Bayesian Inference with Coupled Oscillator Models

Prashant Mehta

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 nonlinear filtering, 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:

Inference (prediction) is believed to be a fundamentally important computational function for biological sensory systems. For example, the Bayesian model of sensory (e.g., visual) signal processing postulates that the cortical networks in the brain encode a probabilistic belief about reality. The belief state (modeled as a posterior distribution in the Bayes' formalism) is updated based on comparison between the novel stimuli (from senses) and the internal prediction.

A natural question to ask then is whether there is a rigorous methodology (and algorithms) to implement complex forms of prediction (via Bayes theorem) at the level of neurons - the computing elements of the brain? In this talk I will provide a qualified answer to this question 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.

A natural question to ask then is whether there is a rigorous methodology (and algorithms) to implement complex forms of prediction (via Bayes theorem) at the level of neurons - the computing elements of the brain? In this talk I will provide a qualified answer to this question 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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