In high-dimensional settings, where the number of features pis much larger than the number of samples n, methods that systematically examine arbitrary combinations of features have only recently begun to be explored. However, none of the current methods is able to assess the association between feature combinations and a target variable while conditioning on a categorical covariate. As a result, many false discoveries might occur due to unaccounted confounding effects. We propose the Fast Automatic Conditional Search (FACS) algorithm, a significant discriminative itemset mining method which conditions on categorical covariates and only scales as O(klog k), where k is the number of states of the categorical covariate. Based on the Cochran-Mantel-Haenszel Test, FACS demonstrates superior speed and statistical power on simulated and real-world datasets compared to the state of the art, opening the door to numerous applications in biomedicine.

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.

In high-dimensional settings, where the number of features p is much larger than the number of samples n, methods that systematically examine arbitrary combinations of features have only recently begun to be explored. However, none of the current methods is able to assess the association between feature combinations and a target variable while conditioning on a categorical covariate. As a result, many false discoveries might occur due to unaccounted confounding effects. We propose the Fast Automatic Conditional Search (FACS) algorithm, a significant discriminative itemset mining method which conditions on categorical covariates and only scales as O(k log k), where k is the number of states of the categorical covariate. Based on the Cochran-Mantel-Haenszel Test, FACS demonstrates superior speed and statistical power on simulated and real-world datasets compared to the state of the art, opening the door to numerous applications in biomedicine.

Logistic Regression (LR) is a widely used statistical method in empirical binary classification studies. However, real-life scenarios oftentimes share complexities that prevent from the use of the as-is LR model, and instead highlight the need to include high-order interactions to capture data variability. This becomes even more challenging because of: (i) datasets growing wider, with more and more variables; (ii) studies being typically conducted in strongly imbalanced settings; (iii) samples going from very large to extremely small; (iv) the need of providing both predictive models and interpretable results. In this paper we present a novel algorithm, Learning high-order Interactions via targeted Pattern Search (LIPS), to select interaction terms of varying order to include in a LR model for an imbalanced binary classification task when input data are categorical. LIPS's rationale stems from the duality between item sets and categorical interactions. The algorithm relies on an interaction learning step based on a well-known frequent item set mining algorithm, and a novel dissimilarity-based interaction selection step that allows the user to specify the number of interactions to be included in the LR model. In addition, we particularize two variants (Scores LIPS and Clusters LIPS), that can address even more specific needs. Through a set of experiments we validate our algorithm and prove its wide applicability to real-life research scenarios, showing that it outperforms a benchmark state-of-the-art algorithm.

In high-dimensional settings, where the number of features p is typically much larger than the number of samples n, methods which can systematically examine arbitrary combinations of features, a huge 2^p-dimensional space, have recently begun to be explored. However, none of the current methods is able to assess the association between feature combinations and a target variable while conditioning on a categorical covariate, in order to correct for potential confounding effects. We propose the Fast Automatic Conditional Search (FACS) algorithm, a significant discriminative itemset mining method which conditions on categorical covariates and only scales as O(k log k), where k is the number of states of the categorical covariate. Based on the Cochran-Mantel-Haenszel Test, FACS demonstrates superior speed and statistical power on simulated and real-world datasets compared to the state of the art, opening the door to numerous applications in biomedicine.