Abstract: Markov Chain Monte Carlo (MCMC) algorithms provide samples from arbitrary probability distributions and they are often used for posterior inference in statistical and machine learning models. Most modern algorithms are based on numeric integration of some augmented dynamic system and their computational efficiency depends on the curvature of the distribution. Geometric MCMC algorithms account for the local curvature by operating in a Riemannian geometry induced by the Fisher information of the underlying probabilistic model, but the theoretical advantage of more efficient exploration is lost in vastly increased computation for each iteration caused by the need to compute and invert the metric tensor.

We propose a new alternative metric that also accounts for the local curvature of the target distribution. We express the distribution locally as a Monge patch and use pure geometric reasoning to derive the metric. It is related to the one induced by the Fisher information, but has efficient inverse and hence can be used for speeding up geometric MCMC methods. We demonstrate it in the context of a particular method of Lagrangian Monte Carlo, for which we get explicit numeric integrator that does not require matrix inversions or computational of determinants.

Speakers:  Arto Klami
Arto Klami is an Associate Professor of Computer Science at University of Helsinki, and the Coordinating Professor of the FCAI Highlight on Easy and Privacy-preserving Modeling Tools. He works both on fundamental research on inference and modelling, as well as applications of machine learning in diverse areas.

Affiliation: University of Helsinki

Place of Seminar:  Zoom

Meeting ID: 624 1249 4245

Passcode: 698407