Sparse Modal Regression with Mode-Invariant Skew Noise

Abstract

Sparse regression methods have been widely used in many fields for their statistical effectiveness and high interpretability. However, there are few sparse regression methods with skew noise, although statistical modeling using skewness is becoming more important, e.g., in the medical field. The Azzalini's skew-normal distribution and its extensions are well-used for skew noise. Such skew regression methods have a severe problem with statistical interpretability because they model neither mean, median, nor mode. To overcome this problem, we propose a novel sparse regression method based on mode-invariant skew-normal noise. The regression model is easy to interpret in the proposed method because it always models a mode regardless of skewness. The proposed method is simple to implement and optimize, suggesting it is highly scalable to other machine-learning methods. We also provide theoretical guarantees of the proposed method for the average excess risk and the estimation error. Numerical experiments on artificial and real-world data demonstrate that the proposed method performs significantly better and is more stable than other existing methods for various skew-noise data.