相关论文: When Bayesian Tensor Completion Meets Multioutput …

In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…

We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of…

This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix…

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

Most contemporary multi-task learning methods assume linear models. This setting is considered shallow in the era of deep learning. In this paper, we present a new deep multi-task representation learning framework that learns cross-task…

The prevalent fully-connected tensor network (FCTN) has achieved excellent success to compress data. However, the FCTN decomposition suffers from slow computational speed when facing higher-order and large-scale data. Naturally, there…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical…