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Title: Reluctant interaction modeling in GLMs Authors:  Guo Yu - University of California Santa Barbara (United States) [presenting]
Abstract: While including pairwise interactions in a regression model can better approximate the response surface, fitting such an interaction model is a well-known difficult problem. In particular, analyzing contemporary high-dimensional datasets often leads to extremely large-scale interaction modeling problem, where the challenge is posed to identify important interactions among millions or even billions of candidate interactions. While several methods have recently been proposed to tackle this challenge, they are mostly designed by (1) focusing on linear models with interactions and (or) (2) assuming the hierarchy assumption among the important interactions. In practice, however, neither of these two building blocks has to hold. We propose an interaction modeling framework in generalized linear models (GLMs) which is free of any assumptions on hierarchy. The basic premise is a non-trivial extension of the reluctance principle to interaction selection in GLMs, where main effects are preferred over interactions if all else is equal. The proposed method is easy to implement, and is highly scalable to large-scale datasets. We show favorable theoretical properties of the proposed method. Numerical results show that the proposed method does not sacrifice any statistical performance in the presence of significant computational gain.