Assessing the Quality of Binomial Samplers: A Statistical Distance Framework

TL;DR

This paper introduces a statistical distance framework to evaluate and improve the quality of Binomial samplers, addressing approximation errors in standard implementations and enhancing the reliability of randomized algorithms.

Contribution

It provides the first rigorous analysis of Binomial sampler quality using statistical distance, deriving bounds, and proposing an interface for better control and monitoring.

Findings

Derived bounds on statistical distance for standard Binomial samplers

Enhanced APSEst model counter with improved error guarantees

Proposed interface extension for user-controlled sampling accuracy

Abstract

Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is computationally challenging, leading standard library implementations to rely on heuristics. These heuristics, while efficient, suffer from approximation and system representation errors, causing deviations from the ideal distribution. Although seemingly minor, such deviations can accumulate in downstream applications requiring large-scale sampling, potentially undermining algorithmic guarantees. In this work, we propose statistical distance as a robust metric for analyzing the quality of Binomial samplers, quantifying deviations from the ideal distribution. We derive rigorous bounds on the statistical distance for standard implementations and demonstrate the practical utility of our framework by enhancing APSEst, a DNF model counter, with improved reliability and error guarantees. To support practical adoption, we propose an interface extension that allows users to control and monitor statistical distance via explicit input/output parameters. Our findings emphasize the critical need for thorough and systematic error analysis in sampler design. As the first work to focus exclusively on Binomial samplers, our approach lays the groundwork for extending rigorous analysis to other common distributions, opening avenues for more robust and reliable randomized algorithms.