A Normative Bayesian Model of Classification for Agents with Bounded Memory

Abstract

Perceptual classification, one canonical form of decision-making, entails assigning stimuli to 13 discrete classes according to internal criteria. Accordingly, the standard formalisms of perceptual decision-14 making have incorporated both stimulus and criterion as necessary components, but granted them unequal 15 representational status, stimulus a random variable and criterion a scalar variable. This representational 16 inconsistency obscures identifying the origins of behavioral or neural variability in perceptual classification. 17Here, we redress this problem by presenting an alternative formalism in which criterion, as a latent random 18 variable, plays causal roles in forming decision variable on equal footings with stimulus. By implementing 19 this formalism into a Bayes-optimal algorithm, we could predict, simulate, and explain the key human 20 classification behaviors with high fidelity and coherency. Further, by acquiring concurrent fMRI 21 measurements from humans engaged in classification, we demonstrated an ensemble of brain activities 22 that embodies the causal interactions between stimulus, criterion, and decision variable as the algorithm 23 prescribes. 25Classification, the act of assigning objects or events to discrete classes according to a criterion, is a 26 necessary precursor to the emergence of rigorous scientific constructs (e.g., taxonomies in physics, 27 biology, psychiatry; (Ghiselin, 1981; Hempel, 1965). Classification is required to generate and understand 28 basic linguistic propositions such as predication (e.g., 'small/large', 'near/far', 'dark/bright'; Rips and 29 Turnbull, 1980). Mirroring these roles in science and language, classification is considered among the most 30 fundamental of all decision-makings (Ashby, 2001; Ashby and Ell, 2001) and exercised countlessly in daily life: 31 a weatherperson forecasts whether the upcoming summer will be cool or hot; a sommelier tells us that 32 the wine of our choice is dry or sweet. 33Perceptual classification 1 , the most basic form of classification, requires comparing a sensed 34 quantity of a stimulus feature (e.g., 'sensed sweetness of a particular wine') against a criterion quantity 35 learnt prior to comparison (e.g., 'a typical sweetness of wines'). This means that a 'classifying' brain needs 36 to form two representations, one for stimulus ( ) and the other for criterion ( ). Accordingly, these two 37 representations are incorporated into standard formalisms for perceptual decision-making, such as the 38 signal detection theory (Green and Swets, 1966). 39These standard formalisms and their modern extensions, despite their remarkable successes in 40 guiding behavioral and neural studies on perception (Gold and Shadlen, 2007), all share a fundamental 41 inconsistency in formalizing and : is a random variable that causes sensory measurements via a 42 stochastic process whereas is a scalar variable that is determined on a rather arbitrary basis. 43Consequentially, while rigorous normative algorithms have been developed for infer...