Related papers: Matrix Completion with Weighted Constraint for Hap…
Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
Rank minimization methods have attracted considerable interest in various areas, such as computer vision and machine learning. The most representative work is nuclear norm minimization (NNM), which can recover the matrix rank exactly under…
Large-scale general domain pretraining followed by downstream-specific finetuning has become a predominant paradigm in machine learning. However, discrepancies between the pretraining and target domains can still lead to performance…
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank…
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…
In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem…
Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries…
The single nucleotide polymorphism (SNP) is the most widely studied type of genetic variation. A haplotype is defined as the sequence of alleles at SNP sites on each haploid chromosome. Haplotype information is essential in unravelling the…
In this paper, we propose an analytical framework to quantify the amount of data samples needed to obtain accurate state estimation in a power system - a problem known as sample complexity analysis in computer science. Motivated by the…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…
Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In…
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…
In this article, we propose two quantitative methods for calculating weight vectors for incomplete pairwise comparison matrices using reference values. Both procedures are extensions of arithmetic and geometric heuristic estimation (HRE)…
The completion of matrices with missing values under the rank constraint is a non-convex optimization problem. A popular convex relaxation is based on minimization of the nuclear norm (sum of singular values) of the matrix. For this…
This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…