Reviews: Finding significant combinations of features in the presence of categorical covariates

The paper is well written and clearly organized, especially where it motivates the problem and the goals of the paper. It is a novel point of view to aim to find all feature subsets for which a statistical association test rejects the null hypothesis, and thus allowing to correct for a confounding categorical covariate. The authors results in the scope of the paper demonstrates that FACS keeps the computational efficiency, statistical power and the ability to correct for multiple hypothesis testing of existing method. The introduction of the branch-and-bound algorithm for conditional statistical association tests is novel and well-explained. Along with the results, the authors provide good intuition behind the methods and the key aspects, such as the appropriate testability criterion for the CMH test and the pruning criterion for the CMH test.