Related papers: Matrix Completion under Interval Uncertainty
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
The Nystrom method is an efficient technique to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by…
A new message-passing (MP) method is considered for the matrix completion problem associated with recommender systems. We attack the problem using a (generative) factor graph model that is related to a probabilistic low-rank matrix…
Estimating uncertainty in image-to-image networks is an important task, particularly as such networks are being increasingly deployed in the biological and medical imaging realms. In this paper, we introduce a new approach to this problem…
The noisy matrix completion problem, which aims to recover a low-rank matrix $\mathbf{X}$ from a partial, noisy observation of its entries, arises in many statistical, machine learning, and engineering applications. In this paper, we…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…
Cutting out an object and estimating its opacity mask, known as image matting, is a key task in image and video editing. Due to the highly ill-posed issue, additional inputs, typically user-defined trimaps or scribbles, are usually needed…
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…
Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely…
This paper investigates the asymmetric low-rank matrix completion problem, which can be formulated as an unconstrained non-convex optimization problem with a nonlinear least-squares objective function, and is solved via gradient descent…
The parallel full approximation scheme in space and time (PFASST) is a parallel-in-time integrator that allows to integrate multiple time-steps simultaneously. It has been shown to extend scaling limits of spatial parallelization strategies…
We consider the problem of uncertainty quantification for an unknown low-rank matrix $\mathbf{X}$, given a partial and noisy observation of its entries. This quantification of uncertainty is essential for many real-world problems, including…
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
The use of quaternions as a novel tool for color image representation has yielded impressive results in color image processing. By considering the color image as a unified entity rather than separate color space components, quaternions can…
Pairwise comparison matrix as a crucial component of AHP, presents the prefer- ence relations among alternatives. However, in many cases, the pairwise comparison matrix is difficult to complete, which obstructs the subsequent operations of…
Recovering a dense depth image from sparse LiDAR scans is a challenging task. Despite the popularity of color-guided methods for sparse-to-dense depth completion, they treated pixels equally during optimization, ignoring the uneven…
Matrix completion problem has been investigated under many different conditions since Netflix announced the Netflix Prize problem. Many research work has been done in the field once it has been discovered that many real life dataset could…