67 lines
2.0 KiB
TeX
67 lines
2.0 KiB
TeX
\documentclass[addpoints,10pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
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-- 11/06/2014}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{questions}
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\question A subject was presented two possible objects for a very
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brief time ($50$ms). The task of the subject was to report which of
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the two objects was shown. In {\tt decisions.mat} you find an array
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that stores which object was presented in each trial and which
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object was reported by the subject.
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\begin{parts}
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\part Plot the data appropriately.
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\part Compute a 2-d histogram that shows how often different
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combinations of reported and presented came up.
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\part Normalize the histogram such that it sums to one (i.e. make
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it a probability distribution $P(x,y)$ where $x$ is the presented
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object and $y$ is the reported object). Compute the probability
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distributions $P(x)$ and $P(y)$ in the same way.
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\part Use that probability distribution to compute the mutual
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information $$I[x:y] = \sum_{x\in\{1,2\}}\sum_{y\in\{1,2\}} P(x,y)
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\log_2\frac{P(x,y)}{P(x)P(y)}$$ that the answers provide about the
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actually presented object.
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\part What is the maximally achievable mutual information (try to
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find out by generating your own dataset; the situation in which
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the information is maximal is pretty straightforward)?
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\part Use bootstrapping to compute the $95\%$ confidence interval
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for the mutual information estimate in that dataset.
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\end{parts}
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\end{questions}
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\end{document}
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