Sharp finite-sample concentration of independent variables
Akshay Balsubramani
TL;DR
This paper extends Sanov's theorem to provide finite-sample concentration bounds for independent variables, offering a broad, sample-size-agnostic, information-theoretic approach to tail probability control.
Contribution
It introduces a novel extension of Sanov's theorem that applies to finite samples with simple proof techniques, broadening its applicability.
Findings
Provides finite-sample concentration bounds for i.i.d. variables
Uses elementary information-theoretic methods for proof
Applicable to samples of any size
Abstract
We show an extension of Sanov's theorem on large deviations, controlling the tail probabilities of i.i.d. random variables with matching concentration and anti-concentration bounds. This result has a general scope, applies to samples of any size, and has a short information-theoretic proof using elementary techniques.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Statistical Methods and Inference · Bayesian Methods and Mixture Models