Bridging the Gap Between Theory and Practice of Approximate Bayesian Inference

Abstract

Iris van Rooij (i.vanrooij@donders.ru.nl)Radboud University Nijmegen, Donders Institute for Brain, Cognition and Behaviour Montessorilaan 3, 6525 HR Nijmegen, The Netherlands AbstractIn computational cognitive science, many cognitive processes seem to be successfully modeled as Bayesian computations.Yet, many such Bayesian computations has 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.

Optimal planning of eye movements

“…Models of 237 eye movements selection have so far used ideal observers 3,5,6 without planning. 238 Probabilistic, Bayesian formulations of optimality in perceptual tasks 36,37 , cog-239 nitive tasks 38,39 , reasoning 40 , motorcontrol 41 , learning 42 , and planning 43 have 240 lead to a better understanding of human behavior and the quest to unravel, how 241 the brain could implement these computations [44][45][46] , which are known in general 242 to be intractable 47 Task. In our task subjects searched for a hidden target within irregularly bounded shapes 257 (Fig.…”