Related papers: Completing correlation matrices

The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…

The rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite-dimensional positive-definite Toeplitz matrix…

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to…

We address the rectangular matrix completion problem by lifting the unknown matrix to a positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over the semidefinite factor using a simple gradient descent…

We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex…

Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely…

In this paper we study the complementarity spectrum of digraphs, with special attention to the problem of digraph characterization through this complementarity spectrum. That is, whether two non-isomorphic digraphs with the same number of…

The matrix completion problem has been studied broadly under many underlying conditions. The problem has been explored under adaptive or non-adaptive, exact or estimation, single-phase or multi-phase, and many other categories. In most of…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Multi-task learning has attracted much attention due to growing multi-purpose research with multiple related data sources. Moreover, transduction with matrix completion is a useful method in multi-label learning. In this paper, we propose a…

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…

This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…

We present an efficient algorithm for the construction of a holographic simple tree graph model that realizes a given entropy vector, subject to a specific ``chordality'' condition first introduced in arXiv:2412.18018. We further develop…

Matrix completion is a widely adopted framework in recommender systems, as predicting the missing entries in the user-item rating matrix enables a comprehensive understanding of user preferences. However, current graph neural network…

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…

Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…

Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the…

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…