Sensory adaptation as Kalman filtering: theory and illustration with contrast adaptation

Sensory adaptation allows biological systems to adjust to variations in the environment. A recent theoretical work postulated that the goal of adaptation is to minimize errors in the performance of particular tasks. The proposed minimization was Bayesian and required prior knowledge of the environment and of the limitations of the mechanisms processing the information. One problem with that formulation is that the environment changes in time and the theory did not specify how to know what the current state of the environment is. Here, we extend that theory to estimate optimally the environmental state from the temporal stream of responses. We show that such optimal estimation is a generalized form of Kalman filtering. An application of this new Kalman-filtering framework is worked out for retinal contrast adaptation. It is shown that this application can account for surprising features of the data. For example, it accounts for the differences in responses to increases and decreases of mean contrasts in the environment. In addition, it accounts for the two-phase decay of contrast gain when the mean contrast in the environment rises suddenly. The success of this and related theories suggest that sensory adaptation is a form of constrained biological optimization.