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Related papers: Classification with Sparse Overlapping Groups

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Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…

Machine Learning · Statistics 2015-05-19 Pablo Sprechmann , Ignacio Ramírez , Guillermo Sapiro , Yonina Eldar

We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the…

Machine Learning · Statistics 2011-10-05 Guillaume Obozinski , Laurent Jacob , Jean-Philippe Vert

In several applications, input samples are more naturally represented in terms of similarities between each other, rather than in terms of feature vectors. In these settings, machine-learning algorithms can become very computationally…

Computer Vision and Pattern Recognition · Computer Science 2017-12-19 Ambra Demontis , Marco Melis , Battista Biggio , Giorgio Fumera , Fabio Roli

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…

Statistics Theory · Mathematics 2010-11-30 Fengrong Wei , Jian Huang

We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern,…

Statistics Theory · Mathematics 2012-08-21 Karim Lounici , Massimiliano Pontil , Alexandre B. Tsybakov , Sara van de Geer

Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM)…

Methodology · Statistics 2017-12-04 Xiaohan Yan , Jacob Bien

We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…

Methodology · Statistics 2018-10-25 J. Kenneth Tay , Jerome Friedman , Robert Tibshirani

Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…

Machine Learning · Statistics 2012-04-09 Suvrit Sra

Recently, to solve large-scale lasso and group lasso problems, screening rules have been developed, the goal of which is to reduce the problem size by efficiently discarding zero coefficients using simple rules independently of the others.…

Machine Learning · Statistics 2014-10-28 Seunghak Lee , Eric P. Xing

Sparse feature selection is necessary when we fit statistical models, we have access to a large group of features, don't know which are relevant, but assume that most are not. Alternatively, when the number of features is larger than the…

Applications · Statistics 2017-04-04 Emiliano Diaz

One of the most important steps toward interpretability and explainability of neural network models is feature selection, which aims to identify the subset of relevant features. Theoretical results in the field have mostly focused on the…

Machine Learning · Computer Science 2020-10-19 Vu Dinh , Lam Si Tung Ho

We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…

Statistics Theory · Mathematics 2023-01-18 Tomer Levy , Felix Abramovich

In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…

Methodology · Statistics 2010-06-08 X. Jessie Jeng And Z. John Daye

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

Machine Learning · Statistics 2013-02-28 Aleksandr Y. Aravkin , James V. Burke , Alessandro Chiuso , Gianluigi Pillonetto

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Data Structures and Algorithms · Computer Science 2023-05-29 Jonathan Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…

Machine Learning · Statistics 2012-08-21 Karim Lounici , Massimiliano Pontil , Alexandre B. Tsybakov , Sara van de Geer

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

Methodology · Statistics 2019-06-25 Jean Feng , Noah Simon

Much work has been done recently to make neural networks more interpretable, and one obvious approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or $\ell_1$-regularized) regression…

Machine Learning · Statistics 2021-06-17 Ismael Lemhadri , Feng Ruan , Louis Abraham , Robert Tibshirani

Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible…

Machine Learning · Statistics 2024-01-03 Ryan Thompson , Amir Dezfouli , Robert Kohn

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group…

Statistics Theory · Mathematics 2013-01-07 Jian Huang , Patrick Breheny , Shuangge Ma