Related papers: A variational approach to stable principal compone…

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…

This paper proposes a novel sparse principal component analysis algorithm with self-learning ability for successive modes, where synaptic intelligence is employed to measure the importance of variables and a regularization term is added to…

Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…

Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…

Seismic attributes calculated by conventional methods are susceptible to noise. Conventional filtering reduces the noise in the cost of losing the spectral bandwidth. The challenge of having a high-resolution and robust signal processing…

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

We propose a data-driven Model Predictive Control (MPC) framework that employs a transformer encoder to generate multi-step predictions. To handle the nonconvex attention mechanism, we derive difference of convex (DC) representations of the…

Direct numerical simulation of dense rigid body suspensions poses significant computational challenges. A popular approach to resolve collisions necessitates solving a linear complementary problem (LCP) per time step. Each matrix vector…

Methods for global measurement of transcript abundance such as microarrays and RNA-Seq generate datasets in which the number of measured features far exceeds the number of observations. Extracting biologically meaningful and experimentally…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting…

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…

Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…

The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN). In its original conception, this model was restricted to a cascade of convolutional…