Related papers: Nearly unbiased variable selection under minimax c…
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…
We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in…
The statistics literature of the past 15 years has established many favorable properties for sparse diminishing-bias regularization: techniques which can roughly be understood as providing estimation under penalty functions spanning the…
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…
Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine. Nowadays, this type of data is increasingly wide, sometimes containing thousands of…
Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…
Traditional variable selection methods could fail to be sign consistent when irrepresentable conditions are violated. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this…
In linear regression, SLOPE is a new convex analysis method that generalizes the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized more heavily. This magnitude-dependent regularization requires an input of penalty…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic…
We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…
Missing values in covariates due to censoring by signal interference or lack of sensitivity in the measuring devices are common in industrial problems. We propose a full Bayesian solution to the prediction problem with an efficient Markov…
We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…
Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…
Many statistical methods have been proposed for variable selection in the past century, but few balance inference and prediction tasks well. Here we report on a novel variable selection approach called Penalized regression with…
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
The root-cause diagnostics of product quality defects in multistage manufacturing processes often requires a joint identification of crucial stages and process variables. To meet this requirement, this paper proposes a novel penalized…
The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…