+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 work two and two together. 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.
+
+
+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 work two and two together. 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/Project1/ipynb/ipynb-Project1-src.tar.gz b/doc/Projects/2018/Project1/ipynb/ipynb-Project1-src.tar.gz
new file mode 100644
index 000000000..cb896340e
Binary files /dev/null and b/doc/Projects/2018/Project1/ipynb/ipynb-Project1-src.tar.gz differ
diff --git a/doc/Projects/2018/Project1/pdf/Project1.p.tex b/doc/Projects/2018/Project1/pdf/Project1.p.tex
new file mode 100644
index 000000000..dcd8e3f9b
--- /dev/null
+++ b/doc/Projects/2018/Project1/pdf/Project1.p.tex
@@ -0,0 +1,277 @@
+%%
+%% Automatically generated file from DocOnce source
+%% (https://github.com/hplgit/doconce/)
+%%
+%%
+% #ifdef PTEX2TEX_EXPLANATION
+%%
+%% The file follows the ptex2tex extended LaTeX format, see
+%% 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
+%% see examples). If doconce ptex2tex has envir=minted, it enables the
+%% minted style without needing -DMINTED.
+% #endif
+
+% #define PREAMBLE
+
+% #ifdef PREAMBLE
+%-------------------- begin preamble ----------------------
+
+\documentclass[%
+oneside, % oneside: electronic viewing, twoside: printing
+final, % draft: marks overfull hboxes, figures with paths
+10pt]{article}
+
+\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,
+ urlcolor=linkcolor,
+ citecolor=black,
+ filecolor=black,
+ %filecolor=blue,
+ pdfmenubar=true,
+ 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
+\renewcommand{\headrulewidth}{0pt}
+\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}
+ \renewcommand{\headrulewidth}{0mm}
+}
+% 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}
+
+
+% prevent orhpans and widows
+\clubpenalty = 10000
+\widowpenalty = 10000
+
+% --- end of standard preamble for documents ---
+
+
+% 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 1 on Machine Learning, deadline October 1
+\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}
+May 2018
+\end{center}
+% --- end date ---
+
+\vspace{1cm}
+
+
+\subsection{Regression analysis and classification}
+
+\paragraph{Introduction.}
+\paragraph{Part a): The data.}
+\subsection{Background literature}
+
+
+
+
+\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 work two and two together. 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/Project1/pdf/Project1.pdf b/doc/Projects/2018/Project1/pdf/Project1.pdf
new file mode 100644
index 000000000..970d35209
Binary files /dev/null and b/doc/Projects/2018/Project1/pdf/Project1.pdf differ
diff --git a/doc/Projects/2018/Project1/pdf/Project1.tex b/doc/Projects/2018/Project1/pdf/Project1.tex
new file mode 100644
index 000000000..9232c49a0
--- /dev/null
+++ b/doc/Projects/2018/Project1/pdf/Project1.tex
@@ -0,0 +1,249 @@
+%%
+%% Automatically generated file from DocOnce source
+%% (https://github.com/hplgit/doconce/)
+%%
+%%
+
+
+%-------------------- begin preamble ----------------------
+
+\documentclass[%
+oneside, % oneside: electronic viewing, twoside: printing
+final, % draft: marks overfull hboxes, figures with paths
+10pt]{article}
+
+\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,
+ urlcolor=linkcolor,
+ citecolor=black,
+ filecolor=black,
+ %filecolor=blue,
+ pdfmenubar=true,
+ 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
+\renewcommand{\headrulewidth}{0pt}
+\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}
+ \renewcommand{\headrulewidth}{0mm}
+}
+% 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}
+
+
+% prevent orhpans and widows
+\clubpenalty = 10000
+\widowpenalty = 10000
+
+% --- end of standard preamble for documents ---
+
+
+% 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 1 on Machine Learning, deadline October 1
+\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}
+May 2018
+\end{center}
+% --- end date ---
+
+\vspace{1cm}
+
+
+\subsection*{Regression analysis and classification}
+
+\paragraph{Introduction.}
+\paragraph{Part a): The data.}
+\subsection*{Background literature}
+
+
+
+
+\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 work two and two together. 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/src/Projects/2018/Project1/Project1.do.txt b/doc/src/Projects/2018/Project1/Project1.do.txt
new file mode 100644
index 000000000..ac2a84a73
--- /dev/null
+++ b/doc/src/Projects/2018/Project1/Project1.do.txt
@@ -0,0 +1,100 @@
+TITLE: Project 1 on Machine Learning, deadline October 1
+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: May 2018
+
+
+===== Regression analysis and classification =====
+
+=== Introduction ===
+
+
+
+=== Part a): The data ===
+
+
+===== Background literature =====
+
+
+
+
+===== 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 work two and two together. 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/Project1/clean.sh b/doc/src/Projects/2018/Project1/clean.sh
new file mode 100755
index 000000000..2e5da2c72
--- /dev/null
+++ b/doc/src/Projects/2018/Project1/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/Project1/make.sh b/doc/src/Projects/2018/Project1/make.sh
new file mode 100755
index 000000000..cf5d38365
--- /dev/null
+++ b/doc/src/Projects/2018/Project1/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\n",
+ "\\end{equation}\n",
+ "for $\\gamma$ small enough, then $F(\\mathbf{x}_{k+1}) \\leq F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma$ we moves towards smaller function values, i.e a minimum.\n",
+ "\n",
+ "This observation is the basis of the gradient descent (GD) method. One starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and compute new approximations according to\n",
+ "\n",
+ "\\begin{equation}\n",
+ "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
+ "\\end{equation}\n",
+ "\n",
+ "Ideally the sequence $\\{ \\mathbf{x}_k \\}_{k=0}$ converges to a __global__ minimum of the function $F$. In general we do not know if we are in a global or local minimum. In the special case when $F$ is a convex function, all local minima are also global minima, so in this case gradient descent can converge to the global solution. We will explore this further in the exercises.\n",
+ "\n",
+ "In a practical implementation we have to choose a criterion for when to stop the iteration. One such condition would be to stop when \n",
+ "\n",
+ "\\begin{equation}\n",
+ "||\\nabla F(\\mathbf{x})|| < \\epsilon,\n",
+ "\\end{equation}\n",
+ "where $\\epsilon$ is some small number. \n",
+ "\n",
+ "\n",
+ "The parameter $\\gamma$ is referred to as the step size and is constant in the simplest Gradient Descent scheme. We will consider generalizations later where $\\gamma$ is adaptet during each iteration in order to obtain faster convergence or esacpe local minima.\n",
+ "\n",
+ "Another point worth noticing is that in order to use gradient descent all we need to know is the function and its gradient. Computing the gradient may be difficult depending on the complexity of the function we want to minimize. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Exercise 1\n",
+ "We start by considering functions of a single variable since they are easy to work with and we can compute exact minima to compare our implementation. Furthermore, single variable functions captures much of the problems we experience computing minima of more complex, multi-variable functions.\n",
+ "\n",
+ "a) Consider the function $f(x) = x^2+1$. Show that $f(x_{k+1}) \\leq f(x_k)$ when $0 \\leq \\gamma \\leq 1$.\n",
+ "\n",
+ "Hint: Use that (GD step) $x_{k+1} = x_k - \\gamma f'(x_k)$ and solve the resulting inequality.\n",
+ "\n",
+ "Solution: \n",
+ "\n",
+ "\\begin{align}\n",
+ "x_k^2(1-2\\gamma)^2 + 1 &\\leq x_k^2+1 \\\\\n",
+ "(1-2\\gamma)^2 &\\leq 1 \\\\\n",
+ "\\gamma(1-\\gamma) &\\leq 0 \\\\\n",
+ "\\Rightarrow 0 \\leq \\gamma &\\leq 1.\n",
+ "\\end{align}\n",
+ "\n",
+ "b) Show/convince yourself that f has its minimum at $x=0$ with $f(0) = 1$. \n",
+ "\n",
+ "Write a function computes the minimum using the GD method, with $x_0 = -3$ as initial guess. Try to write the function in a general way such that you in principle can use it on any function.\n",
+ "\n",
+ "Experiment with different step sizes in the range $0 < \\gamma < 1$ and check how many iterations you need in order for the solution to converge within a precision of $10^{-6}$. \n",
+ "\n",
+ "Since the derivative has to be zero in a minimum you can use $$|f'(x_k)| < \\epsilon,$$ with $\\epsilon = 10^{-6}$ as a criterion for convergence. (The choice of $10^{-6}$ as precision is arbitrary).\n",
+ "\n",
+ "What happens if you choose $\\gamma$ exactly equal to 1? What happens if $\\gamma$ is slighly larger than 1? One way to get a better visual understanding of whats going on is to plot the function and the function values at each iteration, $f(x_k)$, within the same plot."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Converged: True\n",
+ "Number of iterations for convergence: 18\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "#Program that solves exercise 1b.\n",
+ "%matplotlib inline\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "def gradient_descent(xk,dx_f,gamma):\n",
+ " return xk-gamma*dx_f\n",
+ "\n",
+ "def quadratic(a,b,c,x):\n",
+ " return a*x**2+b*x+c\n",
+ "\n",
+ "def dx_quadratic(a,b,x):\n",
+ " return 2*a*x+b\n",
+ "\n",
+ "#One variable examples\n",
+ "a,b,c = 1,0,1\n",
+ "x = np.linspace(-5,5,101)\n",
+ "quad = quadratic(a,b,c,x)\n",
+ "dx_quad = dx_quadratic(a,b,x)\n",
+ "\n",
+ "xk = -3\n",
+ "xk_vec = [xk]\n",
+ "fxk_vec = [quadratic(a,b,c,xk)]\n",
+ "gamma = 0.3\n",
+ "iters = 0\n",
+ "max_iters = 1000\n",
+ "converged = False\n",
+ "\n",
+ "while(abs(dx_quadratic(a,b,xk)) > 1e-6 and iters < max_iters):\n",
+ " xk = gradient_descent(xk,dx_quadratic(a,b,xk),gamma)\n",
+ " xk_vec.append(xk)\n",
+ " fxk_vec.append(quadratic(a,b,c,xk))\n",
+ " iters += 1\n",
+ "\n",
+ "if(iters < max_iters):\n",
+ " converged = True\n",
+ "\n",
+ "print (\"Converged: %s\" % converged)\n",
+ "print (\"Number of iterations for convergence: %d\" % iters)\n",
+ "\n",
+ "plt.figure(1)\n",
+ "plt.plot(x,quad)\n",
+ "plt.plot(xk_vec,fxk_vec,'o')\n",
+ "plt.legend([\"f(x)\",\"GD-iterates\"])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "c) Quadratic functions as the one in exercise b) are particularly forigiving to work with since they only have one minimum/maximum, which in turn is global. A third order polynomial can have a maximum and a minimum or a saddle point. A fourth order polynomial may have two local minima. The point of the following exercise is to investigate the how GD depends on the initial guess, $x_0$.\n",
+ "\n",
+ "Consider the function\n",
+ "\\begin{equation}\n",
+ "f(x) = \\frac{(x+4)(x+1)(x-1)(x-3)}{14} + \\frac{1}{2},\n",
+ "\\end{equation}\n",
+ "with derivative \n",
+ "\\begin{equation}\n",
+ "f'(x) = \\frac{1}{14}\\left( 4x^3 + 3x^2 - 26x -1 \\right).\n",
+ "\\end{equation}\n",
+ "\n",
+ "Make a plot of the function for $x \\in [-5,4]$. The function has a global minimum at $x \\approx -2.9354$, a local maximum at $x \\approx -0.038301$ and a local minimum at $x \\approx 2.2237$. Choose $\\gamma = 0.1$ as step length and use GD descent to compute the minimum. \n",
+ "\n",
+ "* Expermient with different initial values $x_0 \\in [-5,-0.1]$ and $x_0 \\in [0.1, 4]$. \n",
+ "* What happens if you choose $x_0 = -0.038301$ (i.e at the local maximum)? Explain why this happens. \n",
+ "* What happens if you choose $x_0$ slightly smaller/larger than $-0.038301$? \n",
+ "* Furthermore you can experiment with different step sizes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Converged: True\n",
+ "Number of iterations for convergence: 67\n"
+ ]
+ },
+ {
+ "data": {
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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def quartic(x):\n",
+ " return (x+4)*(x+1)*(x-1)*(x-3)/14.0 + 0.5\n",
+ "def dx_quartic(x):\n",
+ " return (1.0/14.0)*(4*x**3 + 3*x**2 - 26*x - 1)\n",
+ "\n",
+ "x = np.linspace(-5,4,101)\n",
+ "quart = quartic(x)\n",
+ "dx_quart = dx_quartic(x)\n",
+ "\n",
+ "xk = -0.02\n",
+ "xk_vec = [xk]\n",
+ "fxk_vec = [quartic(xk)]\n",
+ "gamma = 0.1\n",
+ "iters = 0\n",
+ "max_iters = 200\n",
+ "converged = False\n",
+ "\n",
+ "while(abs(dx_quartic(xk)) > 1e-6 and iters < max_iters):\n",
+ " xk = gradient_descent(xk,dx_quartic(xk),gamma)\n",
+ " xk_vec.append(xk)\n",
+ " fxk_vec.append(quartic(xk))\n",
+ " iters += 1\n",
+ "\n",
+ "if(iters < max_iters):\n",
+ " converged = True\n",
+ "\n",
+ "print (\"Converged: %s\" % converged)\n",
+ "print (\"Number of iterations for convergence: %d\" % iters)\n",
+ "\n",
+ "plt.figure(1)\n",
+ "plt.plot(x,quart)\n",
+ "plt.plot(xk_vec,fxk_vec,'o')\n",
+ "plt.legend([\"f(x)\",\"GD-iterates\"])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "d) In this exercise we will look at function of two variables. \n",
+ "\n",
+ "Consider the function \n",
+ "\\begin{equation}\n",
+ "z(x,y) = x^2+10y^2-1.\n",
+ "\\end{equation}\n",
+ "\n",
+ "* Compute the gradient and show that $z(x,y)$ has its minimum at $x=0, y=0$.\n",
+ "* Extend your program such that it can compute the minimum of a multivariate function. The main difference now is that the points and derivative/gradient now are vectors/arrays and not just scalars. Also try to make relevant visualizations, such as surface or contour plots.\n",
+ "* As before, experiment with different step sizes $\\gamma$ and intitial values $\\mathbf{x}_0 = (x_0,y_0)$.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
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+ "
Probability theory and statistical methods play a central role in science. Nowadays we are
@@ -569,7 +610,7 @@ tools of probability theory, the aim of this course is to expose you to central
This course covers thus topics like Monte Carlo methods and Markov chains, Bayesian statistics, error estimates, various linear methods, optimization of data and error analysis and central algorithms in machine learning.
The course has several numerical projects and numerical exercises that are meant to illustrate the theory.
-
Learning outcomes
+
Learning outcomes
The course introduces a variety of central algorithms and methods
@@ -586,19 +627,19 @@ essential for studies of data analysis and machine learning. The course is proje
Work on numerical projects to illustrate the theory. The projects play a central role and students are expected to know modern programming languages like Python or C++.
-
Prerequisites
+
Prerequisites
Basic knowledge in programming and numerics. Required courses are the equivalents to the University of Oslo mathematics courses MAT1100, MAT1110, MAT1120 and at least one of the corresponding computing and programming courses INF1000/INF1110 or MAT-INF1100/MAT-INF1100L/BIOS1100/KJM-INF1xxx.
-
The course has two central parts
+
The course has two central parts
Statistical analysis and optimization of data
Machine learning
-
Statistical analysis and optimization of data
+
Statistical analysis and optimization of data
The following topics will be covered
@@ -615,7 +656,7 @@ The following topics will be covered
Practical optimization using Singular-value decomposition and least squares for parameterizing data.
-
Machine learning
+
Machine learning
The following topics will be covered
@@ -631,7 +672,7 @@ The following topics will be covered
All the above topics will be supported by examples, hands-on exercises and project work.
-