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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