Log In Sign Up

Alternating linear scheme in a Bayesian framework for low-rank tensor approximation

by   Clara Menzen, et al.

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets can be facilitated. In this paper, we find a low-rank representation for a given tensor by solving a Bayesian inference problem. This is achieved by dividing the overall inference problem into sub-problems where we sequentially infer the posterior distribution of one tensor decomposition component at a time. This leads to a probabilistic interpretation of the well-known iterative algorithm alternating linear scheme (ALS). In this way, the consideration of measurement noise is enabled, as well as the incorporation of application-specific prior knowledge and the uncertainty quantification of the low-rank tensor estimate. To compute the low-rank tensor estimate from the posterior distributions of the tensor decomposition components, we present an algorithm that performs the unscented transform in tensor train format.


page 24

page 25


Solving for the low-rank tensor components of a scattering wave function

Atomic and molecular breakup reactions, such as multiple-ionisation, are...

Tensor-based EDMD for the Koopman analysis of high-dimensional systems

Recent years have seen rapid advances in the data-driven analysis of dyn...

Bayesian inversion for electromyography using low-rank tensor formats

The reconstruction of the structure of biological tissue using electromy...

Nonlinear system identification with regularized Tensor Network B-splines

This article introduces the Tensor Network B-spline model for the regula...

Soft Tensor Regression

Statistical methods relating tensor predictors to scalar outcomes in a r...

A low-rank tensor method to reconstruct sparse initial states for PDEs with Isogeometric Analysis

When working with PDEs the reconstruction of a previous state often prov...

High-Dimensional Uncertainty Quantification via Active and Rank-Adaptive Tensor Regression

Uncertainty quantification based on stochastic spectral methods suffers ...