PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Kernels, Regularization and Differential Equations
F. Steinke and B. Schölkopf
Pattern Recognition Volume 41, Number 11, pp. 3271-3286, 2008.

Abstract

Many common machine learning methods such as Support Vector Machines or Gaussian process inference make use of positive definite kernels, reproducing kernel Hilbert spaces, Gaussian processes, and regularization operators. In this work these objects are presented in a general, unifying framework, and interrelations are highlighted. With this in mind we then show how linear stochastic differential equation models can be incorporated naturally into the kernel framework. And vice versa, many kernel machines can be interpreted in terms of differential equations. We focus especially on ordinary differential equations, also known as dynamical systems, and it is shown that standard kernel inference algorithms are equivalent to Kalman filter methods based on such models. In order not to cloud qualitative insights with heavy mathematical machinery, we restrict ourselves to finite domains, implying that differential equations are treated via their corresponding finite difference equations.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Brain Computer Interfaces
Theory & Algorithms
ID Code:4320
Deposited By:Bernhard Schölkopf
Deposited On:13 March 2009