Date 
September 24, 2010 
Speaker 
Dr. Marco Cuturi, Graduate School of Informatics Kyoto University 
Title 
Autoregressive Kernels for Multivariate Time Series

Abstract 
We propose a new family of kernels for multivariate variablelength time
series. Our work builds upon the vector autoregressive (VAR) model
for multivariate stochastic processes. For each parameter θ of the
VAR model, the distribution p_{θ(x)} is used as a feature
extractor for a multivariate time series x. Given two such multivariate
series x and x', x and x' are compared using
the features p_{θ(x)} and
p_{θ(x')}. We propose a kernel which is
the product p_{θ(x)} p_{θ(x')} integrated out with respect
to a conjugate prior for θ. Not only can this kernel be computed
analytically but it additionally remains meaningful when the dimension
d of the time series is much higher than the length of the considered
sequences x and x'.
We then show how it is possible to propose a nonlinear generalization of
this kernel based on the Gram matrix of all vectors enumerated in x and
x'. We describe a computationally efficient implementation of this kernel
relying on lowrank matrix factorization techniques. We provide experimental
evidence that these kernels are useful in challenging tasks involving
highdimensional timeseries.

