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Model selection is difficult to analyse yet theoretically and empirically important, especially for high-dimensional data analysis. Recently the least absolute shrinkage and selection operator (Lasso) has been applied in the statistical and…

In the era of "big data", it is becoming more of a challenge to not only build state-of-the-art predictive models, but also gain an understanding of what's really going on in the data. For example, it is often of interest to know which, if…

Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…

Estimating a prediction function is a fundamental component of many data analyses. The super learner ensemble, a particular implementation of stacking, has desirable theoretical properties and has been used successfully in many…

In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…

Cross-validation (CV) is a popular approach for assessing and selecting predictive models. However, when the number of folds is large, CV suffers from a need to repeatedly refit a learning procedure on a large number of training datasets.…

Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…

For many scientific questions, understanding the underlying mechanism is the goal. To help investigators better understand the underlying mechanism, variable selection is a crucial step that permits the identification of the most associated…

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…

This paper investigates the estimation problem in a regression-type model. To be able to deal with potential high dimensions, we provide a procedure called LOL, for Learning Out of Leaders with no optimization step. LOL is an auto-driven…

We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…

Cross-validation is a widely used technique for evaluating the performance of prediction models, ranging from simple binary classification to complex precision medicine strategies. It helps correct for optimism bias in error estimates,…

Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional…

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…

In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection…

The lasso procedure is ubiquitous in the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso…

Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection operator), the use of which requires…

In a regression model, prediction is typically performed after model selection. The large variability in the model selection makes the prediction unstable. Thus, it is essential to reduce the variability in model selection and improve…

Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…

Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…