Score-Based Interaction Testing in Pairwise Experiments

Interaction tests are crucial in the sciences, particularly in pairwise perturbation experiments where they can be used to reveal causal relationships in a system. Recently, Zuheng et al. [2024] proposed a framework and statistical tests for detecting pairwise interactions from unstructured data like images. While effective, these tests can be prohibitively expensive due to training costs that are quadratic in the number of perturbations. To address this, we explore alternative score-based interaction tests that can be linear in the number of perturbations. In particular, we propose using the aggregated Kernelized Stein Discrepancy (KSD, Schrab et al. 2023) as a formal hypothesis test. In our experiments, we compare to the Fisher Divergence(FD)---a score-based test that scales quadratically in the number of experiments---and show that: (i) with low-dimensional inputs, both methods perform well; (ii) with high-dimensional inputs like images, KSD's sensitivity to kernel choice hurts performance; and (iii) projecting high-dimensional data into lower-dimensional spaces solves this issue for KSD, resulting in an effective and computationally-efficient interaction test.