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Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation…

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…

To find efficient screening methods for high dimensional linear regression models, this paper studies the relationship between model fitting and screening performance. Under a sparsity assumption, we show that a subset that includes the…

The explosion of data in recent years has generated an increasing need for new analysis techniques in order to extract knowledge from massive datasets. Machine learning has proved particularly useful to perform this task. Fully automatized…

An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…

Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…

The Forward Search is an iterative algorithm for avoiding outliers in a regression analysis suggested by Hadi and Simonoff (J. Amer. Statist. Assoc. 88 (1993) 1264-1272), see also Atkinson and Riani (Robust Diagnostic Regression Analysis…

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $\gamma$-divergence. A novel feature of the…

Model averaging is an important alternative to model selection with attractive prediction accuracy. However, its application to high-dimensional data remains under-explored. We propose a high-dimensional model averaging method via…

The Fr\'echet regression is a useful method for modeling random objects in a general metric space given Euclidean covariates. However, the conventional approach could be sensitive to outlying objects in the sense that the distance from the…

In this era of big data, feature selection techniques, which have long been proven to simplify the model, makes the model more comprehensible, speed up the process of learning, have become more and more important. Among many developed…

This article considers ultrahigh-dimensional forecasting problems with survival response variables. We propose a two-step model averaging procedure for improving the forecasting accuracy of the true conditional mean of a survival response…

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

High-dimensional prediction typically comprises two steps: variable selection and subsequent least-squares refitting on the selected variables. However, the standard variable selection procedures, such as the lasso, hinge on tuning…

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…

We consider the problem of online linear regression in the stochastic setting. We derive high probability regret bounds for online ridge regression and the forward algorithm. This enables us to compare online regression algorithms more…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…