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We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…

Statistics Theory · Mathematics 2011-03-15 Pierre Alquier , Karim Lounici

We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long…

Machine Learning · Statistics 2015-08-12 Jason D. Lee , Yuekai Sun , Qiang Liu , Jonathan E. Taylor

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

Methodology · Statistics 2022-11-14 Szymon Nowakowski , Piotr Pokarowski , Wojciech Rejchel , Agnieszka Sołtys

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical…

Machine Learning · Statistics 2009-03-17 Junzhou Huang , Tong Zhang

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

Machine Learning · Computer Science 2015-06-05 Paolo Di Lorenzo , Ali H. Sayed

We study the problem of selecting features associated with extreme values in high dimensional linear regression. Normally, in linear modeling problems, the presence of abnormal extreme values or outliers is considered an anomaly which…

Methodology · Statistics 2021-06-16 Andersen Chang , Minjie Wang , Genevera Allen

Prediction rule ensembles (PRE) provide interpretable prediction models with relatively high accuracy.PRE obtain a large set of decision rules from a (boosted) decision tree ensemble, and achieves sparsitythrough application of…

Machine Learning · Statistics 2021-09-29 Benny Markovitch , Marjolein Fokkema

We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…

Statistics Theory · Mathematics 2014-12-16 Jacob Steinhardt , Stefan Wager , Percy Liang

The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…

Methodology · Statistics 2023-05-10 Shaoxiong Hu , Hugo Maruri-Aguliar , Zixiang Ma

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

Methodology · Statistics 2025-02-28 Samhita Pal , Subhashis Ghoshal

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…

Methodology · Statistics 2012-01-05 Kei Hirose , Shohei Tateishi , Sadanori Konishi

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…

Statistics Theory · Mathematics 2014-02-25 Divyanshu Vats , Richard G. Baraniuk

We consider high-dimensional inference when the assumed linear model is misspecified. We describe some correct interpretations and corresponding sufficient assumptions for valid asymptotic inference of the model parameters, which still have…

Methodology · Statistics 2015-08-20 Peter Bühlmann , Sara van de Geer

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

Optimization and Control · Mathematics 2025-01-08 Dimitris Bertsimas , Jean Pauphilet , Bart Van Parys

Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…

Methodology · Statistics 2015-06-12 Hamed Haselimashhadi

Sparse prediction with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection…

Methodology · Statistics 2021-12-22 Szymon Nowakowski , Piotr Pokarowski , Wojciech Rejchel

This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix $\O$ and the difference $\de$ of the mean vectors, we…

Methodology · Statistics 2011-07-19 Tony Cai , Weidong Liu

This study investigates the estimation and the statistical inference about Conditional Average Treatment Effects (CATEs), which have garnered attention as a metric representing individualized causal effects. In our data-generating process,…

Methodology · Statistics 2024-03-07 Masahiro Kato

Lasso regression is a widely employed approach within the $\ell_1$ regularization framework used to promote sparsity and recover piecewise smooth signals $f:[a,b) \rightarrow \mathbb{R}$ when the given observations are obtained from noisy,…

Numerical Analysis · Mathematics 2025-07-01 Yao Xiao , Anne Gelb , Aditya Viswanathan

Common high-dimensional methods for prediction rely on having either a sparse signal model, a model in which most parameters are zero and there are a small number of non-zero parameters that are large in magnitude, or a dense signal model,…

Methodology · Statistics 2017-09-29 Victor Chernozhukov , Christian Hansen , Yuan Liao