Related papers: Deflation-Free Optimal Scoring
We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…
Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to…
It is widely accepted that optimization of imaging system performance should be guided by task-based measures of image quality (IQ). It has been advocated that imaging hardware or data-acquisition designs should be optimized by use of an…
This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on sequential…
To better select the correct training sample and obtain the robust representation of the query sample, this paper proposes a discriminant-based sparse optimization learning model. This learning model integrates discriminant and sparsity…
Feature selection is a crucial step in machine learning, especially for high-dimensional datasets, where irrelevant and redundant features can degrade model performance and increase computational costs. This paper proposes a novel…
Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis…
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…
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to…
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two…
In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computational savings and improved scalability while preserving…
Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional…
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on…
Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic…
Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on model-based DFO methods, where an approximation of the objective function is used to guide…
Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…