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Related papers: Sparsity Within and Across Overlapping Groups

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In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…

Optimization and Control · Mathematics 2025-08-05 Thibaut Bourdais , Nadia Oudjane , Francesco Russo

We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either…

Machine Learning · Computer Science 2012-06-22 Junming Yin , Xi Chen , Eric Xing

The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…

Numerical Analysis · Mathematics 2014-05-12 Gang Liu , Ting-Zhu Huang , Xiao-Guang Lv , Jun Liu

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…

Methodology · Statistics 2009-05-05 Junzhou Huang , Tong Zhang , Dimitris Metaxas

In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…

Optimization and Control · Mathematics 2025-08-14 Lechen Feng , Xun Li , Yuan-Hua Ni

This paper develops a unified nonconvex optimization framework for the design of group-sparse feedback controllers in infinite-horizon linear-quadratic (LQ) problems. We address two prominent extensions of the classical LQ problem: the…

Optimization and Control · Mathematics 2025-08-06 Lechen Feng , Xun Li , Yuan-Hua Ni

Recent work in signal processing and statistics have focused on defining new regularization functions, which not only induce sparsity of the solution, but also take into account the structure of the problem. We present in this paper a class…

Machine Learning · Computer Science 2011-10-21 Julien Mairal , Rodolphe Jenatton , Guillaume Obozinski , Francis Bach

In this work we propose and analyze a novel approach for group sparse recovery. It is based on regularized least squares with an $\ell^0(\ell^2)$ penalty, which penalizes the number of nonzero groups. One distinct feature of the approach is…

Information Theory · Computer Science 2016-12-21 Yuling Jiao , Bangti Jin , Xiliang Lu

Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…

Quantum Physics · Physics 2023-03-20 Maike Drieb-Schön , Kilian Ender , Younes Javanmard , Wolfgang Lechner

This paper deals with the problem of large-scale linear supervised learning in settings where a large number of continuous features are available. We propose to combine the well-known trick of one-hot encoding of continuous features with a…

Machine Learning · Statistics 2019-01-10 Mokhtar Z. Alaya , Simon Bussy , Stéphane Gaïffas , Agathe Guilloux

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical $L_2$ norms and the reproducing kernel Hilbert space (RKHS) norms induced by…

Statistics Theory · Mathematics 2012-11-14 Vladimir Koltchinskii , Ming Yuan

We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a more general penalty that blends the…

Statistics Theory · Mathematics 2010-01-06 J. Friedman , T. Hastie , R. Tibshirani

We consider the problem of forecasting the aggregate demand of a pool of price-responsive consumers of electricity. The price-response of the aggregation is modeled by an optimization problem that is characterized by a set of marginal…

Optimization and Control · Mathematics 2016-07-26 Javier Saez-Gallego , Juan M. Morales

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…

Numerical Analysis · Mathematics 2016-12-30 Sergey Voronin , Ingrid Daubechies

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

Information Theory · Computer Science 2021-01-15 Zeljko Kereta , Johannes Maly , Valeriya Naumova

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,…

Methodology · Statistics 2014-06-10 Yuancheng Zhu , Rina Foygel Barber

This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…

Optimization and Control · Mathematics 2016-04-19 Ivan W. Selesnick , Iker Bayram

In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct…

Machine Learning · Statistics 2014-07-08 Zhihua Zhang , Shibo Zhao , Zebang Shen , Shuchang Zhou

We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art…

Machine Learning · Statistics 2016-04-28 Marc Goessling , Yali Amit

In certain applications it is useful to fit multinomial distributions to observed data with a penalty term that encourages sparsity. For example, in probabilistic latent audio source decomposition one may wish to encode the assumption that…

Sound · Computer Science 2010-09-30 Matthew D. Hoffman