Related papers: A Majorization-Minimization Gauss-Newton Method fo…

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…

We consider fast algorithms for monotone submodular maximization subject to a matroid constraint. We assume that the matroid is given as input in an explicit form, and the goal is to obtain the best possible running times for important…

This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value via low-cost steps leveraging the nonconvex but smooth…

This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization…

Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…

Recent machine learning methods use increasingly large deep neural networks to achieve state of the art results in various tasks. The gains in performance come at the cost of a substantial increase in computation and storage requirements.…

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and…

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…

The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm…

We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between…

Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…

We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such…

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

Low-rank matrix estimation from incomplete measurements recently received increased attention due to the emergence of several challenging applications, such as recommender systems; see in particular the famous Netflix challenge. While the…

Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks, but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR…

Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support…

We consider the finite-sum optimization problem, where each component function is strongly convex and has Lipschitz continuous gradient and Hessian. The recently proposed incremental quasi-Newton method is based on BFGS update and achieves…

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…