mutual information

projects/project_mutualinfo/Makefile

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+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

projects/project_mutualinfo/mutualinfo.tex

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+\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}