Related papers: Mixture Matrix Completion
We consider the problem of completing a matrix with categorical-valued entries from partial observations. This is achieved by extending the formulation and theory of one-bit matrix completion. We recover a low-rank matrix $X$ by maximizing…
CMF is a technique for simultaneously learning low-rank representations based on a collection of matrices with shared entities. A typical example is the joint modeling of user-item, item-property, and user-feature matrices in a recommender…
We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
The Netflix problem (from machine learning) asks the following. Given a ratings matrix in which each entry $(i,j)$ represents the rating of movie $j$ by customer $i$, if customer $i$ has watched movie $j$, and is otherwise missing, we would…
Choi and Yuan (2025) propose a novel approach to applying matrix completion to the problem of estimating causal effects in panel data. The key insight is that even in the presence of structured patterns of missing data -- i.e. selection…
The Rank Minimization Problem asks to find a matrix of lowest rank inside a linear variety of the space of n x n matrices. The Low Rank Matrix Completion problem asks to complete a partially filled matrix such that the resulting matrix has…
The need to predict or fill-in missing data, often referred to as matrix completion, is a common challenge in today's data-driven world. Previous strategies typically assume that no structural difference between observed and missing entries…
In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank…
There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…
We consider a challenging multi-label classification problem where both feature matrix $\X$ and label matrix $\Y$ have missing entries. An existing method concatenated $\X$ and $\Y$ as $[\X; \Y]$ and applied a matrix completion (MC) method…
Recommender systems are one of the most applied methods in machine learning and find applications in many areas, ranging from economics to the Internet of things. This article provides a general overview of modern approaches to recommender…
Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits certain block-wise missing structures -- specifically, where…
Large-scale population-based studies in medicine are a key resource towards better diagnosis, monitoring, and treatment of diseases. They also serve as enablers of clinical decision support systems, in particular Computer Aided Diagnosis…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
A standard model for Recommender Systems is the Matrix Completion setting: given partially known matrix of ratings given by users (rows) to items (columns), infer the unknown ratings. In the last decades, few attempts where done to handle…
In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…
Probe-level microarray data are usually stored in matrices, where the row and column correspond to array and probe, respectively. Scientists routinely summarize each array by a single index as the expression level of each probe set (gene).…
A fundamental component of modern trackers is an online learned tracking model, which is typically modeled either globally or locally. The two kinds of models perform differently in terms of effectiveness and robustness under different…
Recommendation Systems apply Information Retrieval techniques to select the online information relevant to a given user. Collaborative Filtering is currently most widely used approach to build Recommendation System. CF techniques uses the…