
An Iterative Method for Structured Matrix Completion
The task of fillingin or predicting missing entries of a matrix, from a...
read it

Calibrated Elastic Regularization in Matrix Completion
This paper concerns the problem of matrix completion, which is to estima...
read it

Adaptive Estimation of Noise Variance and Matrix Estimation via USVT Algorithm
Consider the problem of denoising a large m× n matrix. This problem has ...
read it

Obtaining errorminimizing estimates and universal entrywise error bounds for lowrank matrix completion
We propose a general framework for reconstructing and denoising single e...
read it

Matrix Completion for Structured Observations
The need to predict or fillin missing data, often referred to as matrix...
read it

Innetwork Sparsityregularized Rank Minimization: Algorithms and Applications
Given a limited number of entries from the superposition of a lowrank m...
read it

Graphon Estimation from Partially Observed Network Data
We consider estimating the edgeprobability matrix of a network generate...
read it
Matrix completion with datadependent missingness probabilities
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and nuclear norm minimization. Most of the past works on this subject assume that there is a single number p such that each entry of the matrix is available independently with probability p and missing otherwise. This assumption may not be realistic for many applications. In this work, we replace it with the assumption that the probability that an entry is available is an unknown function f of the entry itself. For example, if the entry is the rating given to a movie by a viewer, then it seems plausible that high value entries have greater probability of being available than low value entries. We propose two new estimators, based on singular value thresholding and nuclear norm minimization, to recover the matrix under this assumption. The estimators are shown to be consistent under a low rank assumption. We also provide a consistent estimator of the unknown function f.
READ FULL TEXT
Comments
There are no comments yet.