Bridging the gap between theory and practice of approximate Bayesian inference

In computational cognitive science, many cognitive processes seem to be successfully modeled as Bayesian computations. Yet, many such Bayesian computations have been proven to be computationally intractable (NP-hard) for unconstrained input domains, even if only an approximate solution is sought. This computational complexity result seems to be in strong contrast with the ease and speed with which humans can typically make the inferences that are modeled by Bayesian models. This contrast—between theory and practice—poses a considerable theoretical challenge for computational cognitive modelers: How can intractable Bayesian computations be transformed into computationally plausible ‘approximate’ models of human cognition? In this paper, three candidate notions of ‘approximation’ are discussed, each of which has been suggested in the cognitive science literature. We will sketch how (parameterized) computational complexity analyses can yield model variants that are tractable and which can serve as the basis of computationally plausible models of cognition.