Related papers: Non-Concave Penalized Likelihood with NP-Dimension…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This…
Penalized regression methods, such as lasso and elastic net, are used in many biomedical applications when simultaneous regression coefficient estimation and variable selection is desired. However, missing data complicates the…
This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, they lack optimization techniques that guarantee global optimality in…
We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of…
Growing-dimensional data with likelihood unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted likelihood (PETL) for variable selection and parameter estimation for growing dimensional…
There has been an explosion of interest in using $l_1$-regularization in place of $l_0$-regularization for feature selection. We present theoretical results showing that while $l_1$-penalized linear regression never outperforms…
High-dimensional statistical learning (HDSL) has wide applications in data analysis, operations research, and decision-making. Despite the availability of multiple theoretical frameworks, most existing HDSL schemes stipulate the following…
Selecting interactions from an ultrahigh-dimensional statistical model with $n$ observations and $p$ variables when $p\gg n$ is difficult because the number of candidates for interactions is $p(p-1)/2$ and a selected model should satisfy…