Tensor train approximation of multivariate Gaussian density by scaling and squaring

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43976500" target="_blank" >RIV/49777513:23520/25:43976500 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s11222-025-10707-6" target="_blank" >https://doi.org/10.1007/s11222-025-10707-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11222-025-10707-6" target="_blank" >10.1007/s11222-025-10707-6</a>

Result language

angličtina

Original language name

Tensor train approximation of multivariate Gaussian density by scaling and squaring

Original language description

Tensor train decomposition is a promising tool for dealing with high dimensional arrays. Point mass filters utilise such arrays for representing probability density functions of the state. Proofs of concept of the application of the low rank decomposition have been provided in the literature. However, the application requires to design parameters, such as tensor train ranks. Since the parameters dictating the computational requirements are derived from the data according to more abstract hyper-parameters such as precision, an analysis of benchmark examples is needed for allocating resources. This paper studies the ranks in the case of Gaussian densities. The influence of correlation and the effect of rounding are discussed first. Efficiency of the density representation used by standard point mass filters is considered next. Aspects of series expansion of the Gaussian density evaluated over array are considered for the tensor train format. The growth of the ranks is illustrated on a four-dimensional example. An observation of the growth for a multi-dimensional case is made last. The lessons learned are valuable for designing efficient point mass filters. Namely, they show that at least the naive implementations of tensor decomposition methods do not break the curse of dimensionality.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

20205 - Automation and control systems

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Statistics and Computing

ISSN

0960-3174

e-ISSN

1573-1375

Volume of the periodical

35

Issue of the periodical within the volume

6

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

12

Pages from-to

1-12

UT code for WoS article

001562034000001

EID of the result in the Scopus database

2-s2.0-105015071433