Kernel Hypothesis Testing with Set-valued Data
This provides a method for hypothesis testing on set-valued data, addressing a common but previously heuristic-prone problem in fields like healthcare and climate science.
The authors tackled the problem of hypothesis testing on distributions of sets of data, which often have varying sizes and noise levels that bias traditional tests, by proposing kernel tests in a latent space of distributions. They proved consistency and showed outperformance in synthetic experiments, with practical applications in healthcare and climate data.
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.