mlsanityData to 14 Oct 2026

The noise level in linear regression with dependent data

arXiv 2305.11165 ↗First posted 18 May 2023cs.LG math.ST stat.MLcited by 6

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Abstract (arXiv)

We derive upper bounds for random design linear regression with dependent (β-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp instance-optimal non-asymptotics are available in the literature. Up to constant factors, our analysis correctly recovers the variance term predicted by the Central Limit Theorem -- the noise level of the problem -- and thus exhibits graceful degradation as we introduce misspecification. Past a burn-in, our result is sharp in the moderate deviations regime, and in particular does not inflate the leading order term by mixing time factors.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 13 of its 33 references that are in the map. First posted on arXiv 18 May 2023.

Builds on

13 of 33 references.

References · 13

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2016A vector-contraction inequality for Rademacher complexitiescited by 142
  3. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  4. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  5. 2020Least Squares Regression with Markovian Data: Fundamental Limits and Algorithmscited by 56
  6. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  7. 2014Learning without Concentrationcited by 50
  8. 2019Exact minimax risk for linear least squares, and the lower tail of sample covariance matricescited by 34
  9. 2022Learning with little mixingcited by 33
  10. 2021Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systemscited by 17
  11. 2021On Empirical Risk Minimization with Dependent and Heavy-Tailed Datacited by 16
  12. 2014Learning without Concentration for General Loss Functionscited by 13
1 more
  1. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 0; 2026: 1.

6 papers.

  1. 2023A Tutorial on the Non-Asymptotic Theory of System Identificationcited by 26
  2. 2024Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Losscited by 10
  3. 2024High-dimensional analysis of ridge regression for non-identically distributed data with a variance profilecited by 5
  4. 2024Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samplescited by 2
  5. 2024Single Trajectory Conformal Predictioncited by 1
  6. 2026CLT-Optimal Parameter Error Bounds for Linear System Identificationcited by 0