OASIS: An interpretable, finite-sample valid alternative to Pearson's X2 for scientific discovery.

Contingency tables, data represented as counts matrices, are ubiquitous across quantitative research and data-science applications. Existing statistical tests are insufficient however, as none are simultaneously computationally efficient and statistically valid for a finite number of observations. In this work, motivated by a recent application in reference-free genomic inference (1), we develop OASIS (Optimized Adaptive Statistic for Inferring Structure), a family of statistical tests for contingency tables. OASIS constructs a test-statistic which is linear in the normalized data matrix, providing closed form p-value bounds through classical concentration inequalities. In the process, OASIS provides a decomposition of the table, lending interpretability to its rejection of the null. We derive the asymptotic distribution of the OASIS test statistic, showing that these finite-sample bounds correctly characterize the test statistic's p-value up to a variance term. Experiments on genomic sequencing data highlight the power and interpretability of OASIS. The same method based on OASIS significance calls detects SARS-CoV-2 and Mycobacterium Tuberculosis strains de novo, which cannot be achieved with current approaches. We demonstrate in simulations that OASIS is robust to overdispersion, a common feature in genomic data like single cell RNA-sequencing, where under accepted noise models OASIS still provides good control of the false discovery rate, while Pearson's $X^2$ test consistently rejects the null. Additionally, we show on synthetic data that OASIS is more powerful than Pearson's $X^2$ test in certain regimes, including for some important two group alternatives, which we corroborate with approximate power calculations.