Robust Variable Selection and Estimation Based on Kernel Modal Regression

Abstract

Model-free variable selection has attracted increasing interest recently due to its flexibility in algorithmic design and outstanding performance in real-world applications. However, most of the existing statistical methods are formulated under the mean square error (MSE) criterion, and susceptible to non-Gaussian noise and outliers. As the MSE criterion requires the data to satisfy Gaussian noise condition, it potentially hampers the effectiveness of model-free methods in complex circumstances. To circumvent this issue, we present a new model-free variable selection algorithm by integrating kernel modal regression and gradient-based variable identification together. The derived modal regression estimator is related closely to information theoretic learning under the maximum correntropy criterion, and assures algorithmic robustness to complex noise by replacing learning of the conditional mean with the conditional mode. The gradient information of estimator offers a model-free metric to screen the key variables. In theory, we investigate the theoretical foundations of our new model on generalization-bound and variable selection consistency. In applications, the effectiveness of the proposed method is verified by data experiments.

Error Bound of Mode-Based Additive Models

“…In this section, we recall the basic background on modal regression [ 19 , 34 ]. Let be a compact subset of associated with the input covariate vector and be the response variable set.…”

Evolved-Cooperative Correntropy-Based Extreme Learning Machine for Robust Prediction

“…Another approach to improve the robustness via the correntropy is enhancing the feature selection efficiencies [47][48][49]. In [50], the kernel modal regression and gradient-based variable identification were integrated together using the maximum correntropy criterion, which guarantees the robustness of the algorithm. Additionally, in [51], a novel principal component analysis (PCA), based on the correntropy and known as the correntropy-optimized temporal PCA (CTPCA), was adapted to enhance the robustness for rejecting the outlier.…”