CS Forum: Manfred Opper

Score matching and nonparametric estimators of drift functions for stochastic differential equations

Speaker: Professor Manfred Opper (joint work with Philipp Batz and Andreas Ruttor)

Speaker affiliation: Artificial Intelligence group, TU Berlin

Hosts: Jouko Lampinen & Simo Särkkä

Time: 15:15-16:00 (coffee from 15:00)

Venue: Lecture room R037/1023-1024, TUAS building

Score matching and nonparametric estimators of drift functions for stochastic differential equations

Abstract

Score matching is a technique for estimating non-normalised probability densities from data. It avoids the complications of computing the normaliser of the density which would be needed e.g. for maximum likelihood or Bayesian estimators. The method was introduced in [1] and has recently been generalised to a nonparametric, kernel based setting [2] where it often outperforms more classical techniques such as kernel density estimators. In this talk I will discuss a relationship between score matching and learning in stochastic dynamical systems. Properly generalised, the method allows for an estimate of the drift functions for certain classes of stochastic differential equations. I will show the relation to Bayesian estimators for the drift and give applications to second order stochastic differential equations.

[1] Hyvaerinen, “Estimation of Non-Normalised Statistical Models by Score Matching”, JMLR, 2005.

[2] Sriperumbudur, Fukumizu, Kumar, Gretton and Hyvaerinen, ”Density Estimation in Infinite Dimensional Exponential Families”, arXiv:1312.3516v3, 2014.

Bio

Manfred Opper is a professor for Artifical Intelligence at Technical University Berlin since 2006. He has a  PhD in physics and a habilitation degree in theoretical physics from the university of Giessen, Germany. In 1992 he received the Physics Prize of the German Physical Society for his work on learning in neural networks. In 1994 he was awarded a Heisenberg fellowship  from the German research foundation DFG. Before the appointment to Berlin he has held faculty positions at the Neural Computing Research Group at Aston University in Birmingham UK, and at the ISIS group of Southampton University. Manfred Opper works on the development and the analysis of algorithms for approximate Bayesian inference, especially for the case of nonparametric models. In recent years he has concentrated on the problem of inference for continuous time stochastic processes.