Kernel Hypothesis Testing with Set-valued Data

TL;DR

This paper introduces a kernel-based framework for hypothesis testing on set-valued data, effectively handling variability in set size, noise, and nuisance factors, with proven consistency and practical applications in healthcare and climate data.

Contribution

It proposes a novel kernel two-sample and independence testing approach for sets viewed as samples from latent distributions, addressing variability and nuisance factors.

Findings

Tests outperform in synthetic experiments

Proven to be consistent

Effective in healthcare and climate data applications

Abstract

We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of images of a given phenomenon. This observation pattern, however, differs from the common assumptions required for hypothesis testing: each set differs in size, may have differing levels of noise, and also may incorporate nuisance variability, irrelevant for the analysis of the phenomenon of interest; all features that bias test decisions if not accounted for. In this paper, we propose to interpret sets as independent samples from a collection of latent probability distributions, and introduce kernel two-sample and independence tests in this latent space of distributions. We prove the consistency of tests and observe them to outperform in a wide range of synthetic experiments. Finally, we showcase their use in practice with experiments of healthcare and climate data, where previously heuristics were needed for feature extraction and testing.