Related papers: Entry-Specific Matrix Estimation under Arbitrary S…
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…
Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between…
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence $\mathbf{d} \in \mathbb{Z}_+^n$. This matrix arises in a variety of analyses of networked data sets, including modularity-maximization and…
In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…
Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…
Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially…
Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
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…
Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…
Autoencoders are popular among neural-network-based matrix completion models due to their ability to retrieve potential latent factors from the partially observed matrices. Nevertheless, when training data is scarce their performance is…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
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…
This paper proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor…
We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank…