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2013 NIPS NeurIPS 2013

Multilinear Dynamical Systems for Tensor Time Series

Abstract

Many scientific data 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), which treats the observation at each time slice as a vector. In this paper, we propose the multilinear dynamical system (MLDS) for modeling tensor time series and an expectation-maximization (EM) algorithm to estimate the parameters. The MLDS models each time slice of the tensor time series as the multilinear projection of a corresponding member of a sequence of latent, low-dimensional tensors. Compared to the LDS with an equal number of parameters, the MLDS achieves higher prediction accuracy and marginal likelihood for both simulated and real datasets.

🌉 Interdisciplinary Bridge — Data Science & Analytics and Machine Learning
🧭 Keyword Pioneer — tensor time series
🐣 Hot Topic Early Bird — state space model
🐝 Cross-Pollinator — Artificial Intelligence, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Speech & Audio

Authors

Mark Rogers , Lei Li , Stuart Russell

Topics

Machine Learning > Core Methods > Representation Learning Machine Learning > Core Methods > Embedding Learning Data Science & Analytics > Methods > Time Series Data Science & Analytics > Methods > Time Series Analysis Machine Learning > Core Methods > Dimensionality Reduction Machine Learning > Core Methods > Matrix Factorization

Keywords

expectation maximization tensor decomposition time series expectation-maximization tensor time series multilinear dynamical systems latent tensors state space model latent variable prediction accuracy
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