ARFIS: An adaptive robust model for regression with heavy-tailed distribution

As heavy-tailed distributions are ubiquitous in many real applications, robust regression has been extensively applied in machine learning and exhibits the superiority in deal with heavy-tailed distribution. Current existing robust methods for regression are based on independence assumption of features and ignore interaction between them, which may lead to poor generalization due to most datasets unsatisfying the assumption. Actually, interaction features formed by the composition of two or more features are particularly helpful to obtain the high-order information in many applications. In this paper, we propose a novel adaptive robust feature interaction selection model for regression with heavy-tailed distributions, termed Adaptive Robust Feature Interaction Selection (ARFIS). Firstly, we consider pairwise feature interaction by augmenting a feature vector with product of features for regression with heavy tailed distribution. Secondly, we propose feature interaction selection models based on quantile loss with different regularizers to learn parameters. The consistency of the proposed model ARFIS is theoretically proven, and an efficient algorithm is presented for solving proposed model. Finally, experimental results on simulation data, UCI datasets and a real-world dataset validate good accuracy, interpretability and robustness of our proposed models.