Boolean interactions: practice and theory

Thresholding or Boolean behaviors of biomolecules underlie many biological processes.
Decision-trees capture such behaviors and tree-based methods such random forests have been shown to succeed in predictive tasks in genomics and medicine.
In this talk, we use UKBiobank data and a stable version of the random forests, iterative random forests (iRF), to recommend gene and gene-gene interactions that have data evidence for driving a heart disease, Hypertrophic Cardiomyopathy (HCM).
4 out of the 5 recommendations are shown to be causal for HCM in follow-up gene-silencing experiments. This and other empirical successes of iRF motivate a theoretical investigation of its tractable version under a new local sparse and spiky (LSS) model where the regression function is a linear combination of Boolean interactions of features.
The tractable version of iRF is shown to be model selection consistent under this new model with conditions of feature independence and non-overlapping interactions.