Non-Gaussian Bayesian theory of sensorimotor learning with multiple timescales

Various experimental studies have documented that sensorimotor learning phenomena occur on multiple timescales. Many theoretical models have been proposed to explain these experimental observations. However, while successful in certain aspects, these models only focus on average learning behaviors, and they cannot explain some crucial features of learning. For example, they cannot account for the dynamics of the whole distributions of the motor outputs and cannot explain why learning speed and magnitude negatively correlate with the perturbation size. Here we propose a model that includes multiple hidden dynamical variables, which collectively generate the desired motor command. The model is a multi-dimensional Bayesian filter that deals with the dynamics of non-Gaussian joint distributions of those hidden variables. Our model explains simultaneously the dynamics of distributions of the songbird vocal behaviors in various experiments, including: (i) adaptations after step changes or ramps in the error signal, and (ii) dynamics of relaxation following removal of the perturbation. We expect this model can be applied to data from other species and sensorimotor behaviors.