Related papers: Tensor methods for the computation of MTTA in larg…

Surrogate models can reduce computational costs for multivariable functions with an unknown internal structure (black boxes). In a discrete formulation, surrogate modeling is equivalent to restoring a multidimensional array (tensor) from a…

Mining massive spatio-temporal data can help a variety of real-world applications such as city capacity planning, event management, and social network analysis. The tensor representation can be used to capture the correlation between space…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…

In power system dynamic simulation, up to 90% of the computational time is devoted to solve the network equations, i.e., a set of linear equations. Traditional approaches are based on sparse LU factorization, which is inherently sequential.…

Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

One of the fundamental problems of using optimization models that use different time series as data input, is the trade-off between model accuracy and computational tractability. To overcome the computational intractability of these full…

An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$.…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…

This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments…

Tensor structured Markov chains are part of stochastic models of many practical applications, e.g., in the description of complex production or telephone networks. The most interesting question in Markov chain models is the determination of…

We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the…

In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…

We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose…

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…