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 a 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. The goal of our research is to develop neuro-morphic architectures for implementing Bayes rule. One such architecture is the coupled oscillator feedback particle filter model. A single oscillator is a simplified model of a single spiking neuron, and the coupled oscillator model represents a neuronal network.

The mathematics of the coupled oscillator feedback particle filter model is described.

The methodology is described with the aid of a model problem involving estimation of a ''walking gait cycle.''

The mathematics of the coupled oscillator feedback particle filter model is described.

The methodology is described with the aid of a model problem involving estimation of a ''walking gait cycle.''

Tilton, A., P. G. Mehta and S. P. Meyn, ''Multi-dimensional Feedback Particle Filter for Coupled Oscillators,'' In the Proceedings of the American Control Conference, Washington DC, 2421-2427, June 2013.

This paper presents a methodology for state estimation of coupled oscillators from noisy observations. The methodology is comprised of two parts: modeling and estimation. The objective of the modeling is to express dynamics in terms of the so-called phase variables. For nonlinear estimation, a coupled-oscillator feedback particle ﬁlter is introduced.

The ﬁlter is based on the construction of a large population of oscillators with mean-ﬁeld coupling. The empirical distribution of the population encodes the posterior distribution of the phase variables. The methodology is illustrated with two numerical examples.

Tilton, A., E. Hsiao-Wecksler and P. G. Mehta, ''Filtering with Rhythms: Application to Estimation of Gait Cycle,'' In the Proceedings of the American Control Conference, Montreal, 3433-3438, June 2012.

The aim of this paper is to describe a coupled oscillator model for Bayesian inference. The coupled oscillator model comprises of a large number of oscillators with mean- field coupling. The collective dynamics of the oscillators are used to solve an inference problem: the empirical distribution of the population encodes a ‘belief state’ (posterior distribution) that is continuously updated based on noisy measurements. In effect, the coupled oscillator model works as a particle filter.

The framework is described here with the aid of a model problem involving estimation of a walking gait cycle. For this problem, the coupled oscillator particle filter is developed, and demonstrated on experimental data taken from an Ankle-foot Orthosis (AFO) device.

Financial support from the Air Force Office of Scientific Research (AFOSR) grant FA9550-09-1-0190 and the National Science Foundation (NSF) grant 0931416 is gratefully acknowledged.