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In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…

Statistics Theory · Mathematics 2020-05-05 Emmanuel Caron , Jérôme Dedecker , Bertrand Michel

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…

Statistics Theory · Mathematics 2007-06-13 David R. Hunter , Runze Li

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Artificial Intelligence · Computer Science 2007-07-06 Onureena Banerjee , Laurent El Ghaoui , Alexandre d'Aspremont

We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…

Statistics Theory · Mathematics 2010-09-14 Felix Abramovich , Vadim Grinshtein

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…

Methodology · Statistics 2012-02-28 Nicolas Städler , Peter Bühlmann , Sara van de Geer

Despite recent advances in algorithmic fairness, methodologies for achieving fairness with generalized linear models (GLMs) have yet to be explored in general, despite GLMs being widely used in practice. In this paper we introduce two…

Machine Learning · Statistics 2022-06-22 Hyungrok Do , Preston Putzel , Axel Martin , Padhraic Smyth , Judy Zhong

We tackle the problem of penalty selection of regularization on the basis of the minimum description length (MDL) principle. In particular, we consider that the design space of the penalty function is high-dimensional. In this situation,…

Machine Learning · Statistics 2018-04-27 Kohei Miyaguchi , Kenji Yamanishi

We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…

Methodology · Statistics 2010-09-14 Minh-Ngoc Tran , David Nott , Chenlei Leng

Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…

Methodology · Statistics 2016-01-06 Jiahe Lin , Sumanta Basu , Moulinath Banerjee , George Michailidis

High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…

Machine Learning · Statistics 2011-11-11 Yiyuan She

Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…

Methodology · Statistics 2022-06-27 Julien St-Pierre , Karim Oualkacha , Sahir Rai Bhatnagar

This article investigates unsupervised classification techniques for categorical multivariate data. The study employs multivariate multinomial mixture modeling, which is a type of model particularly applicable to multilocus genotypic data.…

Statistics Theory · Mathematics 2014-03-11 Dominique Bontemps , Wilson Toussile

We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…

Statistics Theory · Mathematics 2015-06-04 Gourab Mukherjee , Iain M. Johnstone

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

Methodology · Statistics 2016-07-04 Abhik Ghosh , Ayanendranath Basu

We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…

Methodology · Statistics 2023-04-28 Anatoli Juditsky , Arkadi Nemirovski , Yao Xie , Chen Xu

This work establishes regularity conditions for consistency and asymptotic normality of the multiple parameter maximum likelihood estimator(MLE) from censored data, where the censoring mechanism is in the form of $1$-bit measurements. The…

Statistics Theory · Mathematics 2025-02-11 Jaimin Shah , Martina Cardone , Cynthia Rush , Alex Dytso

In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice…

Machine Learning · Statistics 2019-04-01 Jean Feng , Noah Simon

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…

Machine Learning · Statistics 2026-05-15 Ryan Thompson , Matt P. Wand , Joanna J. J. Wang

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Methodology · Statistics 2026-03-03 Linglingzhi Zhu , Jonghyeok Lee , Yao Xie

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

Statistics Theory · Mathematics 2013-02-19 Felix Abramovich , Vadim Grinshtein