Recent Advances in Nonlinear Filtering with Applications to Neuroscience

Prashant Mehta

Dept. of Mechanical Science & Engineering Coordinated Science Laboratory University of Illinois at Urbana-Champaign Prashant Mehta is an Associate Professor in the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign. He received his Ph.D. in Applied Mathematics from Cornell University in 2004. Prior to joining Illinois, he was a Research Engineer at the United Technologies Research Center (UTRC). His research interests are at the intersection of dynamical systems and control theory, including mean-field games, model reduction, and nonlinear control. He has received several awards including an Outstanding Achievement Award for his research contributions at UTRC, several Best Paper awards with his students at Illinois, and numerous teaching and advising honors at Illinois.

Abstract:

The subject of my talk is a new formulation of nonlinear filter that is based on concepts from optimal control and mean-field game theory. Nonlinear filtering is critical to many applications in engineering, biology, economics, and atmospheric sciences. It is also an important paradigm in neuroscience. The Bayesian model of sensory (e.g., visual) signal processing suggests that the cortical networks in the brain encode a probabilistic ‘belief’ about reality. The belief state is updated based on comparison between the novel stimuli (from senses) and the internal prediction. In my talk, I will introduce the feedback particle filter and show how it admits an innovations error-based feedback control structure. The control is chosen so that the posterior distribution of any particle matches the posterior distribution of the true state given the observations. Applying these results to neuroscience, I will address the question of implementing Bayes rule at the level of neurophysiologically plausible spiking elements, my qualified approach to the problem being based on a coupled oscillator feedback particle filter model. A single oscillator is a simplified model of a single spiking neuron, and the coupled oscillator model solves an inference problem. The methodology will be described with the aid of a model problem involving estimation of a “walking gait cycle.” This work is the result of collaboration with several students and colleagues at the University of Illinois.

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