diff --git a/projects/project_mutualinfo/mutualinfo.tex b/projects/project_mutualinfo/mutualinfo.tex index f2eef9b..9dda5f7 100644 --- a/projects/project_mutualinfo/mutualinfo.tex +++ b/projects/project_mutualinfo/mutualinfo.tex @@ -19,26 +19,34 @@ object was reported by the subject. \begin{parts} - \part Plot the data appropriately. + \part Plot the data appropriately. + \part Compute a 2-d histogram that shows how often different - combinations of reported and presented came up. + 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. + 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. The mutual information is a measure from information theory that is used in neuroscience to quantify, for example, how much information a spike train carries about a sensory stimulus. + \part What is the maximally achievable mutual information (try to find out by generating your own dataset which naturally should yield maximal information)? - \part Use bootstrapping to compute the $95\%$ confidence interval - for the mutual information estimate in that dataset. + + \part Use bootstrapping (permutation test) to compute the $95\%$ + confidence interval for the mutual information estimate in the + dataset from {\tt decisions.mat}. + \end{parts} \end{questions}