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ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS.
This paper proposes the adaptive Elastic-Net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage and establishes the oracle property of the adaptive elastic-Net under weak regularity conditions.
Sure independence screening for ultrahigh dimensional feature space Discussion
Component selection and smoothing in multivariate nonparametric regression
A detailed analysis reveals that the COSSO does model selection by applying a novel soft thresholding type operation to the function components, which leads naturally to an iterative algorithm.
Adaptive Lasso for Cox's proportional hazards model
We investigate the variable selection problem for Cox's proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and…
Component selection and smoothing in smoothing spline analysis of variance models -- COSSO
A detailed analysis reveals that the COSSO applies a novel soft thresholding type operation to the function components and selects the correct model structure with probability tending to one in the special case of a tensor product design with periodic functions.
Gene selection using support vector machines with non-convex penalty
A unified procedure for simultaneous gene selection and cancer classification is provided, achieving high accuracy in both aspects and a successive quadratic algorithm is proposed to convert the non-differentiable and non-convex optimization problem into easily solved linear equation systems.
Principles and Theory for Data Mining and Machine Learning
This book is a thorough introduction to the most important topics in data mining and machine learning. It begins with a detailed review of classical function estimation and proceeds with chapters on…
A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables
Interaction Screening for Ultrahigh-Dimensional Data
Theoretically, the iFOR algorithms prove that they possess sure screening property for ultrahigh-dimensional settings, and are proposed to tackle forward-selection-based procedures called iFOR, which identify interaction effects in a greedy forward fashion while maintaining the natural hierarchical model structure.
Surface Estimation, Variable Selection, and the Nonparametric Oracle Property.
This paper proposes a model selection procedure for nonparametric models, and explores the conditions under which the new method enjoys the aforementioned properties, and demonstrates that the new approach substantially outperforms other existing methods in the finite sample setting.