Related papers: Information Theory of Matrix Completion

We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…

With the huge influx of various data nowadays, extracting knowledge from them has become an interesting but tedious task among data scientists, particularly when the data come in heterogeneous form and have missing information. Many data…

Matrix completion under interval uncertainty can be cast as matrix completion with element-wise box constraints. We present an efficient alternating-direction parallel coordinate-descent method for the problem. We show that the method…

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…

One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to…

In a multi-access channel, completion time refers to the number of channel uses required for users, each with some given fixed bit pool, to complete the transmission of all their data bits. In this paper, the characterization of the…

The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite…

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

In this paper, we present a flexible low-rank matrix completion (LRMC) approach for topological interference management (TIM) in the partially connected K-user interference channel. No channel state information (CSI) is required at the…

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to…

Avoiding overfitting is a central challenge in machine learning, yet many large neural networks readily achieve zero training loss. This puzzling contradiction necessitates new approaches to the study of overfitting. Here we quantify…

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…

We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete

We present algorithms for the Max-Cover and Max-Unique-Cover problems in the data stream model. The input to both problems are $m$ subsets of a universe of size $n$ and a value $k\in [m]$. In Max-Cover, the problem is to find a collection…

A new information theoretic condition is presented for reconstructing a discrete random variable $X$ based on the knowledge of a set of discrete functions of $X$. The reconstruction condition is derived from Shannon's 1953 lattice theory…

Matrix completion has become an extremely important technique as data scientists are routinely faced with large, incomplete datasets on which they wish to perform statistical inferences. We investigate how error introduced via matrix…

We solve the Matrix Completion (MC) problem based on manifold optimization by incorporating the side information under which the columns of the intended matrix are drawn from a union of low dimensional subspaces. It is proved that this side…

This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical…