Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Fortunately, the introduction of so-called screening rules has improved this situation remarkably.

The connection to the offline setting is that ADDIS effectively employs a "discarding" rule, which states

Recent work used mathematical programming, which is computationally slow.

Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we propose a novel and simple screening method based on ordering the absolute sample ridge partial correlations. The proposed method takes into account not only the ridge regularized estimates of the regression coefficients but also the ridge regularized partial variances of the predictor variables providing sure screening property without strong assumptions on the marginal correlations. Simulation study and a real data analysis show that the proposed method has a competitive performance compared with the existing screening procedures. A publicly available software implementing the proposed screening accompanies the article.

In this book, written in Portuguese, we discuss what ill-posed problems are and how the regularization method is used to solve them. In the form of questions and answers, we reflect on the origins and future of regularization, relating the similarities and differences of its meaning in different areas, including inverse problems, statistics, machine learning, and deep learning.