Related papers: Matrix Completion with Nonconvex Regularization: S…
Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…
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…
This paper focuses on recovering an underlying matrix from its noisy partial entries, a problem commonly known as matrix completion. We delve into the investigation of a non-convex regularization, referred to as transformed $L_1$ (TL1),…
We study the problem of symmetric positive semi-definite low-rank matrix completion (MC) with deterministic entry-dependent sampling. In particular, we consider rectified linear unit (ReLU) sampling, where only positive entries are…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…
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…
We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…
We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…
Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature,…
In this paper, we consider the streaming memory-limited matrix completion problem when the observed entries are noisy versions of a small random fraction of the original entries. We are interested in scenarios where the matrix size is very…
Nonconvex methods have emerged as a dominant approach for low-rank matrix estimation, a problem that arises widely in machine learning and AI for learning and representing high-dimensional data. Existing analyses for these methods often…
We study the closure of the projection of the (nonconvex) cone of rank restricted positive semidefinite matrices onto subsets of the matrix entries. This defines the feasible sets for semidefinite completion problems with restrictions on…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm based relaxed…