{
  "id": "1101.0673",
  "version": "v1",
  "published": "2011-01-04T08:44:14.000Z",
  "updated": "2011-01-04T08:44:14.000Z",
  "title": "Autoregressive Kernels For Time Series",
  "authors": [
    "Marco Cuturi",
    "Arnaud Doucet"
  ],
  "categories": [
    "stat.ML"
  ],
  "abstract": "We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_{\\theta}(x) of different parameters \\theta in the VAR model as features to describe x. To compare two time series x and x', we form the product of their features p_{\\theta}(x) p_{\\theta}(x') which is integrated out w.r.t \\theta using a matrix normal-inverse Wishart prior. Among other properties, this kernel can be easily computed when the dimension d of the time series is much larger than the lengths of the considered time series x and x'. It can also be generalized to time series taking values in arbitrary state spaces, as long as the state space itself is endowed with a kernel \\kappa. In that case, the kernel between x and x' is a a function of the Gram matrices produced by \\kappa on observations and subsequences of observations enumerated in x and x'. We describe a computationally efficient implementation of this generalization that uses low-rank matrix factorization techniques. These kernels are compared to other known kernels using a set of benchmark classification tasks carried out with support vector machines.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-04T08:44:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "autoregressive kernels",
      "matrix normal-inverse wishart prior",
      "low-rank matrix factorization techniques",
      "multivariate stochastic processes",
      "multivariate time series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.0673C"
    }
  }
}