相关论文: A Novel Approach to Quantized Matrix Completion Us…

We study the robust matrix completion (RMC) problem subject to both sparse outliers and stochastic noise. A non-convex method termed Accelerated Robust Matrix Completion (ARMC) is proposed, which accelerates a prior non-convex approach by…

In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the…

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

Deploying transformer-based neural networks on resource-constrained edge devices presents a significant challenge. This challenge is often addressed through various techniques, such as low-rank approximation and mixed-precision…

Neural networks have achieved remarkable success in many cognitive tasks. However, when they are trained sequentially on multiple tasks without access to old data, their performance on early tasks tend to drop significantly. This problem is…

Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…

We introduce a new method to reconstruct the density matrix $\rho$ of a system of $n$-qubits and estimate its rank $d$ from data obtained by quantum state tomography measurements repeated $m$ times. The procedure consists in minimizing the…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…

This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…

We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the…

Hydro unit commitment is the problem of maximizing water use efficiency while minimizing start-up costs in the daily operation of multiple hydro plants, subject to constraints on short-term reservoir operation, and long-term goals. A…

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…