Related papers: Information Theoretic Bounds for Low-Rank Matrix C…
Shannon's channel coding theorem characterizes the maximal rate of information that can be reliably transmitted over a communication channel when optimal encoding and decoding strategies are used. In many scenarios, however, practical…
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 novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…
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…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
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 novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general low rank setting. For positive data, we achieve results…
This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack…
In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data must be informative about the unknown parameters. How to…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions…
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…
We consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete-time channels with memory. The channels we consider can have a finite number of states, such as partial…
We consider the problem of multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We formulate it as a combinatorial optimization problem of arranging numbers in a matrix to minimize the…
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…
We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space, as well as the problem of finding an optimal partition of coordinates such that the…
Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these…