Related papers: Sparse Linear Regression: Sequential Convex Relaxa…
The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its…
Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression…
State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference,…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
We introduce Renet, a principled generalization of the Relaxed Lasso to the Elastic Net family of estimators. While, on the one hand, $\ell_1$-regularization is a standard tool for variable selection in high-dimensional regimes and, on the…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
We consider solving a combinatorial optimization problem with unknown knapsack constraints using a membership oracle for each unknown constraint such that, given a solution, the oracle determines whether the constraint is satisfied or not…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Finding the sparse solution of an underdetermined system of linear equations has many applications, especially, it is used in Compressed Sensing (CS), Sparse Component Analysis (SCA), and sparse decomposition of signals on overcomplete…
Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in data analysis. The PCA direction is a linear combination of all features with nonzero loadings -- this impedes interpretability. Sparse PCA…
Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
We aim to compute lifted stationary points of a sparse optimization problem (P0) with complementarity constraints. We define a continuous relaxation problem (Rv) that has the same global minimizers and optimal value with problem (P0).…
We consider a linear regression $y=X\beta+u$ where $X\in\mathbb{\mathbb{{R}}}^{n\times p}$, $p\gg n,$ and $\beta$ is $s$-sparse. Motivated by examples in financial and economic data, we consider the situation where $X$ has highly correlated…