Related papers: Group-Aware Matrix Estimation and Latent Subspace …

We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…

This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them. Given multiple matches computed between a few…

Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on…

Complex multilayer network datasets have become ubiquitous in various applications, including neuroscience, social sciences, economics, and genetics. Notable examples include brain connectivity networks collected across multiple patients or…

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 present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty.…

Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…

A common explanation for the failure of deep networks to generalize out-of-distribution is that they fail to recover the "correct" features. We challenge this notion with a simple experiment which suggests that ERM already learns sufficient…

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…

In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…

We study contextual bandits with low-rank structure where, in each round, if the (context, arm) pair $(i,j)\in [m]\times [n]$ is selected, the learner observes a noisy sample of the $(i,j)$-th entry of an unknown low-rank reward matrix.…

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…

We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Large Language Models (LLMs) have emerged as powerful tools for passage reranking in information retrieval, leveraging their superior reasoning capabilities to address the limitations of conventional models on complex queries. However,…