相关论文: Minimal Polynomial and Reduced Rank Extrapolation …

We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the…

A popular robust alternative of the classic principal component analysis (PCA) is the $\ell_1$-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the $\ell_1$-norm. L1-PCA has shown…

In this paper, we analyze the convergence behavior of the randomized extended Kaczmarz (REK) method for all types of linear systems (consistent or inconsistent, overdetermined or underdetermined, full-rank or rank-deficient). The analysis…

Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…

Mutual exclusion (ME) is one of the most commonly used techniques to handle conflicts in concurrent systems. Traditionally, mutual exclusion algorithms have been designed under the assumption that a process does not fail while…

We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…

A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…

Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However,…

Rotary Position Embedding (RoPE)-extension refers to modifying or generalizing the Rotary Position Embedding scheme to handle longer sequences than those encountered during pre-training. However, current extension strategies are highly…

The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…

Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…

In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying…

A new approximation format for solutions of partial differential equations depending on infinitely many parameters is introduced. By combining low-rank tensor approximation in a selected subset of variables with a sparse polynomial…

The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the…

While most current approaches rely on further training techniques, such as fine-tuning or reinforcement learning, to enhance model capacities, model merging stands out for its ability of improving models without requiring any additional…

Riemannian convex optimization and minimax optimization have recently drawn considerable attention. Their appeal lies in their capacity to adeptly manage the non-convexity of the objective function as well as constraints inherent in the…

Multimodal relation extraction (MRE) is the task of identifying the semantic relationships between two entities based on the context of the sentence image pair. Existing retrieval-augmented approaches mainly focused on modeling the…

We propose the residual expansion (RE) algorithm: a global (or near-global) optimization method for nonconvex least squares problems. Unlike most existing nonconvex optimization techniques, the RE algorithm is not based on either stochastic…