E‐BH Based Interaction Identification for Classification With Ultra‐High Dimensional Binary Features

ABSTRACT While interactions can provide valuable information for classification, identifying meaningful interactions in ultra‐high dimensional settings presents significant challenges. To address this issue, we propose a novel interaction detection method specifically designed for discrete binary features in ultra‐high dimensional scenarios. We first construct a parameter to quantify the interaction strength between feature pairs. After deriving an appropriate estimator and establishing its asymptotic distribution, we employ hypothesis testing to determine whether a given feature pair exhibits statistically significant interaction. A key innovation of our method is its e‐value‐based framework for the entire interaction identification process. This choice is motivated by the e‐value's superior performance in assessing feature relevance compared to traditional ‐values. We provide theoretical guarantees demonstrating that, with probability approaching 1 as sample size increases, our method can correctly identify all interacting feature pairs and effectively control the false discovery rate. Leveraging these identified feature interactions, we develop an enhanced classification model that extends the conventional naïve Bayes framework. Comprehensive numerical studies validate the effectiveness of our approach, showing excellent performance in both interaction identification and subsequent classification.