The ‘Ideal Homunculus’: Statistical Inference from Neural Population Responses

Abstract

What does the response of a neuron, or of a group of neurons mean? What does it say about the stimulus? How distributed and efficient is the encoding of information in population responses? It is suggested here that Bayesian statistical inference can help answer these questions by allowing us to ‘read the neural code’ not only in the time domain[2, 5] but also across a population of neurons. Based on repeated recordings of neural responses to a known set of stimuli, we can estimate the conditional probability distribution of the responses given the stimulus, P(response|stimulus). The behaviourally relevant distribution, i.e. the conditional probability distribution of the stimuli given an observed response from a cell or a group of cells, P(stimulus|response) can be derived using the Bayes rule. This distribution contains all the information present in the response about the stimulus, and gives an upper limit and a useful comparison to the performance of further neural processing stages receiving input from these neurons. As the notion of an ‘ideal observer’ makes the definition of psychophysical efficiency possible[1], this ‘ideal homunculus’ (looking at the neural response instead of the stimulus) can be used to test the efficiency of neural representation. The Bayes rule is: P(s|r) = P(r|s)P(s)/P(r) = P(r|s)P(s)/Σ s P(r|s)P(s), where in this case s stands for stimulus, r for response, and S is the set of possible stimuli.