mlsanityData to 7 Oct 2026

Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm

arXiv 2303.07287 ↗First posted 13 Mar 2023stat.ML cs.LG econ.EMcited by 1

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Abstract (arXiv)

In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function (MGF) is infeasible. To address this, we suggest using the sub-Gaussian intrinsic moment norm [Buldygin and Kozachenko (2000), Theorem 1.3] achieved by maximizing a sequence of normalized moments. Significantly, the suggested norm can not only reconstruct the exponential moment bounds of MGFs but also provide tighter sub-Gaussian concentration inequalities. In practice, we provide an intuitive method for assessing whether data with a finite sample size is sub-Gaussian, utilizing the sub-Gaussian plot. The intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical findings are also applicable to reinforcement learning, including the multi-armed bandit scenario.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 15 of its 54 references that are in the map. First posted on arXiv 13 Mar 2023.

Builds on

15 of 54 references.

References · 15

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  2. 2019Robust subgaussian estimation of a mean vector in nearly linear timecited by 37
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3 more
  1. 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7
  2. 2022Residual Bootstrap Exploration for Stochastic Linear Banditcited by 7
  3. 2019Inference in a class of optimization problems: Confidence regions and finite sample bounds on errors in coverage probabilitiescited by 1

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Citing papers per year: 2023: 1.

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  1. 2023Zero-Inflated Banditscited by 0