アブストラクト
| 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 variable-length 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 pθ(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 pθ(x) and
pθ(x'). We propose a kernel which is
the product pθ(x) pθ(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 low-rank matrix factorization techniques. We provide experimental evidence that these kernels are useful in challenging tasks involving high-dimensional time-series. |