Probabilistic Models of Phase Variables for Visual Representation and Neural Dynamics

My work seeks to contribute to three broad goals: predicting the computational representations found in the brain, developing algorithms that help us infer the computations that the brain performs, and producing better statistical models of natural signals. My thesis is broken down into three major chapters that reflect these three goals. Within each chapter I develop novel probabilistic models of phase variables and apply these models to the invariant representation of visual motion, to the inference of connectivity in networks of coupled neural oscillators, and to the development of statistical models of edge structure in images.