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Uniform error bounds for quantized dynamical models

Abdelkader Metakalard, Fabien Lauer, Kevin Colin, Marion Gilson

TL;DR

Uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification are developed.

Abstract

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.

Uniform error bounds for quantized dynamical models

TL;DR

Uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification are developed.

Abstract

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.
Paper Structure (16 sections, 61 equations, 3 figures, 2 tables)

This paper contains 16 sections, 61 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Paper Organization
  5. Learning Framework
  6. Error Bounds for Quantized Models
  7. Error Bounds for Quantized Dynamical Models
  8. Fast Rate Bounds
  9. Examples
  10. Linear system identification
  11. Switched system identification
  12. Conclusions
  13. Technical Lemmas
  14. Proof of Theorem \ref{['thm:slow-blocks']}
  15. Proof of Theorem \ref{['thm:bernstein-spaced']}
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Two intertwined block sequences: light gray for $\mathbf{S}_1$, black for $\mathbf{S}_2$.
  • Figure 2: Spaced point selection in \ref{['eq:sp']}, showing the first four and the last points, with $a$ points between each pair.
  • Figure 3: Slow and fast rate error bounds as functions of $n$ when modeling \ref{['eq:ex1']}.

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3: Block decomposition approach and fast rates