Related papers: Alignment and matching tests for high-dimensional …

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…

This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…

Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

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…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

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 theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…

We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace…

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…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called…

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…

In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear…

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…