Two problems from neural data analysis: sparse entropy estimation
and adaptive experimental design
Department of Statistics
Friday, September 8, 2006, 12:00pm
Neuroscience has proven to be a rich source of interesting statistical questions. This talk will address two such problems:
1) Nonparametric estimation of information-theoretic quantities (especially the Shannon entropy and mutual information) from sparsely-sampled data. These quantities are nonlinear (in fact singular) functionals of the distribution from which the data were drawn; nevertheless, the entropy and information turn out to be strictly easier to estimate than the underlying distributions.
2) Optimal, adaptive experimental design (how do we select stimuli online to learn the most about the brain in the least amount of time?). We discuss an asymptotic result that quantifies the benefit of adaptive versus nonadaptive designs, and describe numerical work in progress on computing the optimal design very quickly, in the context of real-time
neuroscience experiments (with J. Lewi, Georgia Inst. Tech.).
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