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SSG Seminar Abstract

Nonlinear Path Estimation and its Relationship to Statistical Mechanics and Information Theory

Professor Sanjoy Mitter

In this lecture I present a variational interpretation of non-linear path estimation. This is a consequence of the fact that the conditional distribution corresponding to the optimal path estimation is obtained by minimizing an appropriate Free Energy and hence has a representation as a Gibbs distribution. The duality between Free Energy and Relative Entropy can then be exploited to shed further light on the optimal path estimator. This solves a long-standing open problem of giving a rigorous treatment of the Bryson-Frazier smoothing view of the Kalman filter. Here however we solve the problem even in non-linear situations. Time permitting, I shall discuss the concept of stochastic dissipativeness and how this provides a framework for discussing the stability of the filter against various perturbations. These ideas have connections to recent work in non-equilibrium statistical mechanics.

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