On Inductive Biases for Gaussian Processes from Differential Algebra

We consider the interplay between Gaussian processes, a classical stochastic framework with recent fame in machine learning, with differential algebra. We construct Gaussian process priors that concentrate their probability mass on solutions of certain linear differential equations, which yields a strong inductive bias in the learning algorithm. Technically, Gröbner basis algorithms yield a parametrizations of the solution sets of such differential equations, with is used to push forward a suitable Gaussian process. If time permits, we discuss control, boundary values, and parameter identification as applications.