Related papers: Generalized Linear Models with Structured Sparsity…
For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…
In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
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…
Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…
In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold…
We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
Regularized m-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds,…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…
This paper proposes a bootstrap-assisted procedure to conduct simultaneous inference for high dimensional sparse linear models based on the recent de-sparsifying Lasso estimator (van de Geer et al. 2014). Our procedure allows the dimension…
It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…
We propose a new algorithmic framework for constrained compressed sensing models that admit nonconvex sparsity-inducing regularizers including the log-penalty function as objectives, and nonconvex loss functions such as the Cauchy loss…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…