Towards D-optimal input design for finite-sample system identification

Sándor Kolumbán, Balázs Csanád Csáji

Research output: Contribution to journalConference articlepeer-review

Abstract

Finite-sample system identification methods provide statistical inference, typically in the form of confidence regions, with rigorous non-asymptotic guarantees under minimal distributional assumptions. Data Perturbation (DP) methods constitute an important class of such algorithms, which includes, for example, Sign-Perturbed Sums (SPS) as a special case. Here we study a natural input design problem for DP methods in linear regression models, where we want to select the regressors in a way that the expected volume of the resulting confidence regions are minimized. We suggest a general approach to this problem and analyze it for the fundamental building blocks of all DP confidence regions, namely, for ellipsoids having confidence probability exactly 1/2. We also present experiments supporting that minimizing the expected volumes of such ellipsoids significantly reduces the average sizes of the constructed DP confidence regions.

Original languageEnglish
Pages (from-to)215-220
Number of pages6
JournalIFAC-PapersOnLine
Volume51
Issue number15
DOIs
Publication statusPublished - 8 Oct 2018
Event18th IFAC Symposium on System Identification (SYSID 2018) - Stockholm, Sweden
Duration: 9 Jul 201811 Jul 2018

Keywords

  • confidence regions
  • distribution-free results
  • finite sample results
  • input design
  • least squares
  • parameter estimation
  • system identification

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