Alladi Ramakrishnan Hall

Distribution Testing in the Small Sample Regime

Gunjan Kumar

National University of Singapore

Understanding unknown probability distributions with limited samples is a fundamental challenge in statistics and data analysis, with far-reaching applications spanning diverse scientific domains. Traditional methods for distribution testing often rely on having large amounts of samples, which may not always be available, leading to a
gap in our ability to analyze distributions efficiently. This has prompted a shift towards new algorithmic approaches that work well with fewer samples. These approaches explore alternative sampling models, offering stronger access to the distributions.

The talk will focus on these developments, particularly on recent progress in achieving optimal bounds for equivalence testing—determining if two unknown distributions are identical or distinct—when the algorithm is granted conditional sampling access. Additionally, I will explore the role of distribution testing in other fields such as Approximate Model Counting.