Related papers: Tensor Completion for Weakly-dependent Data on Gra…
The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…
Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…
Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…
Wireless edge caching is a popular strategy to avoid backhaul congestion in the next generation networks, where the content is cached in advance at base stations to serve redundant requests during peak congestion periods. In the edge…
This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples.…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Because tensor data appear more and more frequently in various scientific researches and real-world applications, analyzing the relationship between tensor features and the univariate outcome becomes an elementary task in many fields. To…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
In the field of brain science, data sharing across servers is becoming increasingly challenging due to issues such as industry competition, privacy security, and administrative procedure policies and regulations. Therefore, there is an…
Tensor completion aimes at recovering missing data, and it is one of the popular concerns in deep learning and signal processing. Among the higher-order tensor decomposition algorithms, the recently proposed fully-connected tensor network…
Effective modeling of heterogeneous subpopulations presents a significant challenge due to variations in individual characteristics and behaviors. This paper proposes a novel approach to address this issue through multi-task learning (MTL)…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
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…