[regression] updated exercise infrastructure

regression/exercises/Makefile

@@ -1,34 +1,4 @@
-TEXFILES=$(wildcard exercises??.tex)
-EXERCISES=$(TEXFILES:.tex=.pdf)
-SOLUTIONS=$(EXERCISES:exercises%=solutions%)
+TEXFILES=$(wildcard gradientdescent-?.tex)
 
-.PHONY: pdf exercises solutions watch watchexercises watchsolutions clean
+include ../../exercises.mk
 
-pdf : $(SOLUTIONS) $(EXERCISES)
-
-exercises : $(EXERCISES)
-
-solutions : $(SOLUTIONS)
-
-$(SOLUTIONS) : solutions%.pdf : exercises%.tex instructions.tex
-	{ echo "\\documentclass[answers,12pt,a4paper,pdftex]{exam}"; sed -e '1d' $<; } > $(patsubst %.pdf,%.tex,$@)
-	pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $(patsubst %.pdf,%.tex,$@) || true
-	rm $(patsubst %.pdf,%,$@).[!p]*
-
-$(EXERCISES) : %.pdf : %.tex instructions.tex
-	pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
-
-watch :
-	while true; do ! make -q pdf && make pdf; sleep 0.5; done
-
-watchexercises :
-	while true; do ! make -q exercises && make exercises; sleep 0.5; done
-
-watchsolutions :
-	while true; do ! make -q solutions && make solutions; sleep 0.5; done
-
-clean :
-	rm -f *~ *.aux *.log *.out
-
-cleanup : clean
-	rm -f $(SOLUTIONS) $(EXERCISES)

regression/exercises/checkdescent.m

@@ -0,0 +1,25 @@
+% data:
+load('lin_regression.mat')
+
+% compute mean squared error for a range of slopes and intercepts:
+slopes = -5:0.25:5;
+intercepts = -30:1:30;
+errors = zeros(length(slopes), length(intercepts));
+for i = 1:length(slopes)
+    for j = 1:length(intercepts)
+	      errors(i,j) = lsqError([slopes(i), intercepts(j)], x, y);
+    end
+end
+
+% minimum of error surface:
+[me, mi] = min(errors(:));
+[ia, ib] = ind2sub(size(errors), mi);
+eparams = [errors(ia), errors(ib)];
+
+% gradient descent:
+pstart = [-2. 10.];
+[params, errors] = descent(x, y, pstart);
+
+% comparison:
+fprintf('descent: %6.3f  %6.3f\n', params(1), params(2));
+fprintf('errors:  %6.3f  %6.3f\n', eparams(1), eparams(2));

regression/exercises/descent.m

@@ -0,0 +1,15 @@
+function [params, errors] = descent(xdata, ydata, pstart)
+    mingradient = 0.1;
+    eps = 0.01;
+    
+    errors = [];
+    params = pstart;
+    count = 1;
+    gradient = [100.0, 100.0];
+    while norm(gradient) > mingradient
+        gradient = lsqGradient(params, xdata, ydata);
+        errors(count) = lsqError(params, xdata, ydata);
+        params = params - eps .* gradient; 
+        count = count + 1;
+    end
+end

regression/exercises/descentfit.m

@@ -0,0 +1,22 @@
+clear 
+close all
+load('lin_regression.mat')
+
+pstart = [-2. 10.];
+[params, errors] = descent(x, y, pstart);
+
+figure()
+subplot(2,1,1)
+hold on
+scatter(x, y, 'displayname', 'data')
+xx = min(x):0.01:max(x);
+fx = params(1)*xx + params(2);
+plot(xx, fx, 'displayname', 'fit')
+xlabel('Input')
+ylabel('Output')
+grid on
+legend show
+subplot(2,1,2)
+plot(errors)
+xlabel('optimization steps')
+ylabel('error')

regression/exercises/gradientdescent-1.tex

@@ -1,60 +1,17 @@
 \documentclass[12pt,a4paper,pdftex]{exam}
 
-\usepackage[german]{babel}
-\usepackage{natbib}
-\usepackage{xcolor}
-\usepackage{graphicx}
-\usepackage[small]{caption}
-\usepackage{sidecap}
-\usepackage{pslatex}
-\usepackage{amsmath}
-\usepackage{amssymb}
-\setlength{\marginparwidth}{2cm}
-\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref}
+\newcommand{\exercisetopic}{Resampling}
+\newcommand{\exercisenum}{9}
+\newcommand{\exercisedate}{December 21th, 2020}
 
-%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
-\pagestyle{headandfoot}
-\ifprintanswers
-\newcommand{\stitle}{: Solutions}
-\else
-\newcommand{\stitle}{}
-\fi
-\header{{\bfseries\large Exercise 10\stitle}}{{\bfseries\large Gradient descent}}{{\bfseries\large December 16th, 2019}}
-\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
-  jan.grewe@uni-tuebingen.de}
-\runningfooter{}{\thepage}{}
+\input{../../exercisesheader}
 
-\setlength{\baselineskip}{15pt}
-\setlength{\parindent}{0.0cm}
-\setlength{\parskip}{0.3cm}
-\renewcommand{\baselinestretch}{1.15}
+\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de}
 
-\newcommand{\code}[1]{\texttt{#1}}
-\renewcommand{\solutiontitle}{\noindent\textbf{Solution:}\par\noindent}
-%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage{listings}
-\lstset{
-  language=Matlab,
-  basicstyle=\ttfamily\footnotesize,
-  numbers=left,
-  numberstyle=\tiny,
-  title=\lstname,
-  showstringspaces=false,
-  commentstyle=\itshape\color{darkgray},
-  breaklines=true,
-  breakautoindent=true,
-  columns=flexible,
-  frame=single,
-  xleftmargin=1em,
-  xrightmargin=1em,
-  aboveskip=10pt
-}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{document}
 
-\input{instructions}
+\input{../../exercisestitle}
 
 \begin{questions}
 
@@ -96,7 +53,7 @@
     the parameter values at the minimum of the cost function and a vector
     with the value of the cost function at each step of the algorithm.
     \begin{solution}
-      \lstinputlisting{../code/descent.m}
+      \lstinputlisting{descent.m}
     \end{solution}
 
     \part Plot the data and the straight line with the parameter
@@ -105,7 +62,7 @@
     \part Plot the development of the costs as a function of the
     iteration step.
     \begin{solution}
-      \lstinputlisting{../code/descentfit.m}
+      \lstinputlisting{descentfit.m}
     \end{solution}
 
     \part For checking the gradient descend method from (a) compare
@@ -116,7 +73,7 @@
     minimum gradient. What are good values such that the gradient
     descent gets closest to the true minimum of the cost function?
     \begin{solution}
-      \lstinputlisting{../code/checkdescent.m}
+      \lstinputlisting{checkdescent.m}
     \end{solution}
 
     \part Use the functions \code{polyfit()} and \code{lsqcurvefit()}
@@ -124,7 +81,7 @@
     line that fits the data. Compare the resulting fit parameters of
     those functions with the ones of your gradient descent algorithm.
     \begin{solution}
-      \lstinputlisting{../code/linefit.m}
+      \lstinputlisting{linefit.m}
     \end{solution}
 
   \end{parts}

regression/exercises/linefit.m

@@ -0,0 +1,18 @@
+% data:
+load('lin_regression.mat')
+
+% gradient descent:
+pstart = [-2. 10.];
+[params, errors] = descent(x, y, pstart);
+
+% lsqcurvefit:
+line = @(p, x)  x.* p(1) + p(2);
+cparams = lsqcurvefit(line, pstart, x, y);
+
+% polyfit:
+pparams = polyfit(x, y, 1);
+
+% comparison:
+fprintf('descent:     %6.3f  %6.3f\n', params(1), params(2));
+fprintf('lsqcurvefit: %6.3f  %6.3f\n', cparams(1), cparams(2));
+fprintf('polyfit:     %6.3f  %6.3f\n', pparams(1), pparams(2));