Learning With Coefficient-Based Regularized Regression on Markov Resampling

ALR-HT: A fast and efficient Lasso regression without hyperparameter tuning

Lasso regression, known for its efficacy in high-dimensional data analysis and feature selection, stands as a cornerstone in the realm of supervised learning for regression estimation. However, hyperparameter tuning for Lasso regression is often time-consuming and susceptible to noisy data in big data scenarios. In this paper we introduce a new additive Lasso regression without Hyperparameter Tuning (ALR-HT) by integrating Markov resampling with additive models. We estimate the generalization bounds of the proposed ALR-HT and establish the fast learning rate. The experimental results for benchmark datasets confirm that the proposed ALR-HT algorithm has better performance in terms of sampling and training total time, mean squared error (MSE) compared to other algorithms. We present some discussions on the ALR-HT algorithm and apply it to Ridge regression, to show its versatility and effectiveness in regularized regression scenarios.

Robust Variable Selection and Estimation Based on Kernel Modal Regression

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.