Graphical LASSO based Model Selection for Time Series

A. Jung, G. Hannak, N. Goertz

Research output: Contribution to journalArticleScientificpeer-review

25 Citations (Scopus)

Abstract

We propose a novel graphical model selection scheme for high-dimensional stationary time series or discrete time processes. The method is based on a natural generalization of the graphical LASSO algorithm, introduced originally for the case of i.i.d. samples, and estimates the conditional independence graph of a time series from a finite length observation. The graphical LASSO for time series is defined as the solution of an l1-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers. Our approach is nonparametric as we do not assume a finite dimensional parametric model, but only require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails. Numerical experiments demonstrate the ability of our method to recover the correct conditional independence graph from a limited amount of samples.
Original languageEnglish
Article number7091904
Pages (from-to)1781-1785
Number of pages5
JournalIEEE Signal Processing Letters
Volume22
Issue number10
DOIs
Publication statusPublished - 1 Oct 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Gaussian processes
  • graph theory
  • maximum likelihood estimation
  • time series
  • Gaussian process
  • conditional independence graph
  • discrete time process
  • finite dimensional parametric model
  • finite length observation
  • graphical LASSO algorithm
  • graphical model selection scheme
  • high-dimensional stationary time series
  • l1-regularized maximum likelihood problem
  • optimization problem
  • Algorithm design and analysis
  • Estimation error
  • Graphical models
  • Linear programming
  • Signal processing algorithms
  • Time series analysis
  • Upper bound
  • ADMM
  • graphical LASSO
  • graphical model selection
  • nonparametric time series
  • sparsity

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