Neural implementation of Bayesian inference using efficient population codes

D Ganguli and E P Simoncelli

Published in Computational and Systems Neuroscience (CoSyNe), (II-9), Feb 2012.

This paper has been superseded by:
Efficient sensory encoding and Bayesian inference with heterogeneous neural populations
D Ganguli and E P Simoncelli.
Neural Computation, vol.26(10), pp. 2103--2134, Oct 2014.

Experimental evidence suggests that human judgments of many perceptual attributes are consistent with Bayesian inference, in which noisy sensory measurements are combined with prior knowledge to obtain estimates. How does the brain represent and utilize prior probabilities to achieve this computation? Recent work has shown that a population vector decoder can approximate a Bayes Least Squares Estimator (BLSE), if one assumes a neural population with tuning curves proportional to the likelihood, and preferred stimuli sampled from the sensory prior (Shi & Griffiths 2009; Fischer & Peña 2011). Here, we examine and derive more precise conditions under which this can hold. We assume sensory variables are encoded with a heterogeneous neural population optimized for transmission of sensory information, subject to limitations on the number of neurons (N) and the total average spike rate (R). This encoder implicitly represents the sensory prior in the distribution of preferred stimuli, and is consistent with experimental data for a variety of sensory modalities and attributes (Ganguli & Simoncelli 2010).

Given this encoder, we derive a novel decoder to approximate the BLSE. Similar to the population vector, it computes weighted averages of the preferred stimuli. However, the firing rates are not used directly as weights, but are first convolved with a linear filter then exponentiated. The decoder is neurally plausible, and requires knowledge only of the preferred stimuli and a fixed filter, and not the prior or tuning curves (Jazayeri & Movshon 2009). Simulations demonstrate that it outperforms the standard population vector, and converges to the true BLSE as N increases. In a low signal-to-noise regime, the decoder outperforms a BLSE operating on a resource-matched homogeneous population. We conclude that in a regime where resources are limited, neural representations optimized for transmitting information enable neurally plausible decoding that can utilize implicit prior information to perform Bayesian inference.

  • Listing of all publications