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Manfred Opper

 

Wednesday 13th April 2016

Time: 4.00pm

 

Ground Floor Seminar Room

25 Howland Street, London, W1T 4JG

 

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

 

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. [Joint work with Philipp Batz and
Andreas Ruttor (TU Berlin)]

[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.