Related papers: Low-Rank Tensors for Multi-Dimensional Markov Mode…

Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…

Recently it has been shown that tensor networks (TNs) have the ability to represent the expected return of a single-agent finite Markov decision process (FMDP). The TN represents a distribution model, where all possible trajectories are…

There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…

In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the…

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,…

We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of…

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

Context information plays an indispensable role in the success of semantic segmentation. Recently, non-local self-attention based methods are proved to be effective for context information collection. Since the desired context consists of…

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…