2013年8月5日月曜日

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

Robert C. Wilson, Matthew R. Nassar, Joshua I. Gold
PLoS Comput Biol 9(7): e1003150. doi:10.1371/journal.pcbi.1003150

不安定な環境(例:報酬確率、株価)を試行錯誤しながらどうやって学習するか?
最適な方法はベイズ推定を行うことだが、数学的にはかなりややこしい。また、神経科学的な裏付けもあまりない。
一方、単純な学習方法であるデルタ・ルール(報酬予測誤差学習、強化学習)は神経科学的な裏付けはあるが、最適な学習方法ではない。

本論文で著者らは「単純なデルタ・ルールを組み合わせる事で、最適なベイズ学習を近似できる」ことを示した。
この結果は「我々の脳が単純な計算を組み合わせる事で難しい問題を(近似的に)解いている」可能性を示唆する。

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.

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