English
Related papers

Related papers: Sparse Mixed Linear Regression with Guarantees: Ta…

200 papers

The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…

Computation and Language · Computer Science 2014-11-18 Miao Fan , Deli Zhao , Qiang Zhou , Zhiyuan Liu , Thomas Fang Zheng , Edward Y. Chang

A recent line of research termed unlabeled sensing and shuffled linear regression has been exploring under great generality the recovery of signals from subsampled and permuted measurements; a challenging problem in diverse fields of data…

Information Theory · Computer Science 2019-07-19 Manolis C. Tsakiris , Liangzu Peng

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

Statistics Theory · Mathematics 2008-10-15 Mohamed Hebiri

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this…

Machine Learning · Computer Science 2022-02-11 Dimitris Fotakis , Alkis Kalavasis , Eleni Psaroudaki

Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable"…

Machine Learning · Computer Science 2015-03-05 Luca Baldassarre , Nirav Bhan , Volkan Cevher , Anastasios Kyrillidis , Siddhartha Satpathi

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

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…

Information Theory · Computer Science 2013-11-13 Florent Krzakala , Marc Mézard , Lenka Zdeborová

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Statistics Theory · Mathematics 2016-11-17 D. Motamedvaziri , M. H. Rohban , V. Saligrama

Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods…

Machine Learning · Statistics 2015-01-13 Martin Sundin , Saikat Chatterjee , Magnus Jansson

The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…

Information Theory · Computer Science 2018-10-23 Ali Çivril

This paper introduces an algorithmic solution to a broader class of unlabeled sensing problems with multiple measurement vectors (MMV). The goal is to recover an unknown structured signal matrix, $\mathbf{X}$, from its noisy linear…

Information Theory · Computer Science 2024-06-13 Mohamed Akrout , Amine Mezghani , Faouzi Bellili

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…

Machine Learning · Statistics 2025-03-25 Yujing Liu , Zhixin Liu , Lei Guo

The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…

Methodology · Statistics 2017-01-25 Gerrit J. J. van den Burg , Patrick J. F. Groenen , Andreas Alfons

Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…

Machine Learning · Computer Science 2025-02-06 Aparna Gupte , Neekon Vafa , Vinod Vaikuntanathan

We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects…

Machine Learning · Statistics 2017-03-09 Karthikeyan Shanmugam , Murat Kocaoglu , Alexandros G. Dimakis , Sujay Sanghavi

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

Information Theory · Computer Science 2017-06-20 Alyson K. Fletcher , Mojtaba Sahraee-Ardakan , Philip Schniter , Sundeep Rangan

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 propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…

Information Theory · Computer Science 2017-03-17 Sohail Bahmani , Justin Romberg

Machine learning has played an important role in information retrieval (IR) in recent times. In search engines, for example, query keywords are accepted and documents are returned in order of relevance to the given query; this can be cast…

Machine Learning · Statistics 2018-02-13 Tatsuhiro Aoshima , Kei Kobayashi , Mihoko Minami