Citation
M. Rogers, L. Li, S. Russell. "Multilinear Dynamical Systems for Tensor Time Series". Advances in Neural Information Processing Systems (NIPS), 2013.

Abstract
Data in the sciences frequently occur as sequences of multidimensional arrays called tensors. How can hidden, evolving trends in such data be extracted while preserving the tensor structure? The model that is traditionally used is the linear dynamical system (LDS) with Gaussian noise, which treats the latent state and observation at each time slice as a vector. We present the multilinear dynamical system (MLDS) for modeling tensor time series and an expectation–maximization (EM) algorithm to estimate the parameters. The MLDS models each tensor observation in the time series as the multilinear projection of the corresponding member of a sequence of latent tensors. The latent tensors are again evolving with respect to a multilinear projection. Compared to the LDS with an equal number of parameters, the MLDS achieves higher prediction accuracy and marginal likelihood for both artificial and real datasets.

Electronic downloads

• nips13-tensor.pdf · application/pdf · 710 kbytes

• HTML

  M. Rogers, L. Li, S. Russell. <a
  href="http://robotics.eecs.berkeley.edu/pubs/26.html"
  >Multilinear Dynamical Systems for Tensor Time
  Series</a>, Advances in Neural Information Processing
  Systems (NIPS), 2013.

• Plain text

  M. Rogers, L. Li, S. Russell. "Multilinear Dynamical
  Systems for Tensor Time Series". Advances in Neural
  Information Processing Systems (NIPS), 2013.

• BibTeX

  @inproceedings{RogersLiRussell13_MultilinearDynamicalSystemsForTensorTimeSeries,
      author = {M. Rogers and L. Li and S. Russell},
      title = {Multilinear Dynamical Systems for Tensor Time
                Series},
      booktitle = {Advances in Neural Information Processing Systems
                (NIPS)},
      year = {2013},
      abstract = {Data in the sciences frequently occur as sequences
                of multidimensional arrays called tensors. How can
                hidden, evolving trends in such data be extracted
                while preserving the tensor structure? The model
                that is traditionally used is the linear dynamical
                system (LDS) with Gaussian noise, which treats the
                latent state and observation at each time slice as
                a vector. We present the multilinear dynamical
                system (MLDS) for modeling tensor time series and
                an expectation–maximization (EM) algorithm to
                estimate the parameters. The MLDS models each
                tensor observation in the time series as the
                multilinear projection of the corresponding member
                of a sequence of latent tensors. The latent
                tensors are again evolving with respect to a
                multilinear projection. Compared to the LDS with
                an equal number of parameters, the MLDS achieves
                higher prediction accuracy and marginal likelihood
                for both artificial and real datasets.},
      URL = {http://robotics.eecs.berkeley.edu/pubs/26.html}
  }
  

Posted by Ehsan Elhamifar on 9 Jun 2014.
Groups: ehumans
For additional information, see the Publications FAQ or contact webmaster at robotics eecs berkeley edu.