System identification from partial samples: Non-asymptotic analysis

Milind Rao, Alon Kipnis, Tara Javidi, Yonina C. Eldar, Andrea Goldsmith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The problem of learning the parameters of a vector autoregressive (VAR) process from partial random measurements is considered. This setting arises due to missing data or data corrupted by multiplicative bounded noise. We present an estimator of the covariance matrix of the evolving state-vector from its partial noisy observations. We analyze the non-asymptotic behavior of this estimator and provide an upper bound for its convergence rate. This expression shows that the effect of partial observations on the first order convergence rate is equivalent to reducing the sample size to the average number of observations viewed, implying that our estimator is order-optimal. We then present and analyze two techniques to recover the VAR parameters from the estimated covariance matrix applicable in dense and in sparse high-dimensional settings. We demonstrate the applicability of our estimation techniques in joint state and system identification of a stable linear dynamic system with random inputs.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2938-2944
Number of pages7
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Externally publishedYes
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

Keywords

  • autoregressive processes
  • covariance estimation
  • high-dimensional analysis
  • robust estimation
  • system identification

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