|M.Sc Student||Zananiri Rani|
|Subject||Optimal Encoding in Sensory Systems|
|Department||Department of Electrical Engineering||Supervisor||Professor Ron Meir|
|Full Thesis text|
This project deals with the sensory blocks of the perception action cycle from the optimal encoding point of view. The mathematical framework on which we base our model comes from the theory of Bayesian statistics. Assuming optimality of the decoder, we question the optimal parameters of the tuning curves that minimize the mean squared error function. Comparison of direct minimization to several approximations and bounds is done and show different results despite the wide use of them in the theoretical neuroscience community. The first part of this work deals with better understanding the optimal tuning width through decomposing the error function to bias and variance. Results show that for extremely narrow tuning curves elevated values of bias cause the error, while for wide tuning curves elevated values of error are due to large values of variance. The second part of this work questions the optimality of the positioning of the tuning curves in the state space. Although many population coding models assume homogeneously distributed tuning curves over the state space, mainly to maintain the mathematical tractability, biological data show that the sensory receptors are not distributed in this manner. With the intention of understanding the optimality of tuning curves positions, Cramer-Rao bound and Laplace approximation optimizations were made at first. Although these approximations give mathematically identical results, they give biologically implausible results that are counter intuitive. Before dealing with the direct minimization, the problem was reduced to a simple yet generic problem of optimizing the tuning positions as a function of the prior uncertainty. Results show biologically plausible results that were obtained in literature.