Related papers: Bayesian Matrix Completion via Adaptive Relaxed Sp…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
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…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. However, regularization often shrinks the estimator for relevant features,…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
We study exact matrix completion from partially available data with hidden connectivity patterns. Exact matrix completion was shown to be possible recently by Cosse and Demanet in 2021 with Lasserre's relaxation using the trace of the…
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),…
It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…
Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
This paper presents a new Bayesian estimation technique for hidden Potts-Markov random fields with unknown regularisation parameters, with application to fast unsupervised K-class image segmentation. The technique is derived by first…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…