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

Area of Science:

• Causal inference
• Statistical modeling
• Bioinformatics
• Genomics

Background:

• Identifying cause-effect relationships is crucial in scientific research.
• Existing causal inference methods often prioritize directionality over statistical significance.
• This limitation can lead to spurious findings due to chance patterns in data distributions.

Purpose of the Study:

• To introduce a novel statistical test, the uniform exact function test with continuity correction (UEFTC), for detecting functional dependency between discrete variables.
• To address the shortcomings of current methods by incorporating statistical significance into causal inference.
• To provide a robust and efficient tool for model-free function inference and data-driven knowledge discovery.

Main Methods:

• Design of the uniform exact function test with continuity correction (UEFTC).
• Definition of a null population using an embedded uniform square, differing from methods using observed marginals.
• Development of a fast algorithm for implementing the UEFTC and an open-source R package 'UniExactFunTest'.

Main Results:

• The UEFTC demonstrates accurate directionality, low bias, and robust statistical performance on datasets with known ground truth.
• Discovery of a nonmonotonic response of gene TCB2 to beta-estradiol in engineered yeast strains.
• Identification of pathology-dependent, co-methylated CpG sites near POU2AF1 and LSP1 in the human duodenum, revealing coordinated methylation dynamics.

Conclusions:

• The UEFTC offers improved effectiveness for exact, model-free function inference, advancing data-driven scientific discovery.
• The method successfully identified novel biological insights in yeast and human duodenum studies.
• The availability of an R package facilitates the application of UEFTC in various research fields.