Exact model-free function inference using uniform marginal counts for null population

Recognizing cause-effect relationships is a fundamental inquiry in science. However, current causal inference methods often focus on directionality but not statistical significance. A ramification is chance patterns of uneven marginal distributions achieving a perfect directionality score.

To overcome such issues, we design the uniform exact function test with continuity correction (UEFTC) to detect functional dependency between two discrete random variables. The null hypothesis is two variables being statistically independent. Unique from related tests whose null populations use observed marginals, we define the null population by an embedded uniform square. We also present a fast algorithm to accomplish the test. On datasets with ground truth, the UEFTC exhibits accurate directionality, low biases, and robust statistical behavior over alternatives. We found nonmonotonic response by gene TCB2 to beta-estradiol dosage in engineered yeast strains. In the human duodenum with environmental enteric dysfunction, we discovered pathology-dependent anti-co-methylated CpG sites in the vicinity of genes POU2AF1 and LSP1; such activity represents orchestrated methylation and demethylation along the same gene, unreported previously. The UEFTC has much improved effectiveness in exact model-free function inference for data-driven knowledge discovery.

An open-source R package "UniExactFunTest" implementing the presented uniform exact function tests is available via CRAN at doi: 10.32614/CRAN.package.UniExactFunTest. Computer code to reproduce figures can be found in supplementary file "UEFTC-main.zip."