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Missing value problem in spatiotemporal traffic data has long been a challenging topic, in particular for large-scale and high-dimensional data with complex missing mechanisms and diverse degrees of missingness. Recent studies based on…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…

Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…

We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…

Unsupervised contrastive learning has become a hot research topic in natural language processing. Existing works usually aim at constraining the orientation distribution of the representations of positive and negative samples in the…

Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the…

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…

Low rank tensor approximation is a fundamental tool in modern machine learning and data science. In this paper, we study the characterization, perturbation analysis, and an efficient sampling strategy for two primary tensor CUR…

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized…

The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary…

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…

In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schr\"odinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored…

Time series prediction has been a long-standing research topic and an essential application in many domains. Modern time series collected from sensor networks (e.g., energy consumption and traffic flow) are often large-scale and incomplete…

Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a better nonconvex…

Efficient sampling of two-dimensional statistical physics systems remains a central challenge in computational statistical physics. Traditional Markov chain Monte Carlo (MCMC) methods, including cluster algorithms, provide only partial…

Certain classes of CUR algorithms, also referred to as cross or pseudoskeleton algorithms, are widely used for low-rank matrix approximation when direct access to all matrix entries is costly. Their key advantage lies in constructing a…

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or…

Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to…