Abstract
One goal of a perceptual system is to make unbiased estimates. But biological perceptual systems cannot remain accurate without active processes to keep them calibrated (Helmholtz 1910; Welch 1986; Bedford 1999). Recent theory has described adaptations that achieve other goals, including the optimization of early sensory processing (Grzywacz & Balboa 2002), information transfer between stages of processing (Barlow 1990, Wainright 1999), and evolutionary fitness (Geisler & Diehl 2002). Here we examine the optimal strategy for minimizing bias in a perceptual system that accumulates bias over time, and especially the case in which two methods are available for estimating a single scene parameter. In this situation, the rates at which independent, discrepant estimators should be moved towards the system's best estimate are proportional to estimator variances (Ghahramani, Wolpert & Jordan 1996). We show that the rate at which an estimator accumulates bias (modeled as the diffusion constant in a random walk) must also be taken into account: minimizing system bias requires that learning rates be higher for estimators that accumulate bias more quickly. Since learning rates are set by the system, we suppose they are near optimal. The theory seems useful. For example, under Bayes' theorem, prior belief is equivalent to estimation from data, and we now can unify two previously distinct forms of adaptation: Wallach's informational discrepancy (response to conflict between two data-based estimators), and Gibson's normalization (modeled as response to conflict between an estimator and a prior). A data-based estimator often has lower variance than a prior, making it closer to the system's best estimate; but it also accumulates bias faster, so the system gives it a higher learning rate. Consequently, the data-based estimator moves towards the prior rather than vice-versa. The framework is also useful for predicting sites of adaptation and certain adaptation aftereffects.