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

• URL: http://arxiv.org/abs/2303.07287v2
• Date: Sat, 20 Jan 2024 03:20:20 GMT
• Title: Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm
• Authors: Huiming Zhang, Haoyu Wei, Guang Cheng
• Abstract summary: In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. We suggest using the sub-Gaussian intrinsic moment norm achieved by maximizing a sequence of normalized moments.
• Score: 12.400847321321912
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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