Abstract: We start by addressing a most simple problem, estimation of a one dimensional density function, and argue that despite of the apparent simplicity of the problem, it is surprisingly difficult to solve it in a holistic manner that is both computationally feasible and theoretically justifiable without strong distributional or other assumptions. We demonstrate how the information-theoretic MDL framework can be used for reaching this goal (almost) perfectly, and show how this simple setup gives interesting perspectives on the fundamental concepts in probabilistic modelling and statistical inference. We also discuss ideas for extending the framework to more complex models with additional practical applications.

Speaker: Petri Myllymäki

Affiliation: Professor, University of Helsinki

Place of Seminar: Aalto University