Rational approximations to rational models: Alternative algorithms for category learning

Abstract

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences

Why Higher Working Memory Capacity May Help You Learn: Sampling, Search, and Degrees of Approximation

“…Our use of a representation based on classification and regression trees (CART) was primarily driven by pragmatic reasons, in particular what seemed most natural for the tasks concerned, rather than a theoretical commitment to a particular way of representing categories. We expect similar results to be obtained with alternative category representations, such as those used in the Rational Model of Categorization (Anderson, 1990;Sanborn et al, 2010) and Rational Rules (Goodman et al, 2008), though this remains to be shown.…”

“…Lewandowsky, Griffiths, & Kalish, 2009). Such order effects have been successfully captured by models employing sequential inference with limited samples in a variety of domains, including change detection (Brown & Steyvers, 2009), garden path effects in sentence processing (Levy, Reali, & Griffiths, 2008), and category learning (Sanborn et al, 2010). Such order effects have been successfully captured by models employing sequential inference with limited samples in a variety of domains, including change detection (Brown & Steyvers, 2009), garden path effects in sentence processing (Levy, Reali, & Griffiths, 2008), and category learning (Sanborn et al, 2010).…”

“…Notably, both Sanborn et al (2006Sanborn et al ( , 2010 and Goodman et al (2008), despite considering rather different category representations, considered sample-based inference to be a particularly good candidate as a psychological mechanism for approximating Bayesian inference. We expect similar results to be obtained with alternative category representations, such as those used in the Rational Model of Categorization (Anderson, 1990;Sanborn et al, 2010) and Rational Rules (Goodman et al, 2008), though this remains to be shown. Our use of a representation based on classification and regression trees (CART) was primarily driven by pragmatic reasons, in particular what seemed most natural for the tasks concerned, rather than a theoretical commitment to a particular way of representing categories.…”

Structured event memory: a neuro-symbolic model of event cognition

“…Sequences of stimuli were generated by drawing from walks through this graph. , 2014Sanborn et al, 2010), and this data-efficiency can be significant in sequential problems (Franklin & Frank, 2018) like those that define event cognition.…”

Human Inference in Changing Environments with Temporal Structure

“…First, it is our best-fitting model. Second, it constitutes a generic approach to inference; it was reported to account successfully for other inference and learning behaviors, such as category learning [76,77], conditioning in pigeons [65], sentence processing [64], hidden state inference [14], and visual tracking of multiple objects [78]. Third, out of all the models we consider, it is by far the less demanding on memory: with nine particles, one needs to store 27 numbers (for s, τ , and the weight of each particle) in memory.…”