Sparse Modal Additive Model

Modal-Regression-Based Broad Learning System for Robust Regression and Classification

A novel neural network, namely, broad learning system (BLS), has shown impressive performance on various regression and classification tasks. Nevertheless, most BLS models may suffer serious performance degradation for contaminated data, since they are derived under the least-squares criterion which is sensitive to noise and outliers. To enhance the model robustness, in this article we proposed a modal-regression-based BLS (MRBLS) to tackle the regression and classification tasks of data corrupted by noise and outliers. Specifically, modal regression is adopted to train the output weights instead of the minimum mean square error (MMSE) criterion. Moreover, the l2,1 -norm-induced constraint is used to encourage row sparsity of the connection weight matrix and achieve feature selection. To effectively and efficiently train the network, the half-quadratic theory is used to optimize MRBLS. The validity and robustness of the proposed method are verified on various regression and classification datasets. The experimental results demonstrate that the proposed MRBLS achieves better performance than the existing state-of-the-art BLS methods in terms of both accuracy and robustness.

Gradient Learning under Tilted Empirical Risk Minimization

Gradient Learning (GL), aiming to estimate the gradient of target function, has attracted much attention in variable selection problems due to its mild structure requirements and wide applicability. Despite rapid progress, the majority of the existing GL works are based on the empirical risk minimization (ERM) principle, which may face the degraded performance under complex data environment, e.g., non-Gaussian noise. To alleviate this sensitiveness, we propose a new GL model with the help of the tilted ERM criterion, and establish its theoretical support from the function approximation viewpoint. Specifically, the operator approximation technique plays the crucial role in our analysis. To solve the proposed learning objective, a gradient descent method is proposed, and the convergence analysis is provided. Finally, simulated experimental results validate the effectiveness of our approach when the input variables are correlated.

Error Bound of Mode-Based Additive Models

Due to their flexibility and interpretability, additive models are powerful tools for high-dimensional mean regression and variable selection. However, the least-squares loss-based mean regression models suffer from sensitivity to non-Gaussian noises, and there is also a need to improve the model's robustness. This paper considers the estimation and variable selection via modal regression in reproducing kernel Hilbert spaces (RKHSs). Based on the mode-induced metric and two-fold Lasso-type regularizer, we proposed a sparse modal regression algorithm and gave the excess generalization error. The experimental results demonstrated the effectiveness of the proposed model.