Constraining bridges between levels of analysis: A computational justification for locally Bayesian learning

Abstract

Different levels of analysis provide different insights into behavior: computationallevel analyses determine the problem an organism must solve and algorithmiclevel analyses determine the mechanisms that drive behavior. However, many attempts to model behavior are pitched at a single level of analysis. Research into human and animal learning provides a prime example, with some researchers using computational-level models to understand the sensitivity organisms display to environmental statistics but other researchers using algorithmic-level models to understand organisms' trial order effects, including effects of primacy and recency. Recently, attempts have been made to bridge these two levels of analysis.Locally Bayesian Learning (LBL) creates a bridge by taking a view inspired by evolutionary psychology: Our minds are composed of modules that are each individually Bayesian but communicate with restricted messages. A different inspiration comes from computer science and statistics: Our brains are implementing the algorithms developed for approximating complex probability distributions. We show that these different inspirations for how to bridge levels of analysis are not necessarily in conflict by developing a computational justification for LBL. We Preprint submitted to ElsevierApril 26, 2013 demonstrate that a scheme that maximizes computational fidelity while using a restricted factorized representation produces the trial order effects that motivated the development of LBL. This scheme uses the same modular motivation as LBL, passing messages about the attended cues between modules, but does not use the rapid shifts of attention considered key for the LBL approximation. This work illustrates a new way of tying together psychological and computational constraints.Keywords: rational approximations; locally Bayesian learning; trial order effectsOur goal when we model behavior depends on the level of analysis. If we analyze behavior at Marr (1982)'s computational level, then we aim to determine the problem that people are attempting to solve. Or, as more often found in psychology, we might be interested in the mechanism that drives behavior, placing us at Marr (1982)'s algorithmic level. In human and animal learning, both computational-level (Courville et al., 2005;Danks et al., 2003;Dayan et al., 2000) and algorithmic-level models (Rescorla & Wagner, 1972;Mackintosh, 1975;Pearce & Hall, 1980) have been developed. Models developed at different levels of analysis have different strengths and this can be seen in how these models of human and animal learning are applied: computational-level approaches are used to explain how organisms are sensitive to complex statistics of the environment (De Houwer & Beckers, 2002;Mitchell et al., 2005;Shanks & Darby, 1998) and algorithmiclevel models are used to explain how organisms are sensitive to the presentation order of trials (Chapman, 1991;Hershberger, 1986;Medin & Edelson, 1988).The computational and algorithmic levels provide different perspectives on model d...

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