Neurons as Monte Carlo Samplers: Bayesian Inference and Learning in Spiking Networks

We propose a spiking network model capable of performing both approximate inference and learning for any hidden Markov model. The lower layer sensory neurons detect noisy measurements of hidden world states. The higher layer neurons with recurrent connections infer a posterior distribution over world states from spike trains generated by sensory neurons. We show how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in the population of inference neurons represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution of hidden state. The model provides a functional explanation for the Poissonlike noise commonly observed in cortical responses. Uncertainties in spike times provide the necessary variability for sampling during inference. Unlike previous models, the hidden world state is not observed by the sensory neurons, and the temporal dynamics of the hidden state is unknown. We demonstrate how such networks can sequentially learn hidden Markov models using a spike-timing dependent Hebbian learning rule and achieve power-law convergence rates.