diff --git a/projects/project_mutualinfo/Makefile b/projects/project_mutualinfo/Makefile new file mode 100644 index 0000000..dad25ce --- /dev/null +++ b/projects/project_mutualinfo/Makefile @@ -0,0 +1,10 @@ +latex: + pdflatex *.tex > /dev/null + pdflatex *.tex > /dev/null + +clean: + rm -rf *.log *.aux *.zip *.out auto + rm -f `basename *.tex .tex`.pdf + +zip: latex + zip `basename *.tex .tex`.zip *.pdf *.dat *.mat diff --git a/projects/project_mutualinfo/decisions.mat b/projects/project_mutualinfo/decisions.mat new file mode 100644 index 0000000..918c0de Binary files /dev/null and b/projects/project_mutualinfo/decisions.mat differ diff --git a/projects/project_mutualinfo/mutualinfo.tex b/projects/project_mutualinfo/mutualinfo.tex new file mode 100755 index 0000000..312deed --- /dev/null +++ b/projects/project_mutualinfo/mutualinfo.tex @@ -0,0 +1,66 @@ +\documentclass[addpoints,10pt]{exam} +\usepackage{url} +\usepackage{color} +\usepackage{hyperref} + +\pagestyle{headandfoot} +\runningheadrule +\firstpageheadrule +\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014 + -- 11/06/2014} +%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014} +\firstpagefooter{}{}{} +\runningfooter{}{}{} +\pointsinmargin +\bracketedpoints + +%\printanswers +%\shadedsolutions + + +\begin{document} +%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%% +\sffamily +% \begin{flushright} +% \gradetable[h][questions] +% \end{flushright} + +\begin{center} + \input{../disclaimer.tex} +\end{center} + +%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{questions} + \question A subject was presented two possible objects for a very + brief time ($50$ms). The task of the subject was to report which of + the two objects was shown. In {\tt decisions.mat} you find an array + that stores which object was presented in each trial and which + object was reported by the subject. + + \begin{parts} + \part Plot the data appropriately. + \part Compute a 2-d histogram that shows how often different + combinations of reported and presented came up. + \part Normalize the histogram such that it sums to one (i.e. make + it a probability distribution $P(x,y)$ where $x$ is the presented + object and $y$ is the reported object). Compute the probability + distributions $P(x)$ and $P(y)$ in the same way. + \part Use that probability distribution to compute the mutual + information $$I[x:y] = \sum_{x\in\{1,2\}}\sum_{y\in\{1,2\}} P(x,y) + \log_2\frac{P(x,y)}{P(x)P(y)}$$ that the answers provide about the + actually presented object. + \part What is the maximally achievable mutual information (try to + find out by generating your own dataset; the situation in which + the information is maximal is pretty straightforward)? + \part Use bootstrapping to compute the $95\%$ confidence interval + for the mutual information estimate in that dataset. + \end{parts} + +\end{questions} + + + + + +\end{document}