A confirmation bias in perceptual decision-making due to hierarchical approximate inference
Fig 2
Information flow during hierarchical inference where categorical beliefs are fed back as a prior on sensory features.
a) Generative model that we assume the brain has learned for a discrimination task, which specifies how sensory observations ef depend on the category for the trial, C, in two stages: each sensory observation ef is assumed to be a noisy realization of underlying sensory features, xf, and each frame of sensory features is itself assumed to be selected according to the trial’s category. b-c) Integrating evidence about C requires updating the current belief about C with new information derived from the sensory representation (left-right “integration” and bottom-up “update” arrows). The posterior distribution over x combines top-down expectations (diagonal “prior” arrows) with new evidence from the stimulus, ef (bottom-up “likelihood” arrows). Width of arrows indicates average amount of information communicated; red and blue arrows indicate changes in information flow between conditions. Note that when inference is exact, the prior is subtracted from the information in the update during the integration to prevent double-counting early evidence. While the generative model in (a) operates with discrete frames, f, inference in the brain happens in continuous time, t. b) LSHC: Low sensory information means little information in the likelihood about sensory features xf. High category information means that most of this information is also informative about C. It also means high information in the prior that is fed back to the sensory representation. c) HSLC: High sensory information means high information in the likelihood about sensory features xf. Low category information means that this information is only weakly predictive of C. It also means little information in the prior that is being fed back to the sensory representation.