Approximate inference through active computation accounts for human categorization behavior

Bayesian computations are intractable and expensive, but this is rarely accounted for in existing Bayesian observer models. In this work, we propose that a) the brain can only compute imprecise (noisy) estimates of likelihoods and posteriors, and, b) since computations are expensive, the brain actively chooses which computations to perform to refine such estimates. We call our framework approximate inference through active sampling (AIAS) and study its implications in N-alternative categorization. While it is common in Bayesian observer models to assume that the agent makes noisy measurements of a state of the world, here we introduce an additional noise at a higher level in the computation. We assume that the true (ideal-observer) likelihoods and posteriors of the categories are unknown to the agent. The agent sequentially makes noisy measurements of those likelihoods – each “sample” representing a unit of computation –, one category at a time, thus refining their beliefs over the true likelihoods and their belief over the true posterior probabilities. The brain simulates to decide whether to sample and which category to sample. AIAS accounts for several empirical findings. First, we find that the average number of measurements grows approximately logarithmically with N, as per Hick's law. Second, we account for a puzzling recent finding that decision confidence follows the difference between the two highest posteriors, rather than the highest posterior itself. AIAS not only provides better fits of choice and confidence data in this categorization task, but yields a parameter-free prediction of response times. Third, we show that AIAS is able to explain how categorization behavior changes when the visual contrast varies. Overall, AIAS provides a novel approach to explain human categorization by casting approximate inference as an active-sampling process with imprecise computations.