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

arXiv: https://arxiv.org/abs/2303.07287 · HTML: https://mlsanity.com/paper/2303.07287/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 13 Mar 2023.

## Builds on (most cited first, 15 of 15)

- [Loss minimization and parameter estimation with heavy tails](https://mlsanity.com/paper/1307.1827/) (2013)
- [Robust subgaussian estimation of a mean vector in nearly linear time](https://mlsanity.com/paper/1906.03058/) (2019)
- [Bootstrapping Upper Confidence Bound](https://mlsanity.com/paper/1906.05247/) (2019)
- [Optimal Rates of (Locally) Differentially Private Heavy-tailed Multi-Armed Bandits](https://mlsanity.com/paper/2106.02575/) (2021)
- [Concentration Inequalities for Statistical Inference](https://mlsanity.com/paper/2011.02258/) (2020)
- [Concentration in unbounded metric spaces and algorithmic stability](https://mlsanity.com/paper/1309.1007/) (2013)
- [On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables](https://mlsanity.com/paper/1810.09006/) (2018)
- [Two-sample Test using Projected Wasserstein Distance](https://mlsanity.com/paper/2010.11970/) (2020)
- [Large Deviation Methods for Approximate Probabilistic Inference](https://mlsanity.com/paper/1301.7392/) (2013)
- [Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness](https://mlsanity.com/paper/1712.04594/) (2017)
- [Non-asymptotic Confidence Intervals of Off-policy Evaluation: Primal and Dual Bounds](https://mlsanity.com/paper/2103.05741/) (2021)
- [Sharper Sub-Weibull Concentrations](https://mlsanity.com/paper/2102.02450/) (2021)
- [Residual Bootstrap Exploration for Stochastic Linear Bandit](https://mlsanity.com/paper/2202.11474/) (2022)
- [Exact Statistical Inference for the Wasserstein Distance by Selective Inference](https://mlsanity.com/paper/2109.14206/) (2021)
- [Inference in a class of optimization problems: Confidence regions and finite sample bounds on errors in coverage probabilities](https://mlsanity.com/paper/1905.06491/) (2019)

## Built on by (most cited first, 1 of 1)

- [Zero-Inflated Bandits](https://mlsanity.com/paper/2312.15595/) (2023)

## 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.