Related papers: Sparse Polynomial Regression under Anomalous Data

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive…

Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…

This paper studies the problem of reconstructing spectrally sparse signals from a small random subset of time domain samples via low-rank Hankel matrix completion with the aid of prior information. By leveraging the low-rank structure of…

Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…

In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from…

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…

The econometric challenge of finding sparse mean reverting portfolios based on a subset of a large number of assets is well known. Many current state-of-the-art approaches fall into the field of co-integration theory, where the problem is…

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…

Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…

We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. We derive a baseline algorithm called LinBreg, an accelerated…

We develop and analyze a new `relax-and-split' (RS) approach for compositions of separable nonconvex nonsmooth functions with linear maps. RS uses a relaxation technique together with partial minimization, and brings classic techniques…

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…

Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…

Nowadays, it is still difficult to adapt Convolutional Neural Network (CNN) based models for deployment on embedded devices. The heavy computation and large memory footprint of CNN models become the main burden in real application. In this…

High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension…

We present a novel method for exact hierarchical sparse polynomial regression. Our regressor is that degree $r$ polynomial which depends on at most $k$ inputs, counting at most $\ell$ monomial terms, which minimizes the sum of the squares…

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…