Active Nonparametric Two-Sample Testing with Adaptive Source Selection

This paper addresses the problem of active two-sample testing, where the goal is to quickly determine if two sets of data come from the same distribution. The novelty lies in its nonparametric approach, meaning it makes minimal assumptions about the data distributions, and its active nature, allowing it to adaptively choose which data sources to sample from. This is a significant contribution because it provides a principled way to improve the efficiency of two-sample testing in scenarios with multiple, potentially heterogeneous, data sources. The use of betting-based testing provides a robust framework for controlling error rates.

• •Proposes an active nonparametric two-sample testing procedure.
• •Combines adaptive source selection with testing-by-betting.
• •Controls type-I error and demonstrates power-one property.
• •Provides a principled approach to improve testing efficiency with heterogeneous data sources.