Fig. 2: Spike generation with Poissonian variability can support sampling-based Bayesian inference.
From: Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons
a We use a feedforward network model (no recurrent connections) to demonstrate how spiking variability drives sampling. Neurons receive feedforward inputs, uf, modeled as independent Poisson spike trains, resulting in a Poissonian population response, rt, with means determined by the instantaneous firing rate vector, λt. (b–e) Demonstration of sampling via stochastic spike generation. A population of neurons with Gaussian tuning and firing rates λt (b) generates a realization of a population response, rt (c). A sample from the posterior distribution of the stimulus (d, orange box) can be linearly read out from the population response (c, orange box). e The sampling distribution is obtained by collecting stimulus samples over time. The profile of population firing rates (f) determines the sampling distribution (g). The position of the population firing rate, \({\bar{s}}_{t}\), determines the mean of the sampling distribution, and the variance of the sampling distribution is inversely proportional to the peak firing rate, R. We show two population activity profiles, one in blue and the other in orange, to illustrate these points. h In an E-I network, the precision of the sampling distribution (the inverse of sampling variability) read out from E neurons increases with the height of firing rate, and is consistent with the likelihood directly read out from the feedforward input.
