相关论文: Structured Backward Errors of Sparse Generalized S…

This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

Structured sparsity accelerates training and inference on modern GPUs, yet it still trails unstructured dynamic sparse training (DST) in accuracy. The shortfall stems from a loss of expressivity: whereas a dense layer can realize every…

We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…

We propose a general algorithmic framework for Bayesian model selection. A spike-and-slab Laplacian prior is introduced to model the underlying structural assumption. Using the notion of effective resistance, we derive an EM-type algorithm…

In this paper, we propose a unified approach for solving structure-preserving eigenvalue embedding problem (SEEP) for quadratic regular matrix polynomials with symmetry structures. First, we determine perturbations of a quadratic matrix…

Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator…

The classical WKB method (also known as the WKBJ method, the LG method, or the phase integral method) for solving singularly perturbed linear differential equations has never, as far as we know, been looked at from the structured backward…

For a given class of structured matrices $\mathbb S$, we find necessary and sufficient conditions on vectors $x,w\in \C^{n+m}$ and $y,z \in \C^{n}$ for which there exists $\Delta=[\Delta_1~\Delta_2]$ with $\Delta_1 \in \mathbb S$ and…

Exploiting sparsity enables hardware systems to run neural networks faster and more energy-efficiently. However, most prior sparsity-centric optimization techniques only accelerate the forward pass of neural networks and usually require an…

We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in…

Recently, Krukier et al. [Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems, Numer. Linear Algebra Appl. 21 (2014) 152-170] proposed an efficient generalized skew-Hermitian triangular…

Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…