Improved tracking of time-varying encoding properties of visual neurons by extended recursive least-squares

Traditional approaches to characterizing the transformation from stimulus to response in sensory systems assume both stationarity of the stimulus and time-invariance of the stimulus/response mapping. However, recent studies of sensory function under natural stimulus conditions have demonstrated important features of neural encoding that are in violation of these assumptions. Many sensory neurons respond to changes in the statistical distribution of the stimulus that are characteristic of the natural environment with corresponding changes in their encoding properties. In this paper, an extended recursive least-squares (ERLS) approach to adaptive estimation from stimulus/response observations is detailed. The ERLS approach improves the tracking ability of standard RLS approaches to adaptive estimation by removing a number of assumptions about the underlying system and the stimulus environment. The ERLS framework also incorporates an adaptive learning rate, so that prior knowledge of the relationship between the stimulus and the adaptive nature of the system under investigation can be used to improve tracking performance. Simulated and experimental neural responses are used to demonstrate the ability of the ERLS approach to track adaptation of encoding properties during a single stimulus/response trial. The ERLS framework lends tremendous flexibility to experimental design, facilitating the investigation of sensory function under naturalistic stimulus conditions.