Deep anytime-valid hypothesis testing
Teodora Pandeva Patrick Forré Aaditya Ramdas Shubhanshu Shekhar
We propose a general framework for constructing powerful, sequential
hypothesis tests for a large class of nonparametric testing problems. The null
hypothesis for these problems is defined in an abstract form using the action
of two known operators on the data distribution. This abstraction allows for a
unified treatment of several classical tasks, such as two-sample testing,
independence testing, and conditional-independence testing, as well as modern
problems, such as testing for adversarial robustness of machine learning (ML)
models. Our proposed framework has the following advantages over classical
batch tests: 1) it continuously monitors online data streams and efficiently
aggregates evidence against the null, 2) it provides tight control over the
type I error without the need for multiple testing correction, 3) it adapts the
sample size requirement to the unknown hardness of the problem. We develop a
principled approach of leveraging the representation capability of ML models
within the testing-by-betting framework, a game-theoretic approach for
designing sequential tests. Empirical results on synthetic and real-world
datasets demonstrate that tests instantiated using our general framework are
competitive against specialized baselines on several tasks.