A Mixture of Delta-Rules Approximation to Bayesian Inference in Change-Point Problems

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Abstract
Error-driven learning rules have received considerable attention because of their close relationships to both optimal theory and neurobiological mechanisms. However, basic forms of these rules are effective under only a restricted set of conditions in which the environment is stable. Recent studies have defined optimal solutions to learning problems in more general, potentially unstable, environments, but the relevance of these complex mathematical solutions to how the brain solves these problems remains unclear. Here, we show that one such Bayesian solution can be approximated by a computationally straightforward mixture of simple error-driven ‘Delta’ rules. This simpler model can make effective inferences in a dynamic environment and matches human performance on a predictive-inference task using a mixture of a small number of Delta rules. This model represents an important conceptual advance in our understanding of how the brain can use relatively simple computations to make nearly optimal inferences in a dynamic world. The ability to make accurate predictions is important to thrive in a dynamic world. Many predictions, like those made by a stock picker, are based, at least in part, on historical data thought also to reflect future trends. However, when unexpected changes occur, like an abrupt change in the value of a company that affects its stock price, the past can become irrelevant and we must rapidly update our beliefs. Previous research has shown that, under certain conditions, human predictions are similar to those of mathematical, ideal-observer models that make accurate predictions in the presence of change-points. Despite this progress, these models require superhuman feats of memory and computation and thus are unlikely to be implemented directly in the brain. In this work, we address this conundrum by developing an approximation to the ideal-observer model that drastically reduces the computational load with only a minimal cost in performance. We show that this model better explains human behavior than other models, including the optimal model, and suggest it as a biologically plausible model for learning and prediction.

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