Tight Lower Bound on the Probability of a Binomial Exceeding its Expectation

TL;DR

This paper proves a tight lower bound on the probability that a binomial random variable exceeds its expectation, which is crucial for analyzing deviations in learning theory and generalization bounds.

Contribution

It provides a novel, tight lower bound on binomial tail probabilities, enhancing theoretical tools for statistical learning and deviation analysis.

Findings

Established a tight lower bound for binomial exceeding its expectation

Improved understanding of deviation probabilities in learning theory

Applicable to analysis of unbounded loss functions

Abstract

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.