\n",
- "We have thus"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial{\\cal C}(\\hat{W^L})}{\\partial w_{jk}^L} = \\left(a_j^L - t_j\\right)a_j^L(1-a_j^L)a_k^{L-1},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Defining"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^L = a_j^L(1-a_j^L)\\left(a_j^L - t_j\\right) = f'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and using the Hadamard product of two vectors we can write this as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\hat{\\delta}^L = f'(\\hat{z}^L)\\circ\\frac{\\partial {\\cal C}}{\\partial (\\hat{a}L)}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This is an important expression. The second term on the right handside\n",
- "measures how fast the cost function is changing as a function of the $j$th\n",
- "output activation. If, for example, the cost function doesn't depend\n",
- "much on a particular output node $j$, then $\\delta_j^L$ will be small,\n",
- "which is what we would expect. The first term on the right, measures\n",
- "how fast the activation function $f$ is changing at a given activation\n",
- "value $z_j^L$.\n",
- "\n",
- "Notice that everything in the above equations is easily computed. In\n",
- "particular, we compute $z_j^L$ while computing the behaviour of the\n",
- "network, and it is only a small additional overhead to compute\n",
- "$f'(z^L_j)$. The exact form of the derivative with respect to the\n",
- "output depends on the form of the cost function.\n",
- "However, provided the cost function is known there should be little\n",
- "trouble in calculating"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "With the definition of $\\delta_j^L$ we have a more compact definition of the derivative of the cost function in terms of the weights, namely"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\frac{\\partial{\\cal C}(\\hat{W^L})}{\\partial w_{jk}^L} = \\delta_j^La_k^{L-1}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Derivatives in terms of $z_j^L$\n",
- "\n",
- "It is also easy to see that our previous equation can be written as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^L =\\frac{\\partial {\\cal C}}{\\partial z_j^L}= \\frac{\\partial {\\cal C}}{\\partial a_j^L}\\frac{\\partial a_j^L}{\\partial z_j^L},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "which can also be interpreted as the partial derivative of the cost function with respect to the biases $b_j^L$, namely"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^L = \\frac{\\partial {\\cal C}}{\\partial b_j^L}\\frac{\\partial b_j^L}{\\partial z_j^L}=\\frac{\\partial {\\cal C}}{\\partial b_j^L},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "That is, the error $\\delta_j^L$ is exactly equal to the rate of change of the cost function as a function of the bias. \n",
- "## Bringing it together\n",
- "\n",
- "We have now three equations that are essential for the computations of the derivatives of the cost function at the output layer. These equations are needed to start the algorithm and they are\n",
- "\n",
- "**The starting equations.**"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- "\\frac{\\partial{\\cal C}(\\hat{W^L})}{\\partial w_{jk}^L} = \\delta_j^La_k^{L-1},\n",
- "\\label{_auto8} \\tag{13}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- "\\delta_j^L = f'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)},\n",
- "\\label{_auto9} \\tag{14}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation}\n",
- "\\delta_j^L = \\frac{\\partial {\\cal C}}{\\partial b_j^L},\n",
- "\\label{_auto10} \\tag{15}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "An interesting consequence of the above equations is that when the\n",
- "activation $a_k^{L-1}$ is small, the gradient term, that is the\n",
- "derivative of the cost function with respect to the weights, will also\n",
- "tend to be small. We say then that the weight learns slowly, meaning\n",
- "that it changes slowly when we minimize the weights via say gradient\n",
- "descent. In this case we say the system learns slowly.\n",
- "\n",
- "Another interesting feature is that is when the activation function,\n",
- "represented by the sigmoid function here, is rather flat when we move towards\n",
- "its end values $0$ and $1$ (see the above Python codes). In these\n",
- "cases, the derivatives of the activation function will also be close\n",
- "to zero, meaning again that the gradients will be small and the\n",
- "network learns slowly again.\n",
- "\n",
- "\n",
- "\n",
- "We need a fourth equation and we are set. We are going to propagate\n",
- "backwards in order to the determine the weights and biases. In order\n",
- "to do so we need to represent the error in the layer before the final\n",
- "one $L-1$ in terms of the errors in the final output layer.\n",
- "\n",
- "## Final back propagating equation\n",
- "\n",
- "We have that (replacing $L$ with a general layer $l$)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^l =\\frac{\\partial {\\cal C}}{\\partial z_j^l}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We want to express this in terms of the equations for layer $l+1$. Using the chain rule and summing over all $k$ entries we have"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^l =\\sum_k \\frac{\\partial {\\cal C}}{\\partial z_k^{l+1}}\\frac{\\partial z_k^{l+1}}{\\partial z_j^{l}}=\\sum_k \\delta_k^{l+1}\\frac{\\partial z_k^{l+1}}{\\partial z_j^{l}},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and recalling that"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "z_j^{l+1} = \\sum_{i=1}^{M_{l}}w_{ij}^{l+1}a_j^{l}+b_j^{l+1},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "we obtain"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^l =\\sum_k \\delta_k^{l+1}w_{kj}^{l+1}f'(z_j^l),\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This is our final equation.\n",
- "\n",
- "We are now ready to set up the algorithm for back propagation and learning the weights and biases.\n",
- "\n",
- "## Setting up the Back propagation algorithm\n",
- "\n",
- "\n",
- "\n",
- "The four equations provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.\n",
- "\n",
- "First, we set up the input data $\\hat{x}$ and the activations\n",
- "$\\hat{z}_1$ of the input layer and compute the activation function and\n",
- "the pertinent outputs $\\hat{a}^1$.\n",
- "\n",
- "\n",
- "\n",
- "Secondly, we perform then the feed forward till we reach the output\n",
- "layer and compute all $\\hat{z}_l$ of the input layer and compute the\n",
- "activation function and the pertinent outputs $\\hat{a}^l$ for\n",
- "$l=2,3,\\dots,L$.\n",
- "\n",
- "\n",
- "\n",
- "Thereafter we compute the ouput error $\\hat{\\delta}^L$ by computing all"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^L = f'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,2$ as"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\delta_j^l =\\sum_k \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}f'(z_j^l).\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Finally, we update the weights and the biases using gradient descent for each $l=L-1,L-2,dots,2$ and update the weights and biases according to the rules"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "w_{jk}^l\\leftarrow = w_{jk}^l- \\eta \\delta_j^la_k^{l-1},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^L},\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The parameter $\\eta$ is the learning parameter discussed in connection with the gradient descent methods.\n",
- "Here it is convenient to use stochastic gradient descent (see the examples below) with mini-batches with an outer loop that steps through multiple epochs of training.\n",
- "\n",
- "\n",
- "\n",
- "## Setting up a Multi-layer perceptron model for classification\n",
- "\n",
- "We are now gong to develop an example based on the MNIST data\n",
- "base. This is a classification problem and we need to use our\n",
- "cross-entropy function we discussed in connection with logistic\n",
- "regression. The cross-entropy defines our cost function for the\n",
- "classificaton problems with neural networks.\n",
- "\n",
- "In binary classification with two classes $(0, 1)$ we define the\n",
- "logistic/sigmoid function as the probability that a particular input\n",
- "is in class $0$ or $1$. This is possible because the logistic\n",
- "function takes any input from the real numbers and inputs a number\n",
- "between 0 and 1, and can therefore be interpreted as a probability. It\n",
- "also has other nice properties, such as a derivative that is simple to\n",
- "calculate.\n",
- "\n",
- "For an input $\\boldsymbol{a}$ from the hidden layer, the probability that the input $\\boldsymbol{x}$\n",
- "is in class 0 or 1 is just. We let $\\theta$ represent the unknown weights and biases to be adjusted by our equations). The variable $x$\n",
- "represents our activation values $z$. We have"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp (- \\boldsymbol{x}} ,\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "where $y \\in \\{0, 1\\}$ and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
- "of our network.\n",
- "\n",
- "\n",
- "## Defining the cost function\n",
- "\n",
- "Our cost function is given as (see the Logistic regression lectures)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
- "y_i \\ln[P(y_i = 0)] + (1 - y_i) \\ln [1 - P(y_i = 0)] = \\sum_{i=1}^n \\mathcal{L}_i(\\boldsymbol{\\theta}) .\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n",
- "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$. \n",
- "The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather\n",
- "than maximizing a negative number. \n",
- "\n",
- "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector: \n",
- "\n",
- "$y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n",
- "\n",
- "\n",
- "$y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n",
- "\n",
- "\n",
- "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$).. \n",
- "\n",
- "If $\\boldsymbol{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n",
- "output vector $\\boldsymbol{y}_i$. \n",
- "The probability of $\\boldsymbol{x}_i$ being in class $c$ will be given by the softmax function:"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
- "{\\sum_{c'=0}^{C-1} \\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_{c'})}} ,\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "which reduces to the logistic function in the binary case. \n",
- "The likelihood of this $C$-class classifier\n",
- "is now given as:"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Again we take the negative log-likelihood to define our cost function:"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "$$\n",
- "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n \\sum_{c=0}^{C-1}\n",
- "y_{ic} \\ln[P(y_{ic} = 1)] = \\sum_{i=1}^n\n",
- "\\mathcal{L}_i(\\boldsymbol{\\theta}) .\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!\n",
- "We leave it as an exercise in project 2 to derive these equations.\n",
- "\n",
- "\n",
- "\n",
- "## Developing a code for doing neural networks with back propagation\n",
- "\n",
- "\n",
- "One can identify a set of key steps when using neural networks to solve supervised learning problems: \n",
- "\n",
- "1. Collect and pre-process data \n",
- "\n",
- "2. Define model and architecture \n",
- "\n",
- "3. Choose cost function and optimizer \n",
- "\n",
- "4. Train the model \n",
- "\n",
- "5. Evaluate model performance on test data \n",
- "\n",
- "6. Adjust hyperparameters (if necessary, network architecture)\n",
- "\n",
- "## Collect and pre-process data\n",
- "\n",
- "Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**\n",
- "package. You may also find it for example [here](http://yann.lecun.com/exdb/mnist/). \n",
- "The *MNIST* (Modified National Institute of Standards and Technology) database is a large database\n",
- "of handwritten digits that is commonly used for training various image processing systems. \n",
- "The MNIST dataset consists of 70 000 images of size 28x28 pixels, each labeled from 0 to 9. \n",
- "The scikit-learn dataset we will use consists of a selection of 1797 images of size $8\\times 8$ collected and processed from this database. \n",
- "\n",
- "To feed data into a feed-forward neural network we need to represent\n",
- "the inputs as a feature matrix $X = (n_{inputs}, n_{features})$. Each\n",
- "row represents an *input*, in this case a handwritten digit, and\n",
- "each column represents a *feature*, in this case a pixel. The\n",
- "correct answers, also known as *labels* or *targets* are\n",
- "represented as a 1D array of integers \n",
- "$Y = (n_{inputs}) = (5, 3, 1, 8,...)$.\n",
- "\n",
- "As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from\n",
- "measurements of height (in m) \n",
- "and weight (in kg). If we have measurements of 5 people the feature matrix could be for example: \n",
- "\n",
- "$$ X = \\begin{bmatrix}\n",
- "1.85 & 81\\\\\n",
- "1.71 & 65\\\\\n",
- "1.95 & 103\\\\\n",
- "1.55 & 42\\\\\n",
- "1.63 & 56\n",
- "\\end{bmatrix} ,$$ \n",
- "\n",
- "and the targets would be: \n",
- "\n",
- "$$ Y = (23.7, 22.2, 27.1, 17.5, 21.1) $$ \n",
- "\n",
- "Since each input image is a 2D matrix, we need to flatten the image\n",
- "(i.e. \"unravel\" the 2D matrix into a 1D array) to turn the data into a\n",
- "feature matrix. This means we lose all spatial information in the\n",
- "image, such as locality and translational invariance. More complicated\n",
- "architectures such as Convolutional Neural Networks can take advantage\n",
- "of such information, and are most commonly applied when analyzing\n",
- "images."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)\n",
- "labels = (n_inputs) = (1797,)\n",
- "X = (n_inputs, n_features) = (1797, 64)\n"
- ]
- },
- {
- "data": {
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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# import necessary packages\n",
- "import numpy as np\n",
- "import matplotlib.pyplot as plt\n",
- "from sklearn import datasets\n",
- "\n",
- "\n",
- "# ensure the same random numbers appear every time\n",
- "np.random.seed(0)\n",
- "\n",
- "# display images in notebook\n",
- "%matplotlib inline\n",
- "plt.rcParams['figure.figsize'] = (12,12)\n",
- "\n",
- "\n",
- "# download MNIST dataset\n",
- "digits = datasets.load_digits()\n",
- "\n",
- "# define inputs and labels\n",
- "inputs = digits.images\n",
- "labels = digits.target\n",
- "\n",
- "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
- "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
- "\n",
- "\n",
- "# flatten the image\n",
- "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
- "n_inputs = len(inputs)\n",
- "inputs = inputs.reshape(n_inputs, -1)\n",
- "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
- "\n",
- "\n",
- "# choose some random images to display\n",
- "indices = np.arange(n_inputs)\n",
- "random_indices = np.random.choice(indices, size=5)\n",
- "\n",
- "for i, image in enumerate(digits.images[random_indices]):\n",
- " plt.subplot(1, 5, i+1)\n",
- " plt.axis('off')\n",
- " plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
- " plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Train and test datasets\n",
- "\n",
- "Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions. \n",
- "\n",
- "We will reserve $80 \\%$ of our dataset for training and $20 \\%$ for testing. \n",
- "\n",
- "It is important that the train and test datasets are drawn randomly from our dataset, to ensure\n",
- "no bias in the sampling. \n",
- "Say you are taking measurements of weather data to predict the weather in the coming 5 days.\n",
- "You don't want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data\n",
- "collected from 12.00 to 24.00."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Number of training images: 1437\n",
- "Number of test images: 360\n"
- ]
- }
- ],
- "source": [
- "from sklearn.model_selection import train_test_split\n",
- "\n",
- "# one-liner from scikit-learn library\n",
- "train_size = 0.8\n",
- "test_size = 1 - train_size\n",
- "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
- " test_size=test_size)\n",
- "\n",
- "# equivalently in numpy\n",
- "def train_test_split_numpy(inputs, labels, train_size, test_size):\n",
- " n_inputs = len(inputs)\n",
- " inputs_shuffled = inputs.copy()\n",
- " labels_shuffled = labels.copy()\n",
- " \n",
- " np.random.shuffle(inputs_shuffled)\n",
- " np.random.shuffle(labels_shuffled)\n",
- " \n",
- " train_end = int(n_inputs*train_size)\n",
- " X_train, X_test = inputs_shuffled[:train_end], inputs_shuffled[train_end:]\n",
- " Y_train, Y_test = labels_shuffled[:train_end], labels_shuffled[train_end:]\n",
- " \n",
- " return X_train, X_test, Y_train, Y_test\n",
- "\n",
- "#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)\n",
- "\n",
- "print(\"Number of training images: \" + str(len(X_train)))\n",
- "print(\"Number of test images: \" + str(len(X_test)))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Define model and architecture\n",
- "\n",
- "Our simple feed-forward neural network will consist of an *input* layer, a single *hidden* layer and an *output* layer. The activation $y$ of each neuron is a weighted sum of inputs, passed through an activation function: \n",
- "\n",
- "$$ z = \\sum_{i=1}^n w_i a_i ,$$\n",
- "\n",
- "$$ y = f(z) ,$$\n",
- "\n",
- "where $f$ is the activation function, $a_i$ represents input from neuron $i$ in the preceding layer\n",
- "and $w_i$ is the weight to input $i$. \n",
- "The activation of the neurons in the input layer is just the features (e.g. a pixel value). \n",
- "\n",
- "The simplest activation function for a neuron is the *Heaviside* function:\n",
- "\n",
- "$$ f(z) = \n",
- "\\begin{cases}\n",
- "1, & z > 0\\\\\n",
- "0, & \\text{otherwise}\n",
- "\\end{cases}\n",
- "$$\n",
- "\n",
- "A feed-forward neural network with this activation is known as a *perceptron*. \n",
- "For a binary classifier (i.e. two classes, 0 or 1, dog or not-dog) we can also use this in our output layer. \n",
- "This activation can be generalized to $k$ classes (using e.g. the *one-against-all* strategy), \n",
- "and we call these architectures *multiclass perceptrons*. \n",
- "\n",
- "However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and \n",
- "Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function. \n",
- "\n",
- "Typical choices for activation functions include the sigmoid function, hyperbolic tangent, and Rectified Linear Unit (ReLU). \n",
- "We will be using the sigmoid function $\\sigma(x)$: \n",
- "\n",
- "$$ f(x) = \\sigma(x) = \\frac{1}{1 + e^{-x}} ,$$\n",
- "\n",
- "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011.\n",
- "\n",
- "\n",
- "## Layers\n",
- "\n",
- "* Input \n",
- "\n",
- "Since each input image has 8x8 = 64 pixels or features, we have an input layer of 64 neurons. \n",
- "\n",
- "* Hidden layer\n",
- "\n",
- "We will use 50 neurons in the hidden layer receiving input from the neurons in the input layer. \n",
- "Since each neuron in the hidden layer is connected to the 64 inputs we have 64x50 = 3200 weights to the hidden layer. \n",
- "\n",
- "* Output\n",
- "\n",
- "If we were building a binary classifier, it would be sufficient with a single neuron in the output layer,\n",
- "which could output 0 or 1 according to the Heaviside function. This would be an example of a *hard* classifier, meaning it outputs the class of the input directly. However, if we are dealing with noisy data it is often beneficial to use a *soft* classifier, which outputs the probability of being in class 0 or 1. \n",
- "\n",
- "For a soft binary classifier, we could use a single neuron and interpret the output as either being the probability of being in class 0 or the probability of being in class 1. Alternatively we could use 2 neurons, and interpret each neuron as the probability of being in each class. \n",
- "\n",
- "Since we are doing multiclass classification, with 10 categories, it is natural to use 10 neurons in the output layer. We number the neurons $j = 0,1,...,9$. The activation of each output neuron $j$ will be according to the *softmax* function: \n",
- "\n",
- "$$ P(\\text{class $j$} \\mid \\text{input $\\boldsymbol{a}$}) = \\frac{\\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_j)}}\n",
- "{\\sum_{c=0}^{9} \\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_c)}} ,$$ \n",
- "\n",
- "i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\\boldsymbol{a}$, with $\\boldsymbol{w}_j$ the weights of neuron $j$ to the inputs. \n",
- "The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1. \n",
- "The exponent is just the weighted sum of inputs as before: \n",
- "\n",
- "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i+b_j.$$ \n",
- "\n",
- "Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500\n",
- "weights to the output layer.\n",
- "\n",
- "\n",
- "## Weights and biases\n",
- "\n",
- "Typically weights are initialized with small values distributed around zero, drawn from a uniform\n",
- "or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless. \n",
- "\n",
- "Adding a bias value to the weighted sum of inputs allows the neural network to represent a greater range\n",
- "of values. Without it, any input with the value 0 will be mapped to zero (before being passed through the activation). The bias unit has an output of 1, and a weight to each neuron $j$, $b_j$: \n",
- "\n",
- "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i + 1\\cdot b_j.$$ \n",
- "\n",
- "The bias weights $\\boldsymbol{b}$ are often initialized to zero, but a small value like $0.01$ ensures all neurons have some output which can be backpropagated in the first training cycle."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [],
- "source": [
- "# building our neural network\n",
- "\n",
- "n_inputs, n_features = X_train.shape\n",
- "n_hidden_neurons = 50\n",
- "n_categories = 10\n",
- "\n",
- "# we make the weights normally distributed using numpy.random.randn\n",
- "\n",
- "# weights and bias in the hidden layer\n",
- "hidden_weights = np.random.randn(n_features, n_hidden_neurons)\n",
- "hidden_bias = np.zeros(n_hidden_neurons) + 0.01\n",
- "\n",
- "# weights and bias in the output layer\n",
- "output_weights = np.random.randn(n_hidden_neurons, n_categories)\n",
- "output_bias = np.zeros(n_categories) + 0.01"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Feed-forward pass\n",
- "\n",
- "Denote $F$ the number of features, $H$ the number of hidden neurons and $C$ the number of categories. \n",
- "For each input image we calculate a weighted sum of input features (pixel values) to each neuron $j$ in the hidden layer $l$: \n",
- "\n",
- "$$ z_{j}^{l} = \\sum_{i=1}^{F} w_{ij}^{l} x_i + b_{j}^{l},$$\n",
- "\n",
- "this is then passed through our activation function \n",
- "\n",
- "$$ a_{j}^{l} = f(z_{j}^{l}) .$$ \n",
- "\n",
- "We calculate a weighted sum of inputs (activations in the hidden layer) to each neuron $j$ in the output layer: \n",
- "\n",
- "$$ z_{j}^{L} = \\sum_{i=1}^{H} w_{ij}^{L} a_{i}^{l} + b_{j}^{L}.$$ \n",
- "\n",
- "Finally we calculate the output of neuron $j$ in the output layer using the softmax function: \n",
- "\n",
- "$$ a_{j}^{L} = \\frac{\\exp{(z_j^{L})}}\n",
- "{\\sum_{c=0}^{C-1} \\exp{(z_c^{L})}} .$$ \n",
- "\n",
- "\n",
- "## Matrix multiplication\n",
- "\n",
- "Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden\n",
- "layer have the dimensions \n",
- "$W_{hidden} = (n_{features}, n_{hidden})$,\n",
- "we can easily feed the network all our training data in one go by taking the matrix product \n",
- "\n",
- "$$ X W^{h} = (n_{inputs}, n_{hidden}),$$ \n",
- "\n",
- "and obtain a matrix that holds the weighted sum of inputs to the hidden layer\n",
- "for each input image and each hidden neuron. \n",
- "We also add the bias to obtain a matrix of weighted sums to the hidden layer $Z^{h}$: \n",
- "\n",
- "$$ \\hat{z}^{l} = \\hat{X} \\hat{W}^{l} + \\hat{b}^{l} ,$$\n",
- "\n",
- "meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image. \n",
- "This is then passed through the activation: \n",
- "\n",
- "$$ \\hat{a}^{l} = f(\\hat{z}^l) .$$ \n",
- "\n",
- "This is fed to the output layer: \n",
- "\n",
- "$$ \\hat{z}^{L} = \\hat{a}^{L} \\hat{W}^{L} + \\hat{b}^{L} .$$\n",
- "\n",
- "Finally we receive our output values for each image and each category by passing it through the softmax function: \n",
- "\n",
- "$$ output = softmax (\\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "probabilities = (n_inputs, n_categories) = (1437, 10)\n",
- "probability that image 0 is in category 0,1,2,...,9 = \n",
- "[5.41511965e-04 2.17174962e-03 8.84355903e-03 1.44970586e-03\n",
- " 1.10378326e-04 5.08318298e-09 2.03256632e-04 1.92507116e-03\n",
- " 9.84443254e-01 3.11507992e-04]\n",
- "probabilities sum up to: 1.0\n",
- "\n",
- "predictions = (n_inputs) = (1437,)\n",
- "prediction for image 0: 8\n",
- "correct label for image 0: 6\n"
- ]
- }
- ],
- "source": [
- "# setup the feed-forward pass, subscript h = hidden layer\n",
- "\n",
- "def sigmoid(x):\n",
- " return 1/(1 + np.exp(-x))\n",
- "\n",
- "def feed_forward(X):\n",
- " # weighted sum of inputs to the hidden layer\n",
- " z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
- " # activation in the hidden layer\n",
- " a_h = sigmoid(z_h)\n",
- " \n",
- " # weighted sum of inputs to the output layer\n",
- " z_o = np.matmul(a_h, output_weights) + output_bias\n",
- " # softmax output\n",
- " # axis 0 holds each input and axis 1 the probabilities of each category\n",
- " exp_term = np.exp(z_o)\n",
- " probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
- " \n",
- " return probabilities\n",
- "\n",
- "probabilities = feed_forward(X_train)\n",
- "print(\"probabilities = (n_inputs, n_categories) = \" + str(probabilities.shape))\n",
- "print(\"probability that image 0 is in category 0,1,2,...,9 = \\n\" + str(probabilities[0]))\n",
- "print(\"probabilities sum up to: \" + str(probabilities[0].sum()))\n",
- "print()\n",
- "\n",
- "# we obtain a prediction by taking the class with the highest likelihood\n",
- "def predict(X):\n",
- " probabilities = feed_forward(X)\n",
- " return np.argmax(probabilities, axis=1)\n",
- "\n",
- "predictions = predict(X_train)\n",
- "print(\"predictions = (n_inputs) = \" + str(predictions.shape))\n",
- "print(\"prediction for image 0: \" + str(predictions[0]))\n",
- "print(\"correct label for image 0: \" + str(Y_train[0]))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Choose cost function and optimizer\n",
- "\n",
- "To measure how well our neural network is doing we need to introduce a cost function. \n",
- "We will call the function that gives the error of a single sample output the *loss* function, and the function\n",
- "that gives the total error of our network across all samples the *cost* function.\n",
- "A typical choice for multiclass classification is the *cross-entropy* loss, also known as the negative log likelihood. \n",
- "\n",
- "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector: \n",
- "\n",
- "$$ y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ \n",
- "\n",
- "\n",
- "$$ y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$ \n",
- "\n",
- "\n",
- "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset. \n",
- "\n",
- "Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector. \n",
- "We define the cost function $\\mathcal{C}$ as a sum over the cross-entropy loss for each point $\\boldsymbol{x}_i$ in the dataset:"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation} \\mathcal{C}(\\boldsymbol{\\theta}) = \\sum_{i=1}^N \\mathcal{L}_i (\\boldsymbol{\\theta}) \n",
- "\\label{_auto11} \\tag{16}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "\n",
- "\n",
- "$$\n",
- "\\begin{equation} \n",
- " = -\\sum_{i=1}^N \\sum_{c=0}^{C-1} y_{ic} \\log P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) .\n",
- "\\label{_auto12} \\tag{17}\n",
- "\\end{equation}\n",
- "$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the one-hot representation only one of the terms in the loss function is non-zero, namely the\n",
- "probability of the correct category $c'$ \n",
- "(i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong\n",
- "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\boldsymbol{\\theta}$ represents the parameters of our network, i.e. all the weights and biases. \n",
- "\n",
- "A full derivation is given in the appendix at the end.\n",
- "\n",
- "## Optimizing the cost function\n",
- "\n",
- "The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent\n",
- "is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a *local* minimum of the cost function. \n",
- "Each parameter $\\theta$ is iteratively adjusted according to the rule \n",
- "\n",
- "$$ \\theta_{i+1} = \\theta_i - \\eta \\nabla \\mathcal{C}(\\theta_i) ,$$\n",
- "\n",
- "where $\\eta$ is known as the *learning rate*, which controls how big a step we take towards the minimum. \n",
- "This update can be repeated for any number of iterations, or until we are satisfied with the result. \n",
- "\n",
- "A simple and effective improvement is a variant called *Batch Gradient Descent*. \n",
- "Instead of calculating the gradient on the whole dataset, we calculate an approximation of the gradient\n",
- "on a subset of the data called a *minibatch*. \n",
- "If there are $N$ data points and we have a minibatch size of $M$, the total number of batches\n",
- "is $N/M$. \n",
- "We denote each minibatch $B_k$, with $k = 1, 2,...,N/M$. The gradient then becomes: \n",
- "\n",
- "$$ \\nabla \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
- "\\frac{1}{M} \\sum_{i \\in B_k} \\nabla \\mathcal{L}_i(\\theta) ,$$\n",
- "\n",
- "i.e. instead of averaging the loss over the entire dataset, we average over a minibatch. \n",
- "\n",
- "This has two important benefits: \n",
- "1. Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima. \n",
- "\n",
- "2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient. \n",
- "\n",
- "\n",
- "## Regularization\n",
- "\n",
- "It is common to add an extra term to the cost function, proportional\n",
- "to the size of the weights. This is equivalent to constraining the\n",
- "size of the weights, so that they do not grow out of control.\n",
- "Constraining the size of the weights means that the weights cannot\n",
- "grow arbitrarily large to fit the training data, and in this way\n",
- "reduces *overfitting*.\n",
- "\n",
- "We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes: \n",
- "\n",
- "$$ \\nabla \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
- "\\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}_i(\\theta) + \\lambda \\lvert \\lvert \\boldsymbol{w} \\rvert \\rvert_2^2 \n",
- "= \\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}(\\theta) + \\lambda \\sum_{ij} w_{ij}^2,$$ \n",
- "\n",
- "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n",
- "\n",
- "\n",
- "In order to train the model, we need to calculate the derivative of\n",
- "the cost function with respect to every bias and weight in the\n",
- "network. In total our network has $(64 + 1)\\times 50=3250$ weights in\n",
- "the hidden layer and $(50 + 1)\\times 10=510$ weights to the output\n",
- "layer ($+1$ for the bias), and the gradient must be calculated for\n",
- "every parameter. We use the *backpropagation* algorithm discussed\n",
- "above. This is a clever use of the chain rule that allows us to\n",
- "calculate the gradient efficently. \n",
- "\n",
- "\n",
- "## Matrix multiplication\n",
- "\n",
- "To more efficently train our network these equations are implemented using matrix operations. \n",
- "The error in the output layer is calculated simply as \n",
- "\n",
- "$$ \\delta_L = \\hat{y} - y = (n_{inputs}, n_{categories}) .$$ \n",
- "\n",
- "The gradient for the output weights is calculated as \n",
- "\n",
- "$$ \\nabla W_{L} = \\hat{a}^T \\delta_L = (n_{hidden}, n_{categories}) ,$$\n",
- "\n",
- "where $\\hat{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input. \n",
- "Since we are going backwards we have to transpose the activation matrix. \n",
- "\n",
- "The gradient with respect to the output bias is then \n",
- "\n",
- "$$ \\nabla \\hat{b}_{L} = \\sum_{i=1}^{n_{inputs}} \\delta_L = (n_{categories}) .$$ \n",
- "\n",
- "The error in the hidden layer is \n",
- "\n",
- "$$ \\Delta_h = \\delta_L W_{L}^T \\circ f'(z_{h}) = \\delta_L W_{L}^T \\circ a_{h} \\circ (1 - a_{h}) = (n_{inputs}, n_{hidden}) ,$$ \n",
- "\n",
- "where $f'(a_{h})$ is the derivative of the activation in the hidden layer. The matrix products mean\n",
- "that we are summing up the products for each neuron in the output layer. The symbol $\\circ$ denotes\n",
- "the *Hadamard product*, meaning element-wise multiplication. \n",
- "\n",
- "This again gives us the gradients in the hidden layer: \n",
- "\n",
- "$$ \\nabla W_{h} = X^T \\delta_h = (n_{features}, n_{hidden}) ,$$ \n",
- "\n",
- "$$ \\nabla b_{h} = \\sum_{i=1}^{n_{inputs}} \\delta_h = (n_{hidden}) .$$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Old accuracy on training data: 0.1440501043841336\n"
- ]
- },
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: overflow encountered in exp\n",
- " after removing the cwd from sys.path.\n"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "New accuracy on training data: 0.09394572025052192\n"
- ]
- }
- ],
- "source": [
- "# to categorical turns our integer vector into a onehot representation\n",
- "#from keras.utils import to_categorical\n",
- "\n",
- "# calculate the accuracy score of our model\n",
- "from sklearn.metrics import accuracy_score\n",
- "\n",
- "# one-hot in numpy\n",
- "def to_categorical_numpy(integer_vector):\n",
- " n_inputs = len(integer_vector)\n",
- " n_categories = np.max(integer_vector) + 1\n",
- " onehot_vector = np.zeros((n_inputs, n_categories))\n",
- " onehot_vector[range(n_inputs), integer_vector] = 1\n",
- " \n",
- " return onehot_vector\n",
- "\n",
- "#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)\n",
- "Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)\n",
- "\n",
- "def feed_forward_train(X):\n",
- " # weighted sum of inputs to the hidden layer\n",
- " z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
- " # activation in the hidden layer\n",
- " a_h = sigmoid(z_h)\n",
- " \n",
- " # weighted sum of inputs to the output layer\n",
- " z_o = np.matmul(a_h, output_weights) + output_bias\n",
- " # softmax output\n",
- " # axis 0 holds each input and axis 1 the probabilities of each category\n",
- " exp_term = np.exp(z_o)\n",
- " probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
- " \n",
- " # for backpropagation need activations in hidden and output layers\n",
- " return a_h, probabilities\n",
- "\n",
- "def backpropagation(X, Y):\n",
- " a_h, probabilities = feed_forward_train(X)\n",
- " \n",
- " # error in the output layer\n",
- " error_output = probabilities - Y\n",
- " # error in the hidden layer\n",
- " error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)\n",
- " \n",
- " # gradients for the output layer\n",
- " output_weights_gradient = np.matmul(a_h.T, error_output)\n",
- " output_bias_gradient = np.sum(error_output, axis=0)\n",
- " \n",
- " # gradient for the hidden layer\n",
- " hidden_weights_gradient = np.matmul(X.T, error_hidden)\n",
- " hidden_bias_gradient = np.sum(error_hidden, axis=0)\n",
- "\n",
- " return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient\n",
- "\n",
- "print(\"Old accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))\n",
- "\n",
- "eta = 0.01\n",
- "lmbd = 0.01\n",
- "for i in range(1000):\n",
- " # calculate gradients\n",
- " dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)\n",
- " \n",
- " # regularization term gradients\n",
- " dWo += lmbd * output_weights\n",
- " dWh += lmbd * hidden_weights\n",
- " \n",
- " # update weights and biases\n",
- " output_weights -= eta * dWo\n",
- " output_bias -= eta * dBo\n",
- " hidden_weights -= eta * dWh\n",
- " hidden_bias -= eta * dBh\n",
- "\n",
- "print(\"New accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Improving performance\n",
- "\n",
- "As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image. \n",
- "In order to obtain a network that does something useful, we will have to do a bit more work. \n",
- "\n",
- "The choice of *hyperparameters* such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a *grid-search* is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates $\\eta = 10^{-6}, 10^{-5},...,10^{-1}$ with different regularization parameters $\\lambda = 10^{-6},...,10^{-0}$. \n",
- "\n",
- "Next, we haven't implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an *iteration*, and a full training period\n",
- "going through the entire dataset ($n/M$ batches) an *epoch*.\n",
- "\n",
- "If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers. \n",
- "Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/). \n",
- "\n",
- "## Full object-oriented implementation\n",
- "\n",
- "It is very natural to think of the network as an object, with specific instances of the network\n",
- "being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [],
- "source": [
- "class NeuralNetwork:\n",
- " def __init__(\n",
- " self,\n",
- " X_data,\n",
- " Y_data,\n",
- " n_hidden_neurons=50,\n",
- " n_categories=10,\n",
- " epochs=10,\n",
- " batch_size=100,\n",
- " eta=0.1,\n",
- " lmbd=0.0,\n",
- "\n",
- " ):\n",
- " self.X_data_full = X_data\n",
- " self.Y_data_full = Y_data\n",
- "\n",
- " self.n_inputs = X_data.shape[0]\n",
- " self.n_features = X_data.shape[1]\n",
- " self.n_hidden_neurons = n_hidden_neurons\n",
- " self.n_categories = n_categories\n",
- "\n",
- " self.epochs = epochs\n",
- " self.batch_size = batch_size\n",
- " self.iterations = self.n_inputs // self.batch_size\n",
- " self.eta = eta\n",
- " self.lmbd = lmbd\n",
- "\n",
- " self.create_biases_and_weights()\n",
- "\n",
- " def create_biases_and_weights(self):\n",
- " self.hidden_weights = np.random.randn(self.n_features, self.n_hidden_neurons)\n",
- " self.hidden_bias = np.zeros(self.n_hidden_neurons) + 0.01\n",
- "\n",
- " self.output_weights = np.random.randn(self.n_hidden_neurons, self.n_categories)\n",
- " self.output_bias = np.zeros(self.n_categories) + 0.01\n",
- "\n",
- " def feed_forward(self):\n",
- " # feed-forward for training\n",
- " self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias\n",
- " self.a_h = sigmoid(self.z_h)\n",
- "\n",
- " self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias\n",
- "\n",
- " exp_term = np.exp(self.z_o)\n",
- " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
- "\n",
- " def feed_forward_out(self, X):\n",
- " # feed-forward for output\n",
- " z_h = np.matmul(X, self.hidden_weights) + self.hidden_bias\n",
- " a_h = sigmoid(z_h)\n",
- "\n",
- " z_o = np.matmul(a_h, self.output_weights) + self.output_bias\n",
- " \n",
- " exp_term = np.exp(z_o)\n",
- " probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
- " return probabilities\n",
- "\n",
- " def backpropagation(self):\n",
- " error_output = self.probabilities - self.Y_data\n",
- " error_hidden = np.matmul(error_output, self.output_weights.T) * self.a_h * (1 - self.a_h)\n",
- "\n",
- " self.output_weights_gradient = np.matmul(self.a_h.T, error_output)\n",
- " self.output_bias_gradient = np.sum(error_output, axis=0)\n",
- "\n",
- " self.hidden_weights_gradient = np.matmul(self.X_data.T, error_hidden)\n",
- " self.hidden_bias_gradient = np.sum(error_hidden, axis=0)\n",
- "\n",
- " if self.lmbd > 0.0:\n",
- " self.output_weights_gradient += self.lmbd * self.output_weights\n",
- " self.hidden_weights_gradient += self.lmbd * self.hidden_weights\n",
- "\n",
- " self.output_weights -= self.eta * self.output_weights_gradient\n",
- " self.output_bias -= self.eta * self.output_bias_gradient\n",
- " self.hidden_weights -= self.eta * self.hidden_weights_gradient\n",
- " self.hidden_bias -= self.eta * self.hidden_bias_gradient\n",
- "\n",
- " def predict(self, X):\n",
- " probabilities = self.feed_forward_out(X)\n",
- " return np.argmax(probabilities, axis=1)\n",
- "\n",
- " def predict_probabilities(self, X):\n",
- " probabilities = self.feed_forward_out(X)\n",
- " return probabilities\n",
- "\n",
- " def train(self):\n",
- " data_indices = np.arange(self.n_inputs)\n",
- "\n",
- " for i in range(self.epochs):\n",
- " for j in range(self.iterations):\n",
- " # pick datapoints with replacement\n",
- " chosen_datapoints = np.random.choice(\n",
- " data_indices, size=self.batch_size, replace=False\n",
- " )\n",
- "\n",
- " # minibatch training data\n",
- " self.X_data = self.X_data_full[chosen_datapoints]\n",
- " self.Y_data = self.Y_data_full[chosen_datapoints]\n",
- "\n",
- " self.feed_forward()\n",
- " self.backpropagation()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Evaluate model performance on test data\n",
- "\n",
- "To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data. \n",
- "We measure the performance of the network using the *accuracy* score. \n",
- "The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of $1$. \n",
- "\n",
- "$$ \\text{Accuracy} = \\frac{\\sum_{i=1}^n I(\\hat{y}_i = y_i)}{n} ,$$ \n",
- "\n",
- "where $I$ is the indicator function, $1$ if $\\hat{y}_i = y_i$ and $0$ otherwise."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Accuracy score on test set: 0.9472222222222222\n"
- ]
- }
- ],
- "source": [
- "epochs = 100\n",
- "batch_size = 100\n",
- "\n",
- "dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n",
- " n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n",
- "dnn.train()\n",
- "test_predict = dnn.predict(X_test)\n",
- "\n",
- "# accuracy score from scikit library\n",
- "print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n",
- "\n",
- "# equivalent in numpy\n",
- "def accuracy_score_numpy(Y_test, Y_pred):\n",
- " return np.sum(Y_test == Y_pred) / len(Y_test)\n",
- "\n",
- "#print(\"Accuracy score on test set: \", accuracy_score_numpy(Y_test, test_predict))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Adjust hyperparameters\n",
- "\n",
- "We now perform a grid search to find the optimal hyperparameters for the network. \n",
- "Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around $98\\%$ ($2\\%$ error rate)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "ename": "NameError",
- "evalue": "name 'eta_vals' is not defined",
- "output_type": "error",
- "traceback": [
- "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
- "\u001b[0;31mNameError\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 6\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mtrain_accuracy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meta_vals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlmbd_vals\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[0m\u001b[1;32m 9\u001b[0m \u001b[0mtest_accuracy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meta_vals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlmbd_vals\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 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
- "\u001b[0;31mNameError\u001b[0m: name 'eta_vals' is not defined"
- ]
- }
- ],
- "source": [
- "eta_vals = np.logspace(-5, 1, 7)\n",
- "lmbd_vals = np.logspace(-5, 1, 7)\n",
- "# store the models for later use\n",
- "DNN_numpy = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
- "\n",
- "# grid search\n",
- "for i, eta in enumerate(eta_vals):\n",
- " for j, lmbd in enumerate(lmbd_vals):\n",
- " dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n",
- " n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n",
- " dnn.train()\n",
- " \n",
- " DNN_numpy[i][j] = dnn\n",
- " \n",
- " test_predict = dnn.predict(X_test)\n",
- " \n",
- " print(\"Learning rate = \", eta)\n",
- " print(\"Lambda = \", lmbd)\n",
- " print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n",
- " print()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Visualization"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "# visual representation of grid search\n",
- "# uses seaborn heatmap, you can also do this with matplotlib imshow\n",
- "import seaborn as sns\n",
- "\n",
- "sns.set()\n",
- "\n",
- "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "\n",
- "for i in range(len(eta_vals)):\n",
- " for j in range(len(lmbd_vals)):\n",
- " dnn = DNN_numpy[i][j]\n",
- " \n",
- " train_pred = dnn.predict(X_train) \n",
- " test_pred = dnn.predict(X_test)\n",
- "\n",
- " train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n",
- " test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n",
- "\n",
- " \n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Training Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()\n",
- "\n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Test Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## scikit-learn implementation\n",
- "\n",
- "**scikit-learn** focuses more\n",
- "on traditional machine learning methods, such as regression,\n",
- "clustering, decision trees, etc. As such, it has only two types of\n",
- "neural networks: Multi Layer Perceptron outputting continuous values,\n",
- "*MPLRegressor*, and Multi Layer Perceptron outputting labels,\n",
- "*MLPClassifier*. We will see how simple it is to use these classes.\n",
- "\n",
- "**scikit-learn** implements a few improvements from our neural network,\n",
- "such as early stopping, a varying learning rate, different\n",
- "optimization methods, etc. We would therefore expect a better\n",
- "performance overall."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "from sklearn.neural_network import MLPClassifier\n",
- "# store models for later use\n",
- "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
- "\n",
- "for i, eta in enumerate(eta_vals):\n",
- " for j, lmbd in enumerate(lmbd_vals):\n",
- " dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n",
- " alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n",
- " dnn.fit(X_train, Y_train)\n",
- " \n",
- " DNN_scikit[i][j] = dnn\n",
- " \n",
- " print(\"Learning rate = \", eta)\n",
- " print(\"Lambda = \", lmbd)\n",
- " print(\"Accuracy score on test set: \", dnn.score(X_test, Y_test))\n",
- " print()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Visualization"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 11,
- "metadata": {},
- "outputs": [
- {
- "ename": "NameError",
- "evalue": "name 'eta_vals' is not defined",
- "output_type": "error",
- "traceback": [
- "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
- "\u001b[0;31mNameError\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 6\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mtrain_accuracy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meta_vals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlmbd_vals\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[0m\u001b[1;32m 9\u001b[0m \u001b[0mtest_accuracy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meta_vals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlmbd_vals\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 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
- "\u001b[0;31mNameError\u001b[0m: name 'eta_vals' is not defined"
- ]
- }
- ],
-=======
- "execution_count": 12,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "source": [
- "# optional\n",
- "# visual representation of grid search\n",
- "# uses seaborn heatmap, could probably do this in matplotlib\n",
- "import seaborn as sns\n",
- "\n",
- "sns.set()\n",
- "\n",
- "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "\n",
- "for i in range(len(eta_vals)):\n",
- " for j in range(len(lmbd_vals)):\n",
- " dnn = DNN_scikit[i][j]\n",
- " \n",
- " train_pred = dnn.predict(X_train) \n",
- " test_pred = dnn.predict(X_test)\n",
- "\n",
- " train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n",
- " test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n",
- "\n",
- " \n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Training Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()\n",
- "\n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Test Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Building neural networks in Tensorflow and Keras\n",
- "\n",
- "Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn\n",
- "and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy\n",
- "and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer. \n",
- "\n",
- "In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite\n",
- "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n",
- "NumPy arrays.\n",
- "\n",
- "## Tensorflow\n",
- "\n",
- "Tensorflow is an open source library machine learning library\n",
- "developed by the Google Brain team for internal use. It was released\n",
- "under the Apache 2.0 open source license in November 9, 2015.\n",
- "\n",
- "Tensorflow is a computational framework that allows you to construct\n",
- "machine learning models at different levels of abstraction, from\n",
- "high-level, object-oriented APIs like Keras, down to the C++ kernels\n",
- "that Tensorflow is built upon. The higher levels of abstraction are\n",
- "simpler to use, but less flexible, and our choice of implementation\n",
- "should reflect the problems we are trying to solve.\n",
- "\n",
- "[Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation\n",
- "in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*\n",
- "to represent your model, and then create a Tensorflow *session* to run the graph.\n",
- "\n",
- "In this guide we will analyze the same data as we did in our NumPy and\n",
- "scikit-learn tutorial, gathered from the MNIST database of images. We\n",
- "will give an introduction to the lower level Python Application\n",
- "Program Interfaces (APIs), and see how we use them to build our graph.\n",
- "Then we will build (effectively) the same graph in Keras, to see just\n",
- "how simple solving a machine learning problem can be.\n",
- "\n",
- "To install tensorflow on Unix/Linux systems, use pip as"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 11,
- "metadata": {},
-=======
- "execution_count": 13,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "pip3 install tensorflow"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "and/or if you use **anaconda**, just write (or install from the graphical user interface)"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 12,
- "metadata": {},
-=======
- "execution_count": 14,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "conda install tensorflow"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Collect and pre-process data"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 12,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)\n",
- "labels = (n_inputs) = (1797,)\n",
- "X = (n_inputs, n_features) = (1797, 64)\n"
- ]
- },
- {
- "data": {
- "image/png": "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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
-=======
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "source": [
- "# import necessary packages\n",
- "import numpy as np\n",
- "import matplotlib.pyplot as plt\n",
- "from sklearn import datasets\n",
- "\n",
- "\n",
- "# ensure the same random numbers appear every time\n",
- "np.random.seed(0)\n",
- "\n",
- "# display images in notebook\n",
- "%matplotlib inline\n",
- "plt.rcParams['figure.figsize'] = (12,12)\n",
- "\n",
- "\n",
- "# download MNIST dataset\n",
- "digits = datasets.load_digits()\n",
- "\n",
- "# define inputs and labels\n",
- "inputs = digits.images\n",
- "labels = digits.target\n",
- "\n",
- "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
- "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
- "\n",
- "\n",
- "# flatten the image\n",
- "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
- "n_inputs = len(inputs)\n",
- "inputs = inputs.reshape(n_inputs, -1)\n",
- "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
- "\n",
- "\n",
- "# choose some random images to display\n",
- "indices = np.arange(n_inputs)\n",
- "random_indices = np.random.choice(indices, size=5)\n",
- "\n",
- "for i, image in enumerate(digits.images[random_indices]):\n",
- " plt.subplot(1, 5, i+1)\n",
- " plt.axis('off')\n",
- " plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
- " plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 13,
- "metadata": {},
- "outputs": [
- {
- "ename": "ModuleNotFoundError",
- "evalue": "No module named 'keras'",
- "output_type": "error",
- "traceback": [
- "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
- "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
- "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mkeras\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mutils\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mto_categorical\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel_selection\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtrain_test_split\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;31m# one-hot representation of labels\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mlabels\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mto_categorical\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabels\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
- "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'keras'"
- ]
- }
- ],
-=======
- "execution_count": 16,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "source": [
- "from keras.utils import to_categorical\n",
- "from sklearn.model_selection import train_test_split\n",
- "\n",
- "# one-hot representation of labels\n",
- "labels = to_categorical(labels)\n",
- "\n",
- "# split into train and test data\n",
- "train_size = 0.8\n",
- "test_size = 1 - train_size\n",
- "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
- " test_size=test_size)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Using TensorFlow backend\n",
- "\n",
- "1. Define model and architecture\n",
- "\n",
- "2. Choose cost function and optimizer"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 15,
- "metadata": {},
-=======
- "execution_count": 17,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "import tensorflow as tf\n",
- "\n",
- "class NeuralNetworkTensorflow:\n",
- " def __init__(\n",
- " self,\n",
- " X_train,\n",
- " Y_train,\n",
- " X_test,\n",
- " Y_test,\n",
- " n_neurons_layer1=100,\n",
- " n_neurons_layer2=50,\n",
- " n_categories=2,\n",
- " epochs=10,\n",
- " batch_size=100,\n",
- " eta=0.1,\n",
- " lmbd=0.0,\n",
- " ):\n",
- " \n",
- " # keep track of number of steps\n",
- " self.global_step = tf.Variable(0, dtype=tf.int32, trainable=False, name='global_step')\n",
- " \n",
- " self.X_train = X_train\n",
- " self.Y_train = Y_train\n",
- " self.X_test = X_test\n",
- " self.Y_test = Y_test\n",
- " \n",
- " self.n_inputs = X_train.shape[0]\n",
- " self.n_features = X_train.shape[1]\n",
- " self.n_neurons_layer1 = n_neurons_layer1\n",
- " self.n_neurons_layer2 = n_neurons_layer2\n",
- " self.n_categories = n_categories\n",
- " \n",
- " self.epochs = epochs\n",
- " self.batch_size = batch_size\n",
- " self.iterations = self.n_inputs // self.batch_size\n",
- " self.eta = eta\n",
- " self.lmbd = lmbd\n",
- " \n",
- " # build network piece by piece\n",
- " # name scopes (with) are used to enforce creation of new variables\n",
- " # https://www.tensorflow.org/guide/variables\n",
- " self.create_placeholders()\n",
- " self.create_DNN()\n",
- " self.create_loss()\n",
- " self.create_optimiser()\n",
- " self.create_accuracy()\n",
- " \n",
- " def create_placeholders(self):\n",
- " # placeholders are fine here, but \"Datasets\" are the preferred method\n",
- " # of streaming data into a model\n",
- " with tf.name_scope('data'):\n",
- " self.X = tf.placeholder(tf.float32, shape=(None, self.n_features), name='X_data')\n",
- " self.Y = tf.placeholder(tf.float32, shape=(None, self.n_categories), name='Y_data')\n",
- " \n",
- " def create_DNN(self):\n",
- " with tf.name_scope('DNN'):\n",
- " # the weights are stored to calculate regularization loss later\n",
- " \n",
- " # Fully connected layer 1\n",
- " self.W_fc1 = self.weight_variable([self.n_features, self.n_neurons_layer1], name='fc1', dtype=tf.float32)\n",
- " b_fc1 = self.bias_variable([self.n_neurons_layer1], name='fc1', dtype=tf.float32)\n",
- " a_fc1 = tf.nn.sigmoid(tf.matmul(self.X, self.W_fc1) + b_fc1)\n",
- " \n",
- " # Fully connected layer 2\n",
- " self.W_fc2 = self.weight_variable([self.n_neurons_layer1, self.n_neurons_layer2], name='fc2', dtype=tf.float32)\n",
- " b_fc2 = self.bias_variable([self.n_neurons_layer2], name='fc2', dtype=tf.float32)\n",
- " a_fc2 = tf.nn.sigmoid(tf.matmul(a_fc1, self.W_fc2) + b_fc2)\n",
- " \n",
- " # Output layer\n",
- " self.W_out = self.weight_variable([self.n_neurons_layer2, self.n_categories], name='out', dtype=tf.float32)\n",
- " b_out = self.bias_variable([self.n_categories], name='out', dtype=tf.float32)\n",
- " self.z_out = tf.matmul(a_fc2, self.W_out) + b_out\n",
- " \n",
- " def create_loss(self):\n",
- " with tf.name_scope('loss'):\n",
- " softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=self.Y, logits=self.z_out))\n",
- " \n",
- " regularizer_loss_fc1 = tf.nn.l2_loss(self.W_fc1)\n",
- " regularizer_loss_fc2 = tf.nn.l2_loss(self.W_fc2)\n",
- " regularizer_loss_out = tf.nn.l2_loss(self.W_out)\n",
- " regularizer_loss = self.lmbd*(regularizer_loss_fc1 + regularizer_loss_fc2 + regularizer_loss_out)\n",
- " \n",
- " self.loss = softmax_loss + regularizer_loss\n",
- "\n",
- " def create_accuracy(self):\n",
- " with tf.name_scope('accuracy'):\n",
- " probabilities = tf.nn.softmax(self.z_out)\n",
- " predictions = tf.argmax(probabilities, axis=1)\n",
- " labels = tf.argmax(self.Y, axis=1)\n",
- " \n",
- " correct_predictions = tf.equal(predictions, labels)\n",
- " correct_predictions = tf.cast(correct_predictions, tf.float32)\n",
- " self.accuracy = tf.reduce_mean(correct_predictions)\n",
- " \n",
- " def create_optimiser(self):\n",
- " with tf.name_scope('optimizer'):\n",
- " self.optimizer = tf.train.GradientDescentOptimizer(learning_rate=self.eta).minimize(self.loss, global_step=self.global_step)\n",
- " \n",
- " def weight_variable(self, shape, name='', dtype=tf.float32):\n",
- " initial = tf.truncated_normal(shape, stddev=0.1)\n",
- " return tf.Variable(initial, name=name, dtype=dtype)\n",
- " \n",
- " def bias_variable(self, shape, name='', dtype=tf.float32):\n",
- " initial = tf.constant(0.1, shape=shape)\n",
- " return tf.Variable(initial, name=name, dtype=dtype)\n",
- " \n",
- " def fit(self):\n",
- " data_indices = np.arange(self.n_inputs)\n",
- "\n",
- " with tf.Session() as sess:\n",
- " sess.run(tf.global_variables_initializer())\n",
- " for i in range(self.epochs):\n",
- " for j in range(self.iterations):\n",
- " chosen_datapoints = np.random.choice(data_indices, size=self.batch_size, replace=False)\n",
- " batch_X, batch_Y = self.X_train[chosen_datapoints], self.Y_train[chosen_datapoints]\n",
- " \n",
- " sess.run([DNN.loss, DNN.optimizer],\n",
- " feed_dict={DNN.X: batch_X,\n",
- " DNN.Y: batch_Y})\n",
- " accuracy = sess.run(DNN.accuracy,\n",
- " feed_dict={DNN.X: batch_X,\n",
- " DNN.Y: batch_Y})\n",
- " step = sess.run(DNN.global_step)\n",
- " \n",
- " self.train_loss, self.train_accuracy = sess.run([DNN.loss, DNN.accuracy],\n",
- " feed_dict={DNN.X: self.X_train,\n",
- " DNN.Y: self.Y_train})\n",
- " \n",
- " self.test_loss, self.test_accuracy = sess.run([DNN.loss, DNN.accuracy],\n",
- " feed_dict={DNN.X: self.X_test,\n",
- " DNN.Y: self.Y_test})"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Optimizing and using gradient descent"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 16,
- "metadata": {},
-=======
- "execution_count": 18,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "epochs = 100\n",
- "batch_size = 100\n",
- "n_neurons_layer1 = 100\n",
- "n_neurons_layer2 = 50\n",
- "n_categories = 10\n",
- "eta_vals = np.logspace(-5, 1, 7)\n",
- "lmbd_vals = np.logspace(-5, 1, 7)"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 17,
- "metadata": {},
-=======
- "execution_count": 19,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "DNN_tf = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
- " \n",
- "for i, eta in enumerate(eta_vals):\n",
- " for j, lmbd in enumerate(lmbd_vals):\n",
- " DNN = NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,\n",
- " n_neurons_layer1, n_neurons_layer2, n_categories,\n",
- " epochs=epochs, batch_size=batch_size, eta=eta, lmbd=lmbd)\n",
- " DNN.fit()\n",
- " \n",
- " DNN_tf[i][j] = DNN\n",
- " \n",
- " print(\"Learning rate = \", eta)\n",
- " print(\"Lambda = \", lmbd)\n",
- " print(\"Test accuracy: %.3f\" % DNN.test_accuracy)\n",
- " print()"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 18,
- "metadata": {},
-=======
- "execution_count": 20,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "# optional\n",
- "# visual representation of grid search\n",
- "# uses seaborn heatmap, could probably do this in matplotlib\n",
- "import seaborn as sns\n",
- "\n",
- "sns.set()\n",
- "\n",
- "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "\n",
- "for i in range(len(eta_vals)):\n",
- " for j in range(len(lmbd_vals)):\n",
- " DNN = DNN_tf[i][j]\n",
- "\n",
- " train_accuracy[i][j] = DNN.train_accuracy\n",
- " test_accuracy[i][j] = DNN.test_accuracy\n",
- "\n",
- " \n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Training Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()\n",
- "\n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Test Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 19,
- "metadata": {},
-=======
- "execution_count": 21,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "# optional\n",
- "# we can use log files to visualize our graph in Tensorboard\n",
- "writer = tf.summary.FileWriter('logs/')\n",
- "writer.add_graph(tf.get_default_graph())"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Using Keras\n",
- "\n",
- "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n",
- "that supports Tensorflow, CTNK and Theano as backends. \n",
- "If you have Tensorflow installed Keras is available through the *tf.keras* module. \n",
- "If you have Anaconda installed you may run the following command"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 20,
- "metadata": {},
-=======
- "execution_count": 22,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "conda install keras"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 21,
- "metadata": {},
-=======
- "execution_count": 23,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "pip3 install keras"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "or look up the [instructions here](https://keras.io/)."
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 22,
- "metadata": {},
-=======
- "execution_count": 24,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "from keras.models import Sequential\n",
- "from keras.layers import Dense\n",
- "from keras.regularizers import l2\n",
- "from keras.optimizers import SGD\n",
- "\n",
- "def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):\n",
- " model = Sequential()\n",
- " model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=l2(lmbd)))\n",
- " model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=l2(lmbd)))\n",
- " model.add(Dense(n_categories, activation='softmax'))\n",
- " \n",
- " sgd = SGD(lr=eta)\n",
- " model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
- " \n",
- " return model"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 23,
- "metadata": {},
-=======
- "execution_count": 25,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
- " \n",
- "for i, eta in enumerate(eta_vals):\n",
- " for j, lmbd in enumerate(lmbd_vals):\n",
- " DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,\n",
- " eta=eta, lmbd=lmbd)\n",
- " DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n",
- " scores = DNN.evaluate(X_test, Y_test)\n",
- " \n",
- " DNN_keras[i][j] = DNN\n",
- " \n",
- " print(\"Learning rate = \", eta)\n",
- " print(\"Lambda = \", lmbd)\n",
- " print(\"Test accuracy: %.3f\" % scores[1])\n",
- " print()"
- ]
- },
- {
- "cell_type": "code",
-<<<<<<< HEAD
- "execution_count": 24,
- "metadata": {},
-=======
- "execution_count": 26,
- "metadata": {
- "collapsed": false
- },
->>>>>>> 0c44eedada70ad53b4e4ccede22f51b6f2e4403c
- "outputs": [],
- "source": [
- "# optional\n",
- "# visual representation of grid search\n",
- "# uses seaborn heatmap, could probably do this in matplotlib\n",
- "import seaborn as sns\n",
- "\n",
- "sns.set()\n",
- "\n",
- "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
- "\n",
- "for i in range(len(eta_vals)):\n",
- " for j in range(len(lmbd_vals)):\n",
- " DNN = DNN_keras[i][j]\n",
- "\n",
- " train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]\n",
- " test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]\n",
- "\n",
- " \n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Training Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()\n",
- "\n",
- "fig, ax = plt.subplots(figsize = (10, 10))\n",
- "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
- "ax.set_title(\"Test Accuracy\")\n",
- "ax.set_ylabel(\"$\\eta$\")\n",
- "ax.set_xlabel(\"$\\lambda$\")\n",
- "plt.show()"
- ]
- }
- ],
- "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": "3.7.0"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/doc/pub/Splines/html/._Splines-bs000.html b/doc/pub/Splines/html/._Splines-bs000.html
index 746f6012c..bece1e921 100644
--- a/doc/pub/Splines/html/._Splines-bs000.html
+++ b/doc/pub/Splines/html/._Splines-bs000.html
@@ -79,45 +79,64 @@ Automatically generated HTML file from DocOnce source
None,
'___sec23'),
('Steepest descent example', 2, None, '___sec24'),
- ('Revisiting our first homework', 2, None, '___sec25'),
- ('Gradient descent example', 2, None, '___sec26'),
- ('The derivative of the cost/loss function', 2, None, '___sec27'),
- ('The Hessian matrix', 2, None, '___sec28'),
- ('Simple program', 2, None, '___sec29'),
- ('Gradient Descent Example', 2, None, '___sec30'),
+ ('Conjugate gradient', 2, None, '___sec25'),
+ ('Revisiting our first homework', 2, None, '___sec26'),
+ ('Gradient descent example', 2, None, '___sec27'),
+ ('The derivative of the cost/loss function', 2, None, '___sec28'),
+ ('The Hessian matrix', 2, None, '___sec29'),
+ ('Simple program', 2, None, '___sec30'),
+ ('Gradient Descent Example', 2, None, '___sec31'),
('And a corresponding example using _scikit-learn_',
2,
None,
- '___sec31'),
- ('Gradient descent and Ridge', 2, None, '___sec32'),
- ('Automatic differentiation', 2, None, '___sec33'),
- ('Using autograd', 2, None, '___sec34'),
- ('Autograd with more complicated functions', 2, None, '___sec35'),
+ '___sec32'),
+ ('Gradient descent and Ridge', 2, None, '___sec33'),
+ ('Automatic differentiation', 2, None, '___sec34'),
+ ('Using autograd', 2, None, '___sec35'),
+ ('Autograd with more complicated functions', 2, None, '___sec36'),
('More complicated functions using the elements of their '
'arguments directly',
2,
None,
- '___sec36'),
+ '___sec37'),
('Functions using mathematical functions from Numpy',
2,
None,
- '___sec37'),
- ('More autograd', 2, None, '___sec38'),
- ('And with loops', 2, None, '___sec39'),
- ('Using recursion', 2, None, '___sec40'),
- ('Unsupported functions', 2, None, '___sec41'),
+ '___sec38'),
+ ('More autograd', 2, None, '___sec39'),
+ ('And with loops', 2, None, '___sec40'),
+ ('Using recursion', 2, None, '___sec41'),
+ ('Unsupported functions', 2, None, '___sec42'),
('The syntax a.dot(b) when finding the dot product',
2,
None,
- '___sec42'),
- ('Recommended to avoid', 2, None, '___sec43'),
- ('Stochastic Gradient Descent', 2, None, '___sec44'),
- ('Computation of gradients', 2, None, '___sec45'),
- ('SGD example', 2, None, '___sec46'),
- ('The gradient step', 2, None, '___sec47'),
- ('Simple example code', 2, None, '___sec48'),
- ('When do we stop?', 2, None, '___sec49'),
- ('Slightly different approach', 2, None, '___sec50')]}
+ '___sec43'),
+ ('Recommended to avoid', 2, None, '___sec44'),
+ ('Stochastic Gradient Descent', 2, None, '___sec45'),
+ ('Computation of gradients', 2, None, '___sec46'),
+ ('SGD example', 2, None, '___sec47'),
+ ('The gradient step', 2, None, '___sec48'),
+ ('Simple example code', 2, None, '___sec49'),
+ ('When do we stop?', 2, None, '___sec50'),
+ ('Slightly different approach', 2, None, '___sec51'),
+ ('Program for stochastic gradient', 2, None, '___sec52'),
+ ('Momentum based methods', 2, None, '___sec53'),
+ ('Conjugate gradient method', 2, None, '___sec54'),
+ ('Conjugate gradient method', 2, None, '___sec55'),
+ ('Conjugate gradient method', 2, None, '___sec56'),
+ ('Conjugate gradient method', 2, None, '___sec57'),
+ ('Conjugate gradient method and iterations', 2, None, '___sec58'),
+ ('Conjugate gradient method', 2, None, '___sec59'),
+ ('Conjugate gradient method', 2, None, '___sec60'),
+ ('Conjugate gradient method', 2, None, '___sec61'),
+ ('Simple implementation of the Conjugate gradient algorithm',
+ 2,
+ None,
+ '___sec62'),
+ ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+ 2,
+ None,
+ '___sec63')]}
end of tocinfo -->
@@ -180,32 +199,45 @@ MathJax.Hub.Config({
-We will use linear regression as a case study for the gradient descent
-methods. Linear regression is a great test case for the gradient
-descent methods discussed in the lectures since it has several
-desirable properties such as:
-
-
-
An analytical solution (recall homework set 1).
-
The gradient can be computed analytically.
-
The cost function is convex which guarantees that gradient descent converges for small enough learning rates
-
-
-We revisit the example from homework set 1 where we had
-$$
-y_i = 5x_i^2 + 0.1\xi_i, \ i=1,\cdots,100
-$$
-
-with \( x_i \in [0,1] \) chosen randomly with a uniform distribution. Additionally \( \xi_i \) represents stochastic noise chosen according to a normal distribution \( \cal {N}(0,1) \).
-The linear regression model is given by
-$$
-h_\beta(x) = \hat{y} = \beta_0 + \beta_1 x,
-$$
-
-such that
-$$
-\hat{y}_i = \beta_0 + \beta_1 x_i.
-$$
+
-Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
+We will use linear regression as a case study for the gradient descent
+methods. Linear regression is a great test case for the gradient
+descent methods discussed in the lectures since it has several
+desirable properties such as:
-
-It is convenient to write \( \mathbf{\hat{y}} = X\beta \) where \( X \in \mathbb{R}^{100 \times 2} \) is the design matrix given by
+
+
An analytical solution (recall homework set 1).
+
The gradient can be computed analytically.
+
The cost function is convex which guarantees that gradient descent converges for small enough learning rates
+
+
+We revisit the example from homework set 1 where we had
$$
-X \equiv \begin{bmatrix}
-1 & x_1 \\
-\vdots & \vdots \\
-1 & x_{100} & \\
-\end{bmatrix}.
+y_i = 5x_i^2 + 0.1\xi_i, \ i=1,\cdots,100
$$
-The loss function is given by
+with \( x_i \in [0,1] \) chosen randomly with a uniform distribution. Additionally \( \xi_i \) represents stochastic noise chosen according to a normal distribution \( \cal {N}(0,1) \).
+The linear regression model is given by
$$
-C(\beta) = ||X\beta-\mathbf{y}||^2 = ||X\beta||^2 - 2 \mathbf{y}^T X\beta + ||\mathbf{y}||^2 = \sum_{i=1}^{100} (\beta_0 + \beta_1 x_i)^2 - 2 y_i (\beta_0 + \beta_1 x_i) + y_i^2
+h_\beta(x) = \hat{y} = \beta_0 + \beta_1 x,
$$
-and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
+such that
+$$
+\hat{y}_i = \beta_0 + \beta_1 x_i.
+$$
@@ -269,7 +309,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
-Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show that the gradient can be written as
+Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
+
+
+It is convenient to write \( \mathbf{\hat{y}} = X\beta \) where \( X \in \mathbb{R}^{100 \times 2} \) is the design matrix given by
$$
-\nabla_{\beta} C(\beta) = (\partial C(\beta) / \partial \beta_0, \partial C(\beta) / \partial \beta_1)^T = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
-\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
-\end{bmatrix} = 2X^T(X\beta - \mathbf{y}),
+X \equiv \begin{bmatrix}
+1 & x_1 \\
+\vdots & \vdots \\
+1 & x_{100} & \\
+\end{bmatrix}.
$$
-where \( X \) is the design matrix defined above.
+The loss function is given by
+$$
+C(\beta) = ||X\beta-\mathbf{y}||^2 = ||X\beta||^2 - 2 \mathbf{y}^T X\beta + ||\mathbf{y}||^2 = \sum_{i=1}^{100} (\beta_0 + \beta_1 x_i)^2 - 2 y_i (\beta_0 + \beta_1 x_i) + y_i^2
+$$
+
+and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
@@ -259,7 +301,7 @@ where \( X \) is the design matrix defined above.
-The Hessian matrix of \( C(\beta) \) is given by
+
The derivative of the cost/loss function
+
+
+Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show that the gradient can be written as
$$
-\hat{H} \equiv \begin{bmatrix}
-\frac{\partial^2 C(\beta)}{\partial \beta_0^2} & \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} \\
-\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} & \frac{\partial^2 C(\beta)}{\partial \beta_1^2} & \\
-\end{bmatrix} = 2X^T X.
+\nabla_{\beta} C(\beta) = (\partial C(\beta) / \partial \beta_0, \partial C(\beta) / \partial \beta_1)^T = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
+\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
+\end{bmatrix} = 2X^T(X\beta - \mathbf{y}),
$$
-This result implies that \( C(\beta) \) is a convex function since the matrix \( X^T X \) always is positive semi-definite.
+where \( X \) is the design matrix defined above.
@@ -258,7 +291,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
-We can use the expression we computed for the gradient and let use a
-\( \beta_0 \) be chosen randomly and let \( \gamma = 0.001 \). Stop iterating
-when \( ||\nabla_\beta C(\beta_k) || \leq \epsilon = 10^{-8} \).
+This result implies that \( C(\beta) \) is a convex function since the matrix \( X^T X \) always is positive semi-definite.
-
-And finally we can compare our solution for \( \beta \) with the analytic result given by
-\( \beta= (X^TX)^{-1} X^T \mathbf{y} \).
-
-
-
-
importnumpyasnp
-
-"""
-The following setup is just a suggestion, feel free to write it the way you like.
-"""
-
-#Setup problem described in the exercise
-N =100#Nr of datapoints
-M =2#Nr of features
-x = np.random.rand(N) #Uniformly generated x-values in [0,1]
-y =5*x**2+0.1*np.random.randn(N)
-X = np.c_[np.ones(N),x] #Construct design matrix
-
-#Compute beta according to normal equations to compare with GD solution
-Xt_X_inv = np.linalg.inv(np.dot(X.T,X))
-Xt_y = np.dot(X.transpose(),y)
-beta_NE = np.dot(Xt_X_inv,Xt_y)
-print(beta_NE)
-
-Another simple example is here
+We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to
+$$
+\beta_{k+1} = \beta_k - \gamma \nabla_\beta C(\beta_k), \ k=0,1,\cdots
+$$
+
+
+We can use the expression we computed for the gradient and let use a
+\( \beta_0 \) be chosen randomly and let \( \gamma = 0.001 \). Stop iterating
+when \( ||\nabla_\beta C(\beta_k) || \leq \epsilon = 10^{-8} \).
+
+
+And finally we can compare our solution for \( \beta \) with the analytic result given by
+\( \beta= (X^TX)^{-1} X^T \mathbf{y} \).
-
# Importing various packages
-fromrandomimport random, seed
-importnumpyasnp
-importmatplotlib.pyplotasplt
-frommpl_toolkits.mplot3dimport Axes3D
-frommatplotlibimport cm
-frommatplotlib.tickerimport LinearLocator, FormatStrFormatter
-importsys
+
importnumpyasnp
-x =2*np.random.rand(100,1)
-y =4+3*x+np.random.randn(100,1)
+"""
+The following setup is just a suggestion, feel free to write it the way you like.
+"""
-xb = np.c_[np.ones((100,1)), x]
-beta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
-print(beta_linreg)
-beta = np.random.randn(2,1)
+#Setup problem described in the exercise
+N =100#Nr of datapoints
+M =2#Nr of features
+x = np.random.rand(N) #Uniformly generated x-values in [0,1]
+y =5*x**2+0.1*np.random.randn(N)
+X = np.c_[np.ones(N),x] #Construct design matrix
-eta =0.1
-Niterations =1000
-m =100
-
-foriterinrange(Niterations):
- gradients =2.0/m*xb.T.dot(xb.dot(beta)-y)
- beta -= eta*gradients
-
-print(beta)
-xnew = np.array([[0],[2]])
-xbnew = np.c_[np.ones((2,1)), xnew]
-ypredict = xbnew.dot(beta)
-ypredict2 = xbnew.dot(beta_linreg)
-plt.plot(xnew, ypredict, "r-")
-plt.plot(xnew, ypredict2, "b-")
-plt.plot(x, y ,'ro')
-plt.axis([0,2.0,0, 15.0])
-plt.xlabel(r'$x$')
-plt.ylabel(r'$y$')
-plt.title(r'Gradient descent example')
-plt.show()
+#Compute beta according to normal equations to compare with GD solution
+Xt_X_inv = np.linalg.inv(np.dot(X.T,X))
+Xt_y = np.dot(X.transpose(),y)
+beta_NE = np.dot(Xt_X_inv,Xt_y)
+print(beta_NE)
-We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \),
-$$
-C_{\text{ridge}}(\beta) = ||X\beta -\mathbf{y}||^2 + \lambda ||\beta||^2, \ \lambda \geq 0.
-$$
-
-
-In order to minimize \( C_{\text{ridge}}(\beta) \) using GD we only have adjust the gradient as follows
-$$
-\nabla_\beta C_{\text{ridge}}(\beta) = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
-\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
-\end{bmatrix} + 2\lambda\begin{bmatrix} \beta_0 \\ \beta_1\end{bmatrix} = 2 (X^T(X\beta - \mathbf{y})+\lambda \beta).
-$$
-
-
-We can now extend our program to minimize \( C_{\text{ridge}}(\beta) \) using gradient descent and compare with the analytical solution given by
-$$
-\beta_{\text{ridge}} = \left(X^T X + \lambda I_{2 \times 2} \right)^{-1} X^T \mathbf{y},
-$$
-
-for \( \lambda = {0,1,10,50,100} \) (\( \lambda = 0 \) corresponds to ordinary least squares).
-We can then compute \( ||\beta_{\text{ridge}}|| \) for each \( \lambda \).
+
And a corresponding example using scikit-learn
-
importnumpyasnp
+
# Importing various packages
+fromrandomimport random, seed
+importnumpyasnp
+importmatplotlib.pyplotasplt
+fromsklearn.linear_modelimport SGDRegressor
-"""
-The following setup is just a suggestion, feel free to write it the way you like.
-"""
+x =2*np.random.rand(100,1)
+y =4+3*x+np.random.randn(100,1)
-#Setup problem described in the exercise
-N =100#Nr of datapoints
-M =2#Nr of features
-x = np.random.rand(N)
-y =5*x**2+0.1*np.random.randn(N)
-
-
-#Compute analytic beta for Ridge regression
-X = np.c_[np.ones(N),x]
-XT_X = np.dot(X.T,X)
-
-l =0.1#Ridge parameter lambda
-Id = np.eye(XT_X.shape[0])
-
-Z = np.linalg.inv(XT_X+l*Id)
-beta_ridge = np.dot(Z,np.dot(X.T,y))
-
-print(beta_ridge)
-print(np.linalg.norm(beta_ridge)) #||beta||
+xb = np.c_[np.ones((100,1)), x]
+beta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
+print(beta_linreg)
+sgdreg = SGDRegressor(n_iter =50, penalty=None, eta0=0.1)
+sgdreg.fit(x,y.ravel())
+print(sgdreg.intercept_, sgdreg.coef_)
-Python has tools for so-called automatic differentiation.
-Consider the following example
+
Gradient descent and Ridge
+
+
+We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \),
$$
-f(x) = \sin\left(2\pi x + x^2\right)
+C_{\text{ridge}}(\beta) = ||X\beta -\mathbf{y}||^2 + \lambda ||\beta||^2, \ \lambda \geq 0.
$$
-which has the following derivative
+
+In order to minimize \( C_{\text{ridge}}(\beta) \) using GD we only have adjust the gradient as follows
$$
-f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right)
+\nabla_\beta C_{\text{ridge}}(\beta) = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
+\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
+\end{bmatrix} + 2\lambda\begin{bmatrix} \beta_0 \\ \beta_1\end{bmatrix} = 2 (X^T(X\beta - \mathbf{y})+\lambda \beta).
$$
-Using autograd we have
+
+We can now extend our program to minimize \( C_{\text{ridge}}(\beta) \) using gradient descent and compare with the analytical solution given by
+$$
+\beta_{\text{ridge}} = \left(X^T X + \lambda I_{2 \times 2} \right)^{-1} X^T \mathbf{y},
+$$
+
+for \( \lambda = {0,1,10,50,100} \) (\( \lambda = 0 \) corresponds to ordinary least squares).
+We can then compute \( ||\beta_{\text{ridge}}|| \) for each \( \lambda \).
-
importautograd.numpyasnp
+
importnumpyasnp
-# To do elementwise differentiation:
-fromautogradimport elementwise_grad as egrad
+"""
+The following setup is just a suggestion, feel free to write it the way you like.
+"""
-# To plot:
-importmatplotlib.pyplotasplt
+#Setup problem described in the exercise
+N =100#Nr of datapoints
+M =2#Nr of features
+x = np.random.rand(N)
+y =5*x**2+0.1*np.random.randn(N)
-deff(x):
- return np.sin(2*np.pi*x + x**2)
+#Compute analytic beta for Ridge regression
+X = np.c_[np.ones(N),x]
+XT_X = np.dot(X.T,X)
-deff_grad_analytic(x):
- return np.cos(2*np.pi*x + x**2)*(2*np.pi +2*x)
+l =0.1#Ridge parameter lambda
+Id = np.eye(XT_X.shape[0])
-# Do the comparison:
-x = np.linspace(0,1,1000)
+Z = np.linalg.inv(XT_X+l*Id)
+beta_ridge = np.dot(Z,np.dot(X.T,y))
-f_grad = egrad(f)
-
-computed = f_grad(x)
-analytic = f_grad_analytic(x)
-
-plt.title('Derivative computed from Autograd compared with the analytical derivative')
-plt.plot(x,computed,label='autograd')
-plt.plot(x,analytic,label='analytic')
-
-plt.xlabel('x')
-plt.ylabel('y')
-plt.legend()
-
-plt.show()
-
-print("The max absolute difference is: %g"%(np.max(np.abs(computed - analytic))))
+print(beta_ridge)
+print(np.linalg.norm(beta_ridge)) #||beta||
+Python has tools for so-called automatic differentiation.
+Consider the following example
+$$
+f(x) = \sin\left(2\pi x + x^2\right)
+$$
-
-Here we
-experiment with what kind of functions Autograd is capable
-of finding the gradient of. The following Python functions are just
-meant to illustrate what Autograd can do, but please feel free to
-experiment with other, possibly more complicated, functions as well.
+which has the following derivative
+$$
+f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right)
+$$
+
+Using autograd we have
importautograd.numpyasnp
-fromautogradimport grad
-deff1(x):
- return x**3+1
+# To do elementwise differentiation:
+fromautogradimport elementwise_grad as egrad
-f1_grad = grad(f1)
+# To plot:
+importmatplotlib.pyplotasplt
-# Remember to send in float as argument to the computed gradient from Autograd!
-a =1.0
-# See the evaluated gradient at a using autograd:
-print("The gradient of f1 evaluated at a = %g using autograd is: %g"%(a,f1_grad(a)))
+deff(x):
+ return np.sin(2*np.pi*x + x**2)
-# Compare with the analytical derivative, that is f1'(x) = 3*x**2
-grad_analytical =3*a**2
-print("The gradient of f1 evaluated at a = %g by finding the analytic expression is: %g"%(a,grad_analytical))
+deff_grad_analytic(x):
+ return np.cos(2*np.pi*x + x**2)*(2*np.pi +2*x)
+
+# Do the comparison:
+x = np.linspace(0,1,1000)
+
+f_grad = egrad(f)
+
+computed = f_grad(x)
+analytic = f_grad_analytic(x)
+
+plt.title('Derivative computed from Autograd compared with the analytical derivative')
+plt.plot(x,computed,label='autograd')
+plt.plot(x,analytic,label='analytic')
+
+plt.xlabel('x')
+plt.ylabel('y')
+plt.legend()
+
+plt.show()
+
+print("The max absolute difference is: %g"%(np.max(np.abs(computed - analytic))))
-To differentiate with respect to two (or more) arguments of a Python
-function, Autograd need to know at which variable the function if
-being differentiated with respect to.
+Here we
+experiment with what kind of functions Autograd is capable
+of finding the gradient of. The following Python functions are just
+meant to illustrate what Autograd can do, but please feel free to
+experiment with other, possibly more complicated, functions as well.
importautograd.numpyasnpfromautogradimport grad
-deff2(x1,x2):
- return3*x1**3+ x2*(x1 -5) +1
-# By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1
-f2_grad_x1 = grad(f2,0)
+deff1(x):
+ return x**3+1
-# ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad
-f2_grad_x2 = grad(f2,1)
+f1_grad = grad(f1)
-x1 =1.0
-x2 =3.0
+# Remember to send in float as argument to the computed gradient from Autograd!
+a =1.0
-print("Evaluating at x1 = %g, x2 = %g"%(x1,x2))
-print("-"*30)
+# See the evaluated gradient at a using autograd:
+print("The gradient of f1 evaluated at a = %g using autograd is: %g"%(a,f1_grad(a)))
-# Compare with the analytical derivatives:
-
-# Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:
-f2_grad_x1_analytical =9*x1**2+ x2
-
-# Derivative of f2 w.r.t x2 is: x1 - 5:
-f2_grad_x2_analytical = x1 -5
-
-# See the evaluated derivations:
-print("The derivative of f2 w.r.t x1: %g"%( f2_grad_x1(x1,x2) ))
-print("The analytical derivative of f2 w.r.t x1: %g"%( f2_grad_x1(x1,x2) ))
-
-print()
-
-print("The derivative of f2 w.r.t x2: %g"%( f2_grad_x2(x1,x2) ))
-print("The analytical derivative of f2 w.r.t x2: %g"%( f2_grad_x2(x1,x2) ))
+# Compare with the analytical derivative, that is f1'(x) = 3*x**2
+grad_analytical =3*a**2
+print("The gradient of f1 evaluated at a = %g by finding the analytic expression is: %g"%(a,grad_analytical))
-
-Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.
-
@@ -294,7 +309,7 @@ Note that the grad function will not produce the true gradient of the function.
More complicated functions using the elements of their arguments directly
+
Autograd with more complicated functions
+
+
+To differentiate with respect to two (or more) arguments of a Python
+function, Autograd need to know at which variable the function if
+being differentiated with respect to.
importautograd.numpyasnpfromautogradimport grad
-deff3(x): # Assumes x is an array of length 5 or higher
- return2*x[0] +3*x[1] +5*x[2] +7*x[3] +11*x[4]**2
+deff2(x1,x2):
+ return3*x1**3+ x2*(x1 -5) +1
-f3_grad = grad(f3)
+# By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1
+f2_grad_x1 = grad(f2,0)
-x = np.linspace(0,4,5)
+# ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad
+f2_grad_x2 = grad(f2,1)
-# Print the computed gradient:
-print("The computed gradient of f3 is: ", f3_grad(x))
+x1 =1.0
+x2 =3.0
-# The analytical gradient is: (2, 3, 5, 7, 22*x[4])
-f3_grad_analytical = np.array([2, 3, 5, 7, 22*x[4]])
+print("Evaluating at x1 = %g, x2 = %g"%(x1,x2))
+print("-"*30)
-# Print the analytical gradient:
-print("The analytical gradient of f3 is: ", f3_grad_analytical)
+# Compare with the analytical derivatives:
+
+# Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:
+f2_grad_x1_analytical =9*x1**2+ x2
+
+# Derivative of f2 w.r.t x2 is: x1 - 5:
+f2_grad_x2_analytical = x1 -5
+
+# See the evaluated derivations:
+print("The derivative of f2 w.r.t x1: %g"%( f2_grad_x1(x1,x2) ))
+print("The analytical derivative of f2 w.r.t x1: %g"%( f2_grad_x1(x1,x2) ))
+
+print()
+
+print("The derivative of f2 w.r.t x2: %g"%( f2_grad_x2(x1,x2) ))
+print("The analytical derivative of f2 w.r.t x2: %g"%( f2_grad_x2(x1,x2) ))
-Note that in this case, when sending an array as input argument, the
-output from Autograd is another array. This is the true gradient of
-the function, as opposed to the function in the previous example. By
-using arrays to represent the variables, the output from Autograd
-might be easier to work with, as the output is closer to what one
-could expect form a gradient-evaluting function.
+Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.
@@ -278,7 +326,7 @@ could expect form a gradient-evaluting function.
More complicated functions using the elements of their arguments directly
importautograd.numpyasnpfromautogradimport grad
-deff4(x):
- return np.sqrt(1+x**2) + np.exp(x) + np.sin(2*np.pi*x)
+deff3(x): # Assumes x is an array of length 5 or higher
+ return2*x[0] +3*x[1] +5*x[2] +7*x[3] +11*x[4]**2
-f4_grad = grad(f4)
+f3_grad = grad(f3)
-x =2.7
+x = np.linspace(0,4,5)
-# Print the computed derivative:
-print("The computed derivative of f4 at x = %g is: %g"%(x,f4_grad(x)))
+# Print the computed gradient:
+print("The computed gradient of f3 is: ", f3_grad(x))
-# The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi
-f4_grad_analytical = x/np.sqrt(1+ x**2) + np.exp(x) + np.cos(2*np.pi*x)*2*np.pi
+# The analytical gradient is: (2, 3, 5, 7, 22*x[4])
+f3_grad_analytical = np.array([2, 3, 5, 7, 22*x[4]])
# Print the analytical gradient:
-print("The analytical gradient of f4 at x = %g is: %g"%(x,f4_grad_analytical))
+print("The analytical gradient of f3 is: ", f3_grad_analytical)
+
+Note that in this case, when sending an array as input argument, the
+output from Autograd is another array. This is the true gradient of
+the function, as opposed to the function in the previous example. By
+using arrays to represent the variables, the output from Autograd
+might be easier to work with, as the output is closer to what one
+could expect form a gradient-evaluting function.
+
importautograd.numpyasnpfromautogradimport grad
-deff5(x):
- if x >=0:
- return x**2
- else:
- return-3*x +1
+deff4(x):
+ return np.sqrt(1+x**2) + np.exp(x) + np.sin(2*np.pi*x)
-f5_grad = grad(f5)
+f4_grad = grad(f4)
x =2.7# Print the computed derivative:
-print("The computed derivative of f5 at x = %g is: %g"%(x,f5_grad(x)))
+print("The computed derivative of f4 at x = %g is: %g"%(x,f4_grad(x)))
+
+# The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi
+f4_grad_analytical = x/np.sqrt(1+ x**2) + np.exp(x) + np.cos(2*np.pi*x)*2*np.pi
+
+# Print the analytical gradient:
+print("The analytical gradient of f4 at x = %g is: %g"%(x,f4_grad_analytical))
importautograd.numpyasnpfromautogradimport grad
-deff6_for(x):
- val =0
- for i inrange(10):
- val = val + x**i
- return val
+deff5(x):
+ if x >=0:
+ return x**2
+ else:
+ return-3*x +1
-deff6_while(x):
- val =0
- i =0
- while i <10:
- val = val + x**i
- i = i +1
- return val
+f5_grad = grad(f5)
-f6_for_grad = grad(f6_for)
-f6_while_grad = grad(f6_while)
+x =2.7
-x =0.5
-
-# Print the computed derivaties of f6_for and f6_while
-print("The computed derivative of f6_for at x = %g is: %g"%(x,f6_for_grad(x)))
-print("The computed derivative of f6_while at x = %g is: %g"%(x,f6_while_grad(x)))
-
-
-
-
-
importautograd.numpyasnp
-fromautogradimport grad
-# Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9
-# The analytical derivative is: sum(i*x**(i-1))
-f6_grad_analytical =0
-for i inrange(10):
- f6_grad_analytical += i*x**(i-1)
-
-print("The analytical derivative of f6 at x = %g is: %g"%(x,f6_grad_analytical))
+# Print the computed derivative:
+print("The computed derivative of f5 at x = %g is: %g"%(x,f5_grad(x)))
importautograd.numpyasnpfromautogradimport grad
+deff6_for(x):
+ val =0
+ for i inrange(10):
+ val = val + x**i
+ return val
-deff7(n): # Assume that n is an integer
- if n ==1or n ==0:
- return1
- else:
- return n*f7(n-1)
+deff6_while(x):
+ val =0
+ i =0
+ while i <10:
+ val = val + x**i
+ i = i +1
+ return val
-f7_grad = grad(f7)
+f6_for_grad = grad(f6_for)
+f6_while_grad = grad(f6_while)
-n =2.0
+x =0.5
-print("The computed derivative of f7 at n = %d is: %g"%(n,f7_grad(n)))
-
-# The function f7 is an implementation of the factorial of n.
-# By using the product rule, one can find that the derivative is:
-
-f7_grad_analytical =0
-for i inrange(int(n)-1):
- tmp =1
- for k inrange(int(n)-1):
- if k != i:
- tmp *= (n - k)
- f7_grad_analytical += tmp
-
-print("The analytical derivative of f7 at n = %d is: %g"%(n,f7_grad_analytical))
+# Print the computed derivaties of f6_for and f6_while
+print("The computed derivative of f6_for at x = %g is: %g"%(x,f6_for_grad(x)))
+print("The computed derivative of f6_while at x = %g is: %g"%(x,f6_while_grad(x)))
-Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.
+
+
importautograd.numpyasnp
+fromautogradimport grad
+# Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9
+# The analytical derivative is: sum(i*x**(i-1))
+f6_grad_analytical =0
+for i inrange(10):
+ f6_grad_analytical += i*x**(i-1)
+
+print("The analytical derivative of f6 at x = %g is: %g"%(x,f6_grad_analytical))
+
@@ -282,7 +322,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
-Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
-
-
-Assigning a value to the variable being differentiated with respect to
+
Using recursion
importautograd.numpyasnpfromautogradimport grad
-deff8(x): # Assume x is an array
- x[2] =3
- return x*2
-f8_grad = grad(f8)
+deff7(n): # Assume that n is an integer
+ if n ==1or n ==0:
+ return1
+ else:
+ return n*f7(n-1)
-x =8.4
+f7_grad = grad(f7)
-print("The derivative of f8 is:",f8_grad(x))
+n =2.0
+
+print("The computed derivative of f7 at n = %d is: %g"%(n,f7_grad(n)))
+
+# The function f7 is an implementation of the factorial of n.
+# By using the product rule, one can find that the derivative is:
+
+f7_grad_analytical =0
+for i inrange(int(n)-1):
+ tmp =1
+ for k inrange(int(n)-1):
+ if k != i:
+ tmp *= (n - k)
+ f7_grad_analytical += tmp
+
+print("The analytical derivative of f7 at n = %d is: %g"%(n,f7_grad_analytical))
-Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.
+Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.
@@ -269,6 +313,8 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
+Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
+
+
+Assigning a value to the variable being differentiated with respect to
importautograd.numpyasnpfromautogradimport grad
-deff9(a): # Assume a is an array with 2 elements
- b = np.array([1.0,2.0])
- return a.dot(b)
+deff8(x): # Assume x is an array
+ x[2] =3
+ return x*2
-f9_grad = grad(f9)
+f8_grad = grad(f8)
-x = np.array([1.0,0.0])
+x =8.4
-print("The derivative of f9 is:",f9_grad(x))
+print("The derivative of f8 is:",f8_grad(x))
-Here we are told that the 'dot' function does not belong to Autograd's
-version of a Numpy array. To overcome this, an alternative syntax
-which also computed the dot product can be used:
+Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.
-
-
-
-
importautograd.numpyasnp
-fromautogradimport grad
-deff9_alternative(x): # Assume a is an array with 2 elements
- b = np.array([1.0,2.0])
- return np.dot(x,b) # The same as x_1*b_1 + x_2*b_2
-
-f9_alternative_grad = grad(f9_alternative)
-
-x = np.array([3.0,0.0])
-
-print("The gradient of f9 is:",f9_alternative_grad(x))
-
-# The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively
-# w.r.t x is (b_1, b_2).
-
-The documentation recommends to avoid inplace operations such as
+
The syntax a.dot(b) when finding the dot product
-
a += b
-a -= b
-a*= b
-a /=b
+
importautograd.numpyasnp
+fromautogradimport grad
+deff9(a): # Assume a is an array with 2 elements
+ b = np.array([1.0,2.0])
+ return a.dot(b)
+
+f9_grad = grad(f9)
+
+x = np.array([1.0,0.0])
+
+print("The derivative of f9 is:",f9_grad(x))
+
+
+Here we are told that the 'dot' function does not belong to Autograd's
+version of a Numpy array. To overcome this, an alternative syntax
+which also computed the dot product can be used:
+
+
+
+
+
importautograd.numpyasnp
+fromautogradimport grad
+deff9_alternative(x): # Assume a is an array with 2 elements
+ b = np.array([1.0,2.0])
+ return np.dot(x,b) # The same as x_1*b_1 + x_2*b_2
+
+f9_alternative_grad = grad(f9_alternative)
+
+x = np.array([3.0,0.0])
+
+print("The gradient of f9 is:",f9_alternative_grad(x))
+
+# The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively
+# w.r.t x is (b_1, b_2).
+The documentation recommends to avoid inplace operations such as
-Stochastic gradient descent (SGD) and variants thereof address some of
-the shortcomings of the Gradient descent method discussed above.
-
-
-The underlying idea of SGD comes from the observation that the cost
-function, which we want to minimize, can almost always be written as a
-sum over \( n \) data points \( \{\mathbf{x}_i\}_{i=1}^n \),
-$$
-C(\mathbf{\beta}) = \sum_{i=1}^n c_i(\mathbf{x}_i,
-\mathbf{\beta}).
-$$
+
+
-This in turn means that the gradient can be
-computed as a sum over \( i \)-gradients
-$$
-\nabla_\beta C(\mathbf{\beta}) = \sum_i^n \nabla_\beta c_i(\mathbf{x}_i,
-\mathbf{\beta}).
-$$
+Stochastic gradient descent (SGD) and variants thereof address some of
+the shortcomings of the Gradient descent method discussed above.
-Stochasticity/randomness is introduced by only taking the
-gradient on a subset of the data called minibatches. If there are \( n \)
-data points and the size of each minibatch is \( M \), there will be \( n/M \)
-minibatches. We denote these minibatches by \( B_k \) where
-\( k=1,\cdots,n/M \).
+The underlying idea of SGD comes from the observation that the cost
+function, which we want to minimize, can almost always be written as a
+sum over \( n \) data points \( \{\mathbf{x}_i\}_{i=1}^n \),
+$$
+C(\mathbf{\beta}) = \sum_{i=1}^n c_i(\mathbf{x}_i,
+\mathbf{\beta}).
+$$
@@ -259,6 +289,12 @@ minibatches. We denote these minibatches by \( B_k \) where
-As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \)
-and we choose to have \( M=5 \) minibathces,
-then each minibatch contains two data points. In particular we have
-\( B_1 = (\mathbf{x}_1,\mathbf{x}_2), \cdots, B_5 =
-(\mathbf{x}_9,\mathbf{x}_{10}) \). Note that if you choose \( M=1 \) you
-have only a single batch with all data points and on the other extreme,
-you may choose \( M=n \) resulting in a minibatch for each datapoint, i.e
-\( B_k = \mathbf{x}_k \).
+
Computation of gradients
-The idea is now to approximate the gradient by replacing the sum over
-all data points with a sum over the data points in one the minibatches
-picked at random in each gradient descent step
+This in turn means that the gradient can be
+computed as a sum over \( i \)-gradients
$$
-\nabla_{\beta}
-C(\mathbf{\beta}) = \sum_{i=1}^n \nabla_\beta c_i(\mathbf{x}_i,
-\mathbf{\beta}) \rightarrow \sum_{i \in B_k}^n \nabla_\beta
-c_i(\mathbf{x}_i, \mathbf{\beta}).
+\nabla_\beta C(\mathbf{\beta}) = \sum_i^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta}).
$$
+
+Stochasticity/randomness is introduced by only taking the
+gradient on a subset of the data called minibatches. If there are \( n \)
+data points and the size of each minibatch is \( M \), there will be \( n/M \)
+minibatches. We denote these minibatches by \( B_k \) where
+\( k=1,\cdots,n/M \).
+
+As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \)
+and we choose to have \( M=5 \) minibathces,
+then each minibatch contains two data points. In particular we have
+\( B_1 = (\mathbf{x}_1,\mathbf{x}_2), \cdots, B_5 =
+(\mathbf{x}_9,\mathbf{x}_{10}) \). Note that if you choose \( M=1 \) you
+have only a single batch with all data points and on the other extreme,
+you may choose \( M=n \) resulting in a minibatch for each datapoint, i.e
+\( B_k = \mathbf{x}_k \).
-Thus a gradient descent step now looks like
+The idea is now to approximate the gradient by replacing the sum over
+all data points with a sum over the data points in one the minibatches
+picked at random in each gradient descent step
$$
-\beta_{j+1} = \beta_j - \gamma_j \sum_{i \in B_k}^n \nabla_\beta c_i(\mathbf{x}_i,
-\mathbf{\beta})
+\nabla_{\beta}
+C(\mathbf{\beta}) = \sum_{i=1}^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta}) \rightarrow \sum_{i \in B_k}^n \nabla_\beta
+c_i(\mathbf{x}_i, \mathbf{\beta}).
$$
-
-where \( k \) is picked at random with equal
-probability from \( [1,n/M] \). An iteration over the number of
-minibathces (n/M) is commonly referred to as an epoch. Thus it is
-typical to choose a number of epochs and for each epoch iterate over
-the number of minibatches, as exemplified in the code below.
-
@@ -256,6 +293,14 @@ the number of minibatches, as exemplified in the code below.
+Thus a gradient descent step now looks like
+$$
+\beta_{j+1} = \beta_j - \gamma_j \sum_{i \in B_k}^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta})
+$$
-
-
importnumpyasnp
-
-n =100#100 datapoints
-M =5#size of each minibatch
-m =int(n/M) #number of minibatches
-n_epochs =10#number of epochs
-
-j =0
-for epoch inrange(1,n_epochs+1):
- for i inrange(m):
- k = np.random.randint(m) #Pick the k-th minibatch at random
- #Compute the gradient using the data in minibatch Bk
- #Compute new suggestion for
- j +=1
-
-Taking the gradient only on a subset of the data has two important
-benefits. First, it introduces randomness which decreases the chance
-that our opmization scheme gets stuck in a local minima. Second, if
-the size of the minibatches are small relative to the number of
-datapoints (\( M < n \)), the computation of the gradient is much
-cheaper since we sum over the datapoints in the \( k-th \) minibatch and not
-all \( n \) datapoints.
+where \( k \) is picked at random with equal
+probability from \( [1,n/M] \). An iteration over the number of
+minibathces (n/M) is commonly referred to as an epoch. Thus it is
+typical to choose a number of epochs and for each epoch iterate over
+the number of minibatches, as exemplified in the code below.
-A natural question is when do we stop the search for a new minimum?
-One possibility is to compute the full gradient after a given number
-of epochs and check if the norm of the gradient is smaller than some
-threshold and stop if true. However, the condition that the gradient
-is zero is valid also for local minima, so this would only tell us
-that we are close to a local/global minimum. However, we could also
-evaluate the cost function at this point, store the result and
-continue the search. If the test kicks in at a later stage we can
-compare the values of the cost function and keep the \( \beta \) that
-gave the lowest value.
+
+
+
importnumpyasnp
+
+n =100#100 datapoints
+M =5#size of each minibatch
+m =int(n/M) #number of minibatches
+n_epochs =10#number of epochs
+
+j =0
+for epoch inrange(1,n_epochs+1):
+ for i inrange(m):
+ k = np.random.randint(m) #Pick the k-th minibatch at random
+ #Compute the gradient using the data in minibatch Bk
+ #Compute new suggestion for
+ j +=1
+
+
+Taking the gradient only on a subset of the data has two important
+benefits. First, it introduces randomness which decreases the chance
+that our opmization scheme gets stuck in a local minima. Second, if
+the size of the minibatches are small relative to the number of
+datapoints (\( M < n \)), the computation of the gradient is much
+cheaper since we sum over the datapoints in the \( k-th \) minibatch and not
+all \( n \) datapoints.
-Another approach is to let the step length \( \gamma_j \) depend on the
-number of epochs in such a way that it becomes very small after a
-reasonable time such that we do not move at all.
+A natural question is when do we stop the search for a new minimum?
+One possibility is to compute the full gradient after a given number
+of epochs and check if the norm of the gradient is smaller than some
+threshold and stop if true. However, the condition that the gradient
+is zero is valid also for local minima, so this would only tell us
+that we are close to a local/global minimum. However, we could also
+evaluate the cost function at this point, store the result and
+continue the search. If the test kicks in at a later stage we can
+compare the values of the cost function and keep the \( \beta \) that
+gave the lowest value.
-As an example, let \( e = 0,1,2,3,\cdots \) denote the current epoch and let \( t_0, t_1 > 0 \) be two fixed numbers. Furthermore, let \( t = e \cdot m + i \) where \( m \) is the number of minibatches and \( i=0,\cdots,m-1 \). Then the function $$\gamma_j(t; t_0, t_1) = \frac{t_0}{t+t_1} $$ goes to zero as the number of epochs gets large. I.e. we start with a step length \( \gamma_j (0; t_0, t_1) = t_0/t_1 \) which decays in time \( t \).
-
-
-In this way we can fix the number of epochs, compute \( \beta \) and
-evaluate the cost function at the end. Repeating the computation will
-give a different result since the scheme is random by design. Then we
-pick the final \( \beta \) that gives the lowest value of the cost
-function.
-
-
-
-
-
importnumpyasnp
-
-defstep_length(t,t0,t1):
- return t0/(t+t1)
-
-n =100#100 datapoints
-M =5#size of each minibatch
-m =int(n/M) #number of minibatches
-n_epochs =500#number of epochs
-t0 =1.0
-t1 =10
-
-gamma_j = t0/t1
-j =0
-for epoch inrange(1,n_epochs+1):
- for i inrange(m):
- k = np.random.randint(m) #Pick the k-th minibatch at random
- #Compute the gradient using the data in minibatch Bk
- #Compute new suggestion for beta
- t = epoch*m+i
- gamma_j = step_length(t,t0,t1)
- j +=1
-
-print("gamma_j after %d epochs: %g"% (n_epochs,gamma_j))
-
We will use linear regression as a case study for the gradient descent
@@ -975,7 +980,7 @@ $$
-
Gradient descent example
+
Gradient descent example
Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -1004,7 +1009,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
-
The derivative of the cost/loss function
+
The derivative of the cost/loss function
Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show that the gradient can be written as
@@ -1021,7 +1026,7 @@ where \( X \) is the design matrix defined above.
-
The Hessian matrix
+
The Hessian matrix
The Hessian matrix of \( C(\beta) \) is given by
$$
@@ -1037,7 +1042,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
-
Simple program
+
Simple program
We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to
@@ -1081,7 +1086,7 @@ beta_NE = np.dot(Xt_X_inv,Xt_y)
-
Gradient Descent Example
+
Gradient Descent Example
Another simple example is here
@@ -1131,7 +1136,7 @@ plt.show()
-
And a corresponding example using scikit-learn
+
And a corresponding example using scikit-learn
@@ -1156,7 +1161,7 @@ sgdreg.fit(x,y.ravel())
-
Gradient descent and Ridge
+
Gradient descent and Ridge
We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \),
@@ -1220,7 +1225,7 @@ beta_ridge = np.dot(Z,np.dot(X.T,y))
-
Automatic differentiation
+
Automatic differentiation
Python has tools for so-called automatic differentiation.
Consider the following example
@@ -1280,7 +1285,7 @@ plt.show()
-
Using autograd
+
Using autograd
Here we
@@ -1314,7 +1319,7 @@ grad_analytical = 3*a**Autograd with more complicated functions
+
Autograd with more complicated functions
To differentiate with respect to two (or more) arguments of a Python
@@ -1364,7 +1369,7 @@ Note that the grad function will not produce the true gradient of the function.
-
More complicated functions using the elements of their arguments directly
+
More complicated functions using the elements of their arguments directly
@@ -1398,7 +1403,7 @@ could expect form a gradient-evaluting function.
-
@@ -1534,7 +1539,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
-
Unsupported functions
+
Unsupported functions
Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
@@ -1560,7 +1565,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
-
The syntax a.dot(b) when finding the dot product
+
The syntax a.dot(b) when finding the dot product
@@ -1603,7 +1608,7 @@ x = np.array([3.0,Recommended to avoid
+
Recommended to avoid
The documentation recommends to avoid inplace operations such as
@@ -1617,7 +1622,7 @@ a /=b
-
Stochastic Gradient Descent
+
Stochastic Gradient Descent
Stochastic gradient descent (SGD) and variants thereof address some of
@@ -1637,7 +1642,7 @@ $$
-
Computation of gradients
+
Computation of gradients
This in turn means that the gradient can be
@@ -1659,7 +1664,7 @@ minibatches. We denote these minibatches by \( B_k \) where
-
SGD example
+
SGD example
As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \)
and we choose to have \( M=5 \) minibathces,
then each minibatch contains two data points. In particular we have
@@ -1685,7 +1690,7 @@ $$
-
The gradient step
+
The gradient step
Thus a gradient descent step now looks like
@@ -1706,7 +1711,7 @@ the number of minibatches, as exemplified in the code below.
-
Simple example code
+
Simple example code
@@ -1738,7 +1743,7 @@ all \( n \) datapoints.
-
When do we stop?
+
When do we stop?
A natural question is when do we stop the search for a new minimum?
@@ -1755,7 +1760,7 @@ gave the lowest value.
-
Slightly different approach
+
Slightly different approach
Another approach is to let the step length \( \gamma_j \) depend on the
@@ -1805,6 +1810,432 @@ j = 0
+
+The philosophy of the CG method is to perform searches in various conjugate directions
+of our vectors \( \hat{x}_i \) obeying the above criterion, namely
+
+
+Two vectors are conjugate if they are orthogonal with respect to
+this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is conjugate to \( \hat{t} \), then \( \hat{t} \) is conjugate to \( \hat{s} \).
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+An example is given by the eigenvectors of the matrix
+
+Assume now that we have a symmetric positive-definite matrix \( \hat{A} \) of size
+\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
+
+
+We assume that \( \hat{p}_{i} \) is a sequence of \( n \) mutually conjugate directions.
+Then the \( \hat{p}_{i} \) form a basis of \( R^n \) and we can expand the solution
+$ \hat{A}\hat{x} = \hat{b}$ in this basis, namely
+
+
+If we choose the conjugate vectors \( \hat{p}_k \) carefully,
+then we may not need all of them to obtain a good approximation to the solution
+\( \hat{x} \).
+We want to regard the conjugate gradient method as an iterative method.
+This will us to solve systems where \( n \) is so large that the direct
+method would take too much time.
+
+
+We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \).
+We can assume without loss of generality that
+
+
+and
+\( \hat{x}_0=0 \) it is equal \( -\hat{b} \).
+The other vectors in the basis will be conjugate to the gradient,
+hence the name conjugate gradient method.
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+Let \( \hat{r}_k \) be the residual at the \( k \)-th step:
+
+
+Note that \( \hat{r}_k \) is the negative gradient of \( f \) at
+\( \hat{x}=\hat{x}_k \),
+so the gradient descent method would be to move in the direction \( \hat{r}_k \).
+Here, we insist that the directions \( \hat{p}_k \) are conjugate to each other,
+so we take the direction closest to the gradient \( \hat{r}_k \)
+under the conjugacy constraint.
+This gives the following expression
+
Simple implementation of the Conjugate gradient algorithm
+
+
+
+
+
+
Vector ConjugateGradient(Matrix A, Vector b, Vector x0){
+ int dim = x0.Dimension();
+ constdouble tolerance = 1.0e-14;
+ Vector x(dim),r(dim),v(dim),z(dim);
+ double c,t,d;
+
+ x = x0;
+ r = b - A*x;
+ v = r;
+ c = dot(r,r);
+ int i = 0; IterMax = dim;
+ while(i <= IterMax){
+ z = A*v;
+ t = c/dot(v,z);
+ x = x + t*v;
+ r = r - t*z;
+ d = dot(r,r);
+ if(sqrt(d) < tolerance)
+ break;
+ v = r + (d/c)*v;
+ c = d; i++;
+ }
+ return x;
+}
+
+
+
+
+
+
+
+
Broyden–Fletcher–Goldfarb–Shanno algorithm
+
+
+
+The optimization problem is to minimize \( f(\mathbf {x} ) \) where \( \mathbf {x} \) is a vector in \( R^{n} \), and \( f \) is a differentiable scalar function. There are no constraints on the values that \( \mathbf {x} \) can take.
+
+
+The algorithm begins at an initial estimate for the optimal value \( \mathbf {x}_{0} \) and proceeds iteratively to get a better estimate at each stage.
+
+
+The search direction \( p_k \) at stage \( k \) is given by the solution of the analogue of the Newton equation
+
+where \( B_{k} \) is an approximation to the Hessian matrix, which is
+updated iteratively at each stage, and \( \nabla f(\mathbf {x} _{k}) \)
+is the gradient of the function
+evaluated at \( x_k \).
+A line search in the direction \( p_k \) is then used to
+find the next point \( x_{k+1} \) by minimising
+
We will use linear regression as a case study for the gradient descent
@@ -941,7 +965,7 @@ $$
-
Gradient descent example
+
Gradient descent example
Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -966,7 +990,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
-
The derivative of the cost/loss function
+
The derivative of the cost/loss function
Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show that the gradient can be written as
@@ -981,7 +1005,7 @@ where \( X \) is the design matrix defined above.
-
The Hessian matrix
+
The Hessian matrix
The Hessian matrix of \( C(\beta) \) is given by
$$
\hat{H} \equiv \begin{bmatrix}
@@ -995,7 +1019,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
-
Simple program
+
Simple program
We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to
@@ -1036,7 +1060,7 @@ beta_NE = np.dot(Xt_X_inv,Xt_y)
-
Gradient Descent Example
+
Gradient Descent Example
Another simple example is here
@@ -1085,7 +1109,7 @@ plt.show()
-
And a corresponding example using scikit-learn
+
And a corresponding example using scikit-learn
@@ -1109,7 +1133,7 @@ sgdreg.fit(x,y.ravel())
-
Gradient descent and Ridge
+
Gradient descent and Ridge
We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \),
@@ -1166,7 +1190,7 @@ beta_ridge = np.dot(Z,np.dot(X.T,y))
-
Automatic differentiation
+
Automatic differentiation
Python has tools for so-called automatic differentiation.
Consider the following example
$$
@@ -1221,7 +1245,7 @@ plt.show()
-
Using autograd
+
Using autograd
Here we
@@ -1254,7 +1278,7 @@ grad_analytical = 3*a**Autograd with more complicated functions
+
Autograd with more complicated functions
To differentiate with respect to two (or more) arguments of a Python
@@ -1304,7 +1328,7 @@ Note that the grad function will not produce the true gradient of the function.
-
More complicated functions using the elements of their arguments directly
+
More complicated functions using the elements of their arguments directly
@@ -1338,7 +1362,7 @@ could expect form a gradient-evaluting function.
@@ -1471,7 +1495,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
-
Unsupported functions
+
Unsupported functions
Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
@@ -1497,7 +1521,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
-
The syntax a.dot(b) when finding the dot product
+
The syntax a.dot(b) when finding the dot product
@@ -1539,7 +1563,7 @@ x = np.array([3.0,Recommended to avoid
+
Recommended to avoid
The documentation recommends to avoid inplace operations such as
@@ -1552,7 +1576,7 @@ a /=b
-
Stochastic Gradient Descent
+
Stochastic Gradient Descent
Stochastic gradient descent (SGD) and variants thereof address some of
@@ -1570,7 +1594,7 @@ $$
-
Computation of gradients
+
Computation of gradients
This in turn means that the gradient can be
@@ -1590,7 +1614,7 @@ minibatches. We denote these minibatches by \( B_k \) where
-
SGD example
+
SGD example
As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \)
and we choose to have \( M=5 \) minibathces,
then each minibatch contains two data points. In particular we have
@@ -1614,7 +1638,7 @@ $$
-
The gradient step
+
The gradient step
Thus a gradient descent step now looks like
@@ -1633,7 +1657,7 @@ the number of minibatches, as exemplified in the code below.
-
Simple example code
+
Simple example code
@@ -1665,7 +1689,7 @@ all \( n \) datapoints.
-
When do we stop?
+
When do we stop?
A natural question is when do we stop the search for a new minimum?
@@ -1682,7 +1706,7 @@ gave the lowest value.
-
Slightly different approach
+
Slightly different approach
Another approach is to let the step length \( \gamma_j \) depend on the
@@ -1727,6 +1751,404 @@ j = 0print("gamma_j after %d epochs: %g" % (n_epochs,gamma_j))
+
+In the CG method we define so-called conjugate directions and two vectors
+\( \hat{s} \) and \( \hat{t} \)
+are said to be
+conjugate if
+$$
+\begin{equation*}
+\hat{s}^T\hat{A}\hat{t}= 0.
+\end{equation*}
+$$
+
+The philosophy of the CG method is to perform searches in various conjugate directions
+of our vectors \( \hat{x}_i \) obeying the above criterion, namely
+$$
+\begin{equation*}
+\hat{x}_i^T\hat{A}\hat{x}_j= 0.
+\end{equation*}
+$$
+
+Two vectors are conjugate if they are orthogonal with respect to
+this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is conjugate to \( \hat{t} \), then \( \hat{t} \) is conjugate to \( \hat{s} \).
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+An example is given by the eigenvectors of the matrix
+$$
+\begin{equation*}
+\hat{v}_i^T\hat{A}\hat{v}_j= \lambda\hat{v}_i^T\hat{v}_j,
+\end{equation*}
+$$
+
+which is zero unless \( i=j \).
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+Assume now that we have a symmetric positive-definite matrix \( \hat{A} \) of size
+\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
+$$
+\begin{equation*}
+\hat{x}_{i+1}=\hat{x}_{i}+\alpha_i\hat{p}_{i}.
+\end{equation*}
+$$
+
+We assume that \( \hat{p}_{i} \) is a sequence of \( n \) mutually conjugate directions.
+Then the \( \hat{p}_{i} \) form a basis of \( R^n \) and we can expand the solution
+$ \hat{A}\hat{x} = \hat{b}$ in this basis, namely
+
+$$
+\begin{equation*}
+ \hat{x} = \sum^{n}_{i=1} \alpha_i \hat{p}_i.
+\end{equation*}
+$$
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+The coefficients are given by
+$$
+\begin{equation*}
+ \mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
+\end{equation*}
+$$
+
+Multiplying with \( \hat{p}_k^T \) from the left gives
+
+$$
+\begin{equation*}
+ \hat{p}_k^T \hat{A}\hat{x} = \sum^{n}_{i=1} \alpha_i\hat{p}_k^T \hat{A}\hat{p}_i= \hat{p}_k^T \hat{b},
+\end{equation*}
+$$
+
+and we can define the coefficients \( \alpha_k \) as
+
+$$
+\begin{equation*}
+ \alpha_k = \frac{\hat{p}_k^T \hat{b}}{\hat{p}_k^T \hat{A} \hat{p}_k}
+\end{equation*}
+$$
+
+
+
+
+
+
+
Conjugate gradient method and iterations
+
+
+
+
+
+If we choose the conjugate vectors \( \hat{p}_k \) carefully,
+then we may not need all of them to obtain a good approximation to the solution
+\( \hat{x} \).
+We want to regard the conjugate gradient method as an iterative method.
+This will us to solve systems where \( n \) is so large that the direct
+method would take too much time.
+
+
+We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \).
+We can assume without loss of generality that
+$$
+\begin{equation*}
+\hat{x}_0=0,
+\end{equation*}
+$$
+
+or consider the system
+$$
+\begin{equation*}
+\hat{A}\hat{z} = \hat{b}-\hat{A}\hat{x}_0,
+\end{equation*}
+$$
+
+instead.
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+One can show that the solution \( \hat{x} \) is also the unique minimizer of the quadratic form
+$$
+\begin{equation*}
+ f(\hat{x}) = \frac{1}{2}\hat{x}^T\hat{A}\hat{x} - \hat{x}^T \hat{x} , \quad \hat{x}\in\mathbf{R}^n.
+\end{equation*}
+$$
+
+This suggests taking the first basis vector \( \hat{p}_1 \)
+to be the gradient of \( f \) at \( \hat{x}=\hat{x}_0 \),
+which equals
+$$
+\begin{equation*}
+\hat{A}\hat{x}_0-\hat{b},
+\end{equation*}
+$$
+
+and
+\( \hat{x}_0=0 \) it is equal \( -\hat{b} \).
+The other vectors in the basis will be conjugate to the gradient,
+hence the name conjugate gradient method.
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+Let \( \hat{r}_k \) be the residual at the \( k \)-th step:
+$$
+\begin{equation*}
+\hat{r}_k=\hat{b}-\hat{A}\hat{x}_k.
+\end{equation*}
+$$
+
+Note that \( \hat{r}_k \) is the negative gradient of \( f \) at
+\( \hat{x}=\hat{x}_k \),
+so the gradient descent method would be to move in the direction \( \hat{r}_k \).
+Here, we insist that the directions \( \hat{p}_k \) are conjugate to each other,
+so we take the direction closest to the gradient \( \hat{r}_k \)
+under the conjugacy constraint.
+This gives the following expression
+$$
+\begin{equation*}
+\hat{p}_{k+1}=\hat{r}_k-\frac{\hat{p}_k^T \hat{A}\hat{r}_k}{\hat{p}_k^T\hat{A}\hat{p}_k} \hat{p}_k.
+\end{equation*}
+$$
+
Simple implementation of the Conjugate gradient algorithm
+
+
+
+
+
+
+
Vector ConjugateGradient(Matrix A, Vector b, Vector x0){
+ int dim = x0.Dimension();
+ constdouble tolerance = 1.0e-14;
+ Vector x(dim),r(dim),v(dim),z(dim);
+ double c,t,d;
+
+ x = x0;
+ r = b - A*x;
+ v = r;
+ c = dot(r,r);
+ int i = 0; IterMax = dim;
+ while(i <= IterMax){
+ z = A*v;
+ t = c/dot(v,z);
+ x = x + t*v;
+ r = r - t*z;
+ d = dot(r,r);
+ if(sqrt(d) < tolerance)
+ break;
+ v = r + (d/c)*v;
+ c = d; i++;
+ }
+ return x;
+}
+
+
+
+
+
+
+
+
+
Broyden–Fletcher–Goldfarb–Shanno algorithm
+
+
+
+The optimization problem is to minimize \( f(\mathbf {x} ) \) where \( \mathbf {x} \) is a vector in \( R^{n} \), and \( f \) is a differentiable scalar function. There are no constraints on the values that \( \mathbf {x} \) can take.
+
+
+The algorithm begins at an initial estimate for the optimal value \( \mathbf {x}_{0} \) and proceeds iteratively to get a better estimate at each stage.
+
+
+The search direction \( p_k \) at stage \( k \) is given by the solution of the analogue of the Newton equation
+$$
+B_{k}\mathbf {p} _{k}=-\nabla f(\mathbf {x}_{k}),
+$$
+
+
+where \( B_{k} \) is an approximation to the Hessian matrix, which is
+updated iteratively at each stage, and \( \nabla f(\mathbf {x} _{k}) \)
+is the gradient of the function
+evaluated at \( x_k \).
+A line search in the direction \( p_k \) is then used to
+find the next point \( x_{k+1} \) by minimising
+$$
+f(\mathbf {x}_{k}+\alpha \mathbf {p}_{k}),
+$$
+
+over the scalar \( \alpha > 0 \).
+
+
+
We will use linear regression as a case study for the gradient descent
@@ -946,7 +970,7 @@ $$
-
Gradient descent example
+
Gradient descent example
Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -971,7 +995,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
-
The derivative of the cost/loss function
+
The derivative of the cost/loss function
Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show that the gradient can be written as
@@ -986,7 +1010,7 @@ where \( X \) is the design matrix defined above.
-
The Hessian matrix
+
The Hessian matrix
The Hessian matrix of \( C(\beta) \) is given by
$$
\hat{H} \equiv \begin{bmatrix}
@@ -1000,7 +1024,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
-
Simple program
+
Simple program
We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to
@@ -1041,7 +1065,7 @@ beta_NE = np.
-
Gradient Descent Example
+
Gradient Descent Example
Another simple example is here
@@ -1090,7 +1114,7 @@ plt.show()
-
And a corresponding example using scikit-learn
+
And a corresponding example using scikit-learn
@@ -1114,7 +1138,7 @@ sgdreg.fit(x,y.
-
Gradient descent and Ridge
+
Gradient descent and Ridge
We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \),
@@ -1171,7 +1195,7 @@ beta_ridge = np
-
Automatic differentiation
+
Automatic differentiation
Python has tools for so-called automatic differentiation.
Consider the following example
$$
@@ -1226,7 +1250,7 @@ plt.show()
-
Using autograd
+
Using autograd
Here we
@@ -1259,7 +1283,7 @@ grad_analytical =Autograd with more complicated functions
+
Autograd with more complicated functions
To differentiate with respect to two (or more) arguments of a Python
@@ -1309,7 +1333,7 @@ Note that the grad function will not produce the true gradient of the function.
-
More complicated functions using the elements of their arguments directly
+
More complicated functions using the elements of their arguments directly
@@ -1343,7 +1367,7 @@ could expect form a gradient-evaluting function.
@@ -1476,7 +1500,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
-
Unsupported functions
+
Unsupported functions
Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
@@ -1502,7 +1526,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
-
The syntax a.dot(b) when finding the dot product
+
The syntax a.dot(b) when finding the dot product
@@ -1544,7 +1568,7 @@ x = np.a
-
Recommended to avoid
+
Recommended to avoid
The documentation recommends to avoid inplace operations such as
@@ -1557,7 +1581,7 @@ a /=b
-
Stochastic Gradient Descent
+
Stochastic Gradient Descent
Stochastic gradient descent (SGD) and variants thereof address some of
@@ -1575,7 +1599,7 @@ $$
-
Computation of gradients
+
Computation of gradients
This in turn means that the gradient can be
@@ -1595,7 +1619,7 @@ minibatches. We denote these minibatches by \( B_k \) where
-
SGD example
+
SGD example
As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \)
and we choose to have \( M=5 \) minibathces,
then each minibatch contains two data points. In particular we have
@@ -1619,7 +1643,7 @@ $$
-
The gradient step
+
The gradient step
Thus a gradient descent step now looks like
@@ -1638,7 +1662,7 @@ the number of minibatches, as exemplified in the code below.
-
Simple example code
+
Simple example code
@@ -1670,7 +1694,7 @@ all \( n \) datapoints.
-
When do we stop?
+
When do we stop?
A natural question is when do we stop the search for a new minimum?
@@ -1687,7 +1711,7 @@ gave the lowest value.
-
Slightly different approach
+
Slightly different approach
Another approach is to let the step length \( \gamma_j \) depend on the
@@ -1732,6 +1756,404 @@ j =0print("gamma_j after %d epochs: %g"% (n_epochs,gamma_j))
+
+In the CG method we define so-called conjugate directions and two vectors
+\( \hat{s} \) and \( \hat{t} \)
+are said to be
+conjugate if
+$$
+\begin{equation*}
+\hat{s}^T\hat{A}\hat{t}= 0.
+\end{equation*}
+$$
+
+The philosophy of the CG method is to perform searches in various conjugate directions
+of our vectors \( \hat{x}_i \) obeying the above criterion, namely
+$$
+\begin{equation*}
+\hat{x}_i^T\hat{A}\hat{x}_j= 0.
+\end{equation*}
+$$
+
+Two vectors are conjugate if they are orthogonal with respect to
+this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is conjugate to \( \hat{t} \), then \( \hat{t} \) is conjugate to \( \hat{s} \).
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+An example is given by the eigenvectors of the matrix
+$$
+\begin{equation*}
+\hat{v}_i^T\hat{A}\hat{v}_j= \lambda\hat{v}_i^T\hat{v}_j,
+\end{equation*}
+$$
+
+which is zero unless \( i=j \).
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+Assume now that we have a symmetric positive-definite matrix \( \hat{A} \) of size
+\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
+$$
+\begin{equation*}
+\hat{x}_{i+1}=\hat{x}_{i}+\alpha_i\hat{p}_{i}.
+\end{equation*}
+$$
+
+We assume that \( \hat{p}_{i} \) is a sequence of \( n \) mutually conjugate directions.
+Then the \( \hat{p}_{i} \) form a basis of \( R^n \) and we can expand the solution
+$ \hat{A}\hat{x} = \hat{b}$ in this basis, namely
+
+$$
+\begin{equation*}
+ \hat{x} = \sum^{n}_{i=1} \alpha_i \hat{p}_i.
+\end{equation*}
+$$
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+The coefficients are given by
+$$
+\begin{equation*}
+ \mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
+\end{equation*}
+$$
+
+Multiplying with \( \hat{p}_k^T \) from the left gives
+
+$$
+\begin{equation*}
+ \hat{p}_k^T \hat{A}\hat{x} = \sum^{n}_{i=1} \alpha_i\hat{p}_k^T \hat{A}\hat{p}_i= \hat{p}_k^T \hat{b},
+\end{equation*}
+$$
+
+and we can define the coefficients \( \alpha_k \) as
+
+$$
+\begin{equation*}
+ \alpha_k = \frac{\hat{p}_k^T \hat{b}}{\hat{p}_k^T \hat{A} \hat{p}_k}
+\end{equation*}
+$$
+
+
+
+
+
+
+
Conjugate gradient method and iterations
+
+
+
+
+
+If we choose the conjugate vectors \( \hat{p}_k \) carefully,
+then we may not need all of them to obtain a good approximation to the solution
+\( \hat{x} \).
+We want to regard the conjugate gradient method as an iterative method.
+This will us to solve systems where \( n \) is so large that the direct
+method would take too much time.
+
+
+We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \).
+We can assume without loss of generality that
+$$
+\begin{equation*}
+\hat{x}_0=0,
+\end{equation*}
+$$
+
+or consider the system
+$$
+\begin{equation*}
+\hat{A}\hat{z} = \hat{b}-\hat{A}\hat{x}_0,
+\end{equation*}
+$$
+
+instead.
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+One can show that the solution \( \hat{x} \) is also the unique minimizer of the quadratic form
+$$
+\begin{equation*}
+ f(\hat{x}) = \frac{1}{2}\hat{x}^T\hat{A}\hat{x} - \hat{x}^T \hat{x} , \quad \hat{x}\in\mathbf{R}^n.
+\end{equation*}
+$$
+
+This suggests taking the first basis vector \( \hat{p}_1 \)
+to be the gradient of \( f \) at \( \hat{x}=\hat{x}_0 \),
+which equals
+$$
+\begin{equation*}
+\hat{A}\hat{x}_0-\hat{b},
+\end{equation*}
+$$
+
+and
+\( \hat{x}_0=0 \) it is equal \( -\hat{b} \).
+The other vectors in the basis will be conjugate to the gradient,
+hence the name conjugate gradient method.
+
+
+
+
+
+
+
Conjugate gradient method
+
+
+
+Let \( \hat{r}_k \) be the residual at the \( k \)-th step:
+$$
+\begin{equation*}
+\hat{r}_k=\hat{b}-\hat{A}\hat{x}_k.
+\end{equation*}
+$$
+
+Note that \( \hat{r}_k \) is the negative gradient of \( f \) at
+\( \hat{x}=\hat{x}_k \),
+so the gradient descent method would be to move in the direction \( \hat{r}_k \).
+Here, we insist that the directions \( \hat{p}_k \) are conjugate to each other,
+so we take the direction closest to the gradient \( \hat{r}_k \)
+under the conjugacy constraint.
+This gives the following expression
+$$
+\begin{equation*}
+\hat{p}_{k+1}=\hat{r}_k-\frac{\hat{p}_k^T \hat{A}\hat{r}_k}{\hat{p}_k^T\hat{A}\hat{p}_k} \hat{p}_k.
+\end{equation*}
+$$
+
Simple implementation of the Conjugate gradient algorithm
+
+
+
+
+
+
+
Vector ConjugateGradient(Matrix A, Vector b, Vector x0){
+ int dim = x0.Dimension();
+ constdouble tolerance =1.0e-14;
+ Vector x(dim),r(dim),v(dim),z(dim);
+ double c,t,d;
+
+ x = x0;
+ r = b - A*x;
+ v = r;
+ c = dot(r,r);
+ int i =0; IterMax = dim;
+ while(i <= IterMax){
+ z = A*v;
+ t = c/dot(v,z);
+ x = x + t*v;
+ r = r - t*z;
+ d = dot(r,r);
+ if(sqrt(d) < tolerance)
+ break;
+ v = r + (d/c)*v;
+ c = d; i++;
+ }
+ return x;
+}
+
+
+
+
+
+
+
+
+
Broyden–Fletcher–Goldfarb–Shanno algorithm
+
+
+
+The optimization problem is to minimize \( f(\mathbf {x} ) \) where \( \mathbf {x} \) is a vector in \( R^{n} \), and \( f \) is a differentiable scalar function. There are no constraints on the values that \( \mathbf {x} \) can take.
+
+
+The algorithm begins at an initial estimate for the optimal value \( \mathbf {x}_{0} \) and proceeds iteratively to get a better estimate at each stage.
+
+
+The search direction \( p_k \) at stage \( k \) is given by the solution of the analogue of the Newton equation
+$$
+B_{k}\mathbf {p} _{k}=-\nabla f(\mathbf {x}_{k}),
+$$
+
+
+where \( B_{k} \) is an approximation to the Hessian matrix, which is
+updated iteratively at each stage, and \( \nabla f(\mathbf {x} _{k}) \)
+is the gradient of the function
+evaluated at \( x_k \).
+A line search in the direction \( p_k \) is then used to
+find the next point \( x_{k+1} \) by minimising
+$$
+f(\mathbf {x}_{k}+\alpha \mathbf {p}_{k}),
+$$
+
+over the scalar \( \alpha > 0 \).
+
+
+
+
+
diff --git a/doc/pub/Splines/ipynb/Splines.ipynb b/doc/pub/Splines/ipynb/Splines.ipynb
index 350eb63c0..48e3c51fa 100644
--- a/doc/pub/Splines/ipynb/Splines.ipynb
+++ b/doc/pub/Splines/ipynb/Splines.ipynb
@@ -10,7 +10,7 @@
" \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: **Sep 27, 2018**\n",
+ "Date: **Oct 6, 2018**\n",
"\n",
"Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -844,29 +844,10 @@
{
"cell_type": "code",
"execution_count": 1,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- ""
- ]
- },
- "execution_count": 1,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
@@ -902,19 +883,10 @@
{
"cell_type": "code",
"execution_count": 2,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"pt.axis(\"equal\")\n",
"pt.contour(xmesh, ymesh, fmesh)\n",
@@ -931,7 +903,9 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"x = guesses[-1]\n",
@@ -948,16 +922,10 @@
{
"cell_type": "code",
"execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[ 1.33333333 -0.26666667]\n"
- ]
- }
- ],
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"def f1d(alpha):\n",
" return f(x + alpha*s)\n",
@@ -978,29 +946,10 @@
{
"cell_type": "code",
"execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "[]"
- ]
- },
- "execution_count": 5,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"pt.axis(\"equal\")\n",
"pt.contour(xmesh, ymesh, fmesh, 50)\n",
@@ -1012,6 +961,10 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "## Conjugate gradient\n",
+ "\n",
+ "\n",
+ "\n",
"\n",
"## Revisiting our first homework\n",
"\n",
@@ -1162,6 +1115,9 @@
"source": [
"This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite.\n",
"\n",
+ "\n",
+ "\n",
+ "\n",
"## Simple program\n",
"\n",
"We can now write a program that minimizes $C(\\beta)$ using the gradient descent method with a constant learning rate $\\gamma$ according to"
@@ -1191,7 +1147,9 @@
{
"cell_type": "code",
"execution_count": 6,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -1225,30 +1183,11 @@
},
{
"cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[[3.96812677]\n",
- " [2.93472871]]\n",
- "[[3.96812677]\n",
- " [2.93472871]]\n"
- ]
- },
- {
- "data": {
- "image/png": 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\n",
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- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"\n",
"# Importing various packages\n",
@@ -1301,7 +1240,9 @@
{
"cell_type": "code",
"execution_count": 8,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"# Importing various packages\n",
@@ -1385,7 +1326,9 @@
{
"cell_type": "code",
"execution_count": 9,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -1458,27 +1401,11 @@
},
{
"cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The max absolute difference is: 1.77636e-15\n"
- ]
- }
- ],
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"import autograd.numpy as np\n",
"\n",
@@ -1532,18 +1459,11 @@
},
{
"cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The gradient of f1 evaluated at a = 1 using autograd is: 3\n",
- "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n"
- ]
- }
- ],
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"import autograd.numpy as np\n",
"from autograd import grad\n",
@@ -1578,7 +1498,9 @@
{
"cell_type": "code",
"execution_count": 12,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1629,7 +1551,9 @@
{
"cell_type": "code",
"execution_count": 13,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1669,7 +1593,9 @@
{
"cell_type": "code",
"execution_count": 14,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1701,7 +1627,9 @@
{
"cell_type": "code",
"execution_count": 15,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1761,7 +1689,9 @@
{
"cell_type": "code",
"execution_count": 16,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1785,7 +1715,9 @@
{
"cell_type": "code",
"execution_count": 17,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1832,7 +1764,9 @@
{
"cell_type": "code",
"execution_count": 18,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1860,7 +1794,9 @@
{
"cell_type": "code",
"execution_count": 19,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1888,7 +1824,9 @@
{
"cell_type": "code",
"execution_count": 20,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import autograd.numpy as np\n",
@@ -1918,7 +1856,9 @@
{
"cell_type": "code",
"execution_count": 21,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"a += b\n",
@@ -2043,7 +1983,9 @@
{
"cell_type": "code",
"execution_count": 22,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np \n",
@@ -2105,7 +2047,9 @@
{
"cell_type": "code",
"execution_count": 23,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np \n",
@@ -2133,27 +2077,529 @@
"\n",
"print(\"gamma_j after %d epochs: %g\" % (n_epochs,gamma_j))"
]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Program for stochastic gradient"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# Importing various packages\n",
+ "from math import exp, sqrt\n",
+ "from random import random, seed\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from sklearn.linear_model import SGDRegressor\n",
+ "\n",
+ "x = 2*np.random.rand(100,1)\n",
+ "y = 4+3*x+np.random.randn(100,1)\n",
+ "\n",
+ "xb = np.c_[np.ones((100,1)), x]\n",
+ "theta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)\n",
+ "print(\"Own inversion\")\n",
+ "print(theta_linreg)\n",
+ "sgdreg = SGDRegressor(n_iter = 50, penalty=None, eta0=0.1)\n",
+ "sgdreg.fit(x,y.ravel())\n",
+ "print(\"sgdreg from scikit\")\n",
+ "print(sgdreg.intercept_, sgdreg.coef_)\n",
+ "\n",
+ "\n",
+ "theta = np.random.randn(2,1)\n",
+ "\n",
+ "eta = 0.1\n",
+ "Niterations = 1000\n",
+ "m = 100\n",
+ "\n",
+ "for iter in range(Niterations):\n",
+ " gradients = 2.0/m*xb.T.dot(xb.dot(theta)-y)\n",
+ " theta -= eta*gradients\n",
+ "print(\"theta frm own gd\")\n",
+ "print(theta)\n",
+ "\n",
+ "xnew = np.array([[0],[2]])\n",
+ "xbnew = np.c_[np.ones((2,1)), xnew]\n",
+ "ypredict = xbnew.dot(theta)\n",
+ "ypredict2 = xbnew.dot(theta_linreg)\n",
+ "\n",
+ "\n",
+ "n_epochs = 50\n",
+ "t0, t1 = 5, 50\n",
+ "m = 100\n",
+ "def learning_schedule(t):\n",
+ " return t0/(t+t1)\n",
+ "\n",
+ "theta = np.random.randn(2,1)\n",
+ "\n",
+ "for epoch in range(n_epochs):\n",
+ " for i in range(m):\n",
+ " random_index = np.random.randint(m)\n",
+ " xi = xb[random_index:random_index+1]\n",
+ " yi = y[random_index:random_index+1]\n",
+ " gradients = 2 * xi.T.dot(xi.dot(theta)-yi)\n",
+ " eta = learning_schedule(epoch*m+i)\n",
+ " theta = theta - eta*gradients\n",
+ "print(\"theta from own sdg\")\n",
+ "print(theta)\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "plt.plot(xnew, ypredict, \"r-\")\n",
+ "plt.plot(xnew, ypredict2, \"b-\")\n",
+ "plt.plot(x, y ,'ro')\n",
+ "plt.axis([0,2.0,0, 15.0])\n",
+ "plt.xlabel(r'$x$')\n",
+ "plt.ylabel(r'$y$')\n",
+ "plt.title(r'Random numbers ')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Momentum based methods\n",
+ "\n",
+ "\n",
+ "\n",
+ "## Conjugate gradient method\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",
+ "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",
+ "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",
+ "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",
+ "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",
+ "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",
+ "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",
+ "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": [
+ "## Simple implementation of the Conjugate gradient algorithm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " Vector ConjugateGradient(Matrix A, Vector b, Vector x0){\n",
+ " int dim = x0.Dimension();\n",
+ " const double tolerance = 1.0e-14;\n",
+ " Vector x(dim),r(dim),v(dim),z(dim);\n",
+ " double c,t,d;\n",
+ " \n",
+ " x = x0;\n",
+ " r = b - A*x;\n",
+ " v = r;\n",
+ " c = dot(r,r);\n",
+ " int i = 0; IterMax = dim;\n",
+ " while(i <= IterMax){\n",
+ " z = A*v;\n",
+ " t = c/dot(v,z);\n",
+ " x = x + t*v;\n",
+ " r = r - t*z;\n",
+ " d = dot(r,r);\n",
+ " if(sqrt(d) < tolerance)\n",
+ " break;\n",
+ " v = r + (d/c)*v;\n",
+ " c = d; i++;\n",
+ " }\n",
+ " return x;\n",
+ " } \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Broyden–Fletcher–Goldfarb–Shanno algorithm\n",
+ "The optimization problem is to minimize $f(\\mathbf {x} )$ where $\\mathbf {x}$ is a vector in $R^{n}$, and $f$ is a differentiable scalar function. There are no constraints on the values that $\\mathbf {x}$ can take.\n",
+ "\n",
+ "The algorithm begins at an initial estimate for the optimal value $\\mathbf {x}_{0}$ and proceeds iteratively to get a better estimate at each stage.\n",
+ "\n",
+ "The search direction $p_k$ at stage $k$ is given by the solution of the analogue of the Newton equation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "B_{k}\\mathbf {p} _{k}=-\\nabla f(\\mathbf {x}_{k}),\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "where $B_{k}$ is an approximation to the Hessian matrix, which is\n",
+ "updated iteratively at each stage, and $\\nabla f(\\mathbf {x} _{k})$\n",
+ "is the gradient of the function\n",
+ "evaluated at $x_k$. \n",
+ "A line search in the direction $p_k$ is then used to\n",
+ "find the next point $x_{k+1}$ by minimising"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "f(\\mathbf {x}_{k}+\\alpha \\mathbf {p}_{k}),\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "over the scalar $\\alpha > 0$."
+ ]
}
],
- "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": "3.7.0"
- }
- },
+ "metadata": {},
"nbformat": 4,
"nbformat_minor": 2
}
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@@ -0,0 +1,220 @@
+TITLE: Project 2 on Machine Learning, deadline November 5
+AUTHOR: "Data Analysis and Machine Learning FYS-STK3155/FYS4155":"http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html" {copyright, 1999-present|CC BY-NC} at Department of Physics, University of Oslo, Norway
+DATE: today
+
+
+o add about ising model
+o link to where we have the data
+o explain how to fit the model
+o link to mehta's article
+
+===== Classification and Regression, from linear and logistic regression to neural networks =====
+
+The main aim of this project is to study both classification and
+regression problems, starting with the regression algortihms studied
+in project 1. We will include logistic regresion for classification
+problems and write our own multilayer perceptron code for studying
+both regression and classification problems. The codes developed in
+project 1, including bootstrap and/or cross-validation as well as the
+computation of the mean-squared error and the R2 score function can
+also be utilized (and included in logistic regression and the neural
+network codes) in the present analysis.
+
+We will use the Ising model to generate our training data and will
+focus mainly on supervised training. We will follow closely the recent
+article of "Mehta et al, arXiv
+1803.08823":"https://arxiv.org/abs/1803.08823". This article stands
+out as an excellent review on machine learning (ML) algorithms applied
+to typical physics problems. The added benefit is that each figure and
+model presented in "this article is accompanied by its jupyter
+notebook":"https://physics.bu.edu/~pankajm/MLnotebooks.html". This
+means that we can start using these and compare with our own
+results. In case you wish to use their data for the Ising model, their
+data can be downloaded from the same link which lists to the jupyter
+notebooks. See also at the end of the project description for more
+information on how to install various Python packages.
+
+
+
+With the abovementioned configurations we will determine, using first
+various regression methods, the value of the coupling constant for the
+energy of the one-dimensional Ising model. Thereafter, we will use the
+two-dimensional data, but now computed at different temperatures, in
+order to classify the phase of the Ising model. Below the critical
+temperature, the system will be in a so-called ferromagnetic
+phase. Close to the critical temperature, the final magnetization
+becomes smaller and smaller in absolute value while above the critical
+temperature, the net magnetization is zero. This classification case,
+that is the two-dimensional Ising model, will be studied using
+logistic regression and deep neural networks. The aim is to develop
+your own logistic regression code for the classification of the phases
+(this is a binary model) and your multilayer perceptron code for the
+classification and regression case.
+
+
+Feel free to use the notebooks to benchmark your code. If you wish to
+write your own C++ or Fortran program for say a simple neural network
+model and a logistic regression model, please feel free to do so. You can then benchmark your results
+against the above jupyter notebooks.
+
+
+=== Part a): Producing the data ===
+
+You can use the Ising model data from the article of Mehta *et al.*,
+or generate your own data. If you opt for using your own Ising model
+code, you need to generate $10000$ energy configurations with their
+spin orientations after the system has reached its most likely
+state. These energies and their corresponding spin orientations
+represent then your data. We will use a fixed lattice of $L\times L =
+40 \times 40$ spins in two dimensions and $L=40$ spins in one
+dimension. Make sure the calculations have been equilibrated. For the
+two-dimensional system, compute the configurations for three values of
+the temperature, namely $T=0.75$ (ordered phase), $T=2.3$ (near the
+critical point) and $T=4.0$ (disordered phase). For the
+one-dimensional system it suffices to compute the various
+configurations for one temperature only, say $T=2.0$. These are the
+data you will use to study different ML algorithms. We generate our
+data with $J=1$.
+
+=== Part b): Estimating the coupling constant of the one-dimensional Ising model ===
+
+We start with the one-dimensional Ising model and use the data we have
+generated with $J=1$. Use linear regression, Lasso and Ridge
+regression as described section 6 and in Notebook 4 of "Mehta *et
+al.*":"https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CVI-linreg_ising.html". Discuss
+the methods and how they perform in computing the coupling constant
+$J$. Give a critical analysis and discuss how to evaluate the *cost
+function*. You should feel free to write your own code, see also the
+lecture notes of
+"FYS-STK4155":"https://compphysics.github.io/MachineLearning/doc/web/course.html",
+in particular te material on least square methods. You can use
+scikit-learn to perform these analyses. See below for instruction on
+how to install scikit-learn.
+
+=== Part c): Determine the phase of the two-dimensional Ising model ===
+
+We switch now to binary classification methods and use logistic
+regression to define the phases of the Ising model. Use described
+section 7 and in Notebook 6 of "Mehta *et
+al.*":"https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CVII-logreg_ising.html". Discuss
+the methods and how they perform. Give a critical analysis and discuss
+how to evaluate the *cost function*. You should feel free to write
+your own code.
+
+
+=== Part d): Classifying the Ising model phase using neural networks ===
+
+We end the classification problem of the phases of the Ising model by
+employing the algorithm for so-called feed-forward deep neural
+networks (see section 9 of Mehta *et al.*). The method is described in
+"notebook
+12":"https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html".
+
+You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
+
+===== Background literature =====
+
+
+o The textbook of "Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer":"https://www.springer.com/gp/book/9780387848570", chapters 3 and 7 are the most relevant ones for the analysis here.
+
+o "Mehta et al, arXiv 1803.08823":"https://arxiv.org/abs/1803.08823", *A high-bias, low-variance introduction to Machine Learning for physicists*, ArXiv:1803.08823.
+
+If you wish to read more about the Ising model and statistical physics here are three suggestions.
+
+o "M. Plischke and B. Bergersen":"http://www.worldscientific.com/worldscibooks/10.1142/5660", *Equilibrium Statistical Physics*, World Scientific, see chapters 5 and 6.
+
+o "D. P. Landau and K. Binder":"http://www.cambridge.org/no/academic/subjects/physics/computational-science-and-modelling/guide-monte-carlo-simulations-statistical-physics-4th-edition?format=HB", *A Guide to Monte Carlo Simulations in Statistical Physics*, Cambridge, see chapters 2,3 and 4.
+
+o "M. E. J. Newman and T. Barkema":"https://global.oup.com/academic/product/monte-carlo-methods-in-statistical-physics-9780198517979?cc=no&lang=en&", *Monte Carlo Methods in Statistical Physics*, Oxford, see chapters 3 and 4.
+
+
+
+
+
+===== Introduction to numerical projects =====
+
+Here follows a brief recipe and recommendation on how to write a report for each
+project.
+
+ * Give a short description of the nature of the problem and the eventual numerical methods you have used.
+
+ * Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.
+
+ * Include the source code of your program. Comment your program properly.
+
+ * If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.
+
+ * Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.
+
+ * Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.
+
+ * Try to give an interpretation of you results in your answers to the problems.
+
+ * Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you've made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.
+
+ * Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don't properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.
+
+
+
+
+
+===== Format for electronic delivery of report and programs =====
+
+The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file. As programming language we prefer that you choose between C/C++, Fortran2008 or Python. The following prescription should be followed when preparing the report:
+
+ * Use Devilry to hand in your projects, log in at URL:"http://devilry.ifi.uio.no" with your normal UiO username and password and choose either 'fysstk3155' or 'fysstk4155'. There you can load up the files within the deadline.
+
+ * Upload _only_ the report file! For the source code file(s) you have developed please provide us with your link to your github domain. The report file should include all of your discussions and a list of the codes you have developed. Do not include library files which are available at the course homepage, unless you have made specific changes to them.
+
+ * In your git repository, please include a folder which contains selected results. These can be in the form of output from your code for a selected set of runs and input parameters.
+
+ * In this and all later projects, you should include tests (for example unit tests) of your code(s).
+
+ * Comments from us on your projects, approval or not, corrections to be made etc can be found under your Devilry domain and are only visible to you and the teachers of the course.
+
+
+
+Finally,
+we encourage you to collaborate. Optimal working groups consist of
+2-3 students. You can then hand in a common report.
+
+
+
+===== Software and needed installations =====
+
+If you have Python installed (we 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 tensorflow sympy pandas pillow
+For Python3, replace _pip_ with _pip3_.
+
+See below for a discussion of _tensorflow_ and _scikit-learn_.
+
+For OSX users we recommend also, 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 python2.7)
+etc etc.
+
+If you don't want to install various Python packages with their dependencies separately, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely
+o "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_
+o "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.
+
+Popular software packages written in Python for ML are
+
+* "Scikit-learn":"http://scikit-learn.org/stable/",
+* "Tensorflow":"https://www.tensorflow.org/",
+* "PyTorch":"http://pytorch.org/" and
+* "Keras":"https://keras.io/".
+These are all freely available at their respective GitHub sites. They
+encompass communities of developers in the thousands or more. And the number
+of code developers and contributors keeps increasing.
+
+
+
+
+
+
+
diff --git a/doc/src/Projects/2018/Project2/clean.sh b/doc/src/Projects/2018/Project2/clean.sh
new file mode 100755
index 000000000..2e5da2c72
--- /dev/null
+++ b/doc/src/Projects/2018/Project2/clean.sh
@@ -0,0 +1,3 @@
+#!/bin/sh
+doconce clean
+rm -rf *.pdf *.tex ipynb*.tar.gz *.html ._*.html *~ reveal.js Trash README.txt
diff --git a/doc/src/Projects/2018/Project2/make.sh b/doc/src/Projects/2018/Project2/make.sh
new file mode 100755
index 000000000..cf5d38365
--- /dev/null
+++ b/doc/src/Projects/2018/Project2/make.sh
@@ -0,0 +1,79 @@
+#!/bin/sh
+set -x
+
+function system {
+ "$@"
+ if [ $? -ne 0 ]; then
+ echo "make.sh: unsuccessful command $@"
+ echo "abort!"
+ exit 1
+ fi
+}
+
+if [ $# -eq 0 ]; then
+echo 'bash make.sh slides1|slides2'
+exit 1
+fi
+
+name=$1
+rm -f *.tar.gz
+
+opt="--encoding=utf-8"
+opt=
+
+rm -f *.aux
+
+
+
+# Plain HTML documents
+html=${name}
+system doconce format html $name --pygments_html_style=default --html_style=bloodish --html_links_in_new_window --html_output=$html $opt
+system doconce split_html $html.html --method=space10
+
+# Bootstrap style
+html=${name}-bs
+system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
+system doconce split_html $html.html --method=split --pagination --nav_button=bottom
+
+
+# Ordinary plain LaTeX document
+system doconce format pdflatex $name --print_latex_style=trac --latex_admon=paragraph $opt
+system doconce ptex2tex $name envir=print
+# 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}.pdf
+cp $name.tex ${name}.tex
+
+# Publish
+dest=../../../../Projects/2018
+if [ ! -d $dest/$name ]; then
+mkdir $dest/$name
+mkdir $dest/$name/pdf
+mkdir $dest/$name/html
+mkdir $dest/$name/ipynb
+fi
+cp ${name}*.tex $dest/$name/pdf
+cp ${name}*.pdf $dest/$name/pdf
+cp -r ${name}*.html ._${name}*.html $dest/$name/html
+
+# Figures: cannot just copy link, need to physically copy the files
+if [ -d fig-${name} ]; then
+if [ ! -d $dest/$name/html/fig-$name ]; then
+mkdir $dest/$name/html/fig-$name
+fi
+cp -r fig-${name}/* $dest/$name/html/fig-$name
+fi
+
+cp ${name}.ipynb $dest/$name/ipynb
+ipynb_tarfile=ipynb-${name}-src.tar.gz
+if [ ! -f ${ipynb_tarfile} ]; then
+cat > README.txt < 0$.
+
+!eblock
+
+