Tensors in algebraic statistics

TL;DR

This paper provides an overview of tensor theory and its applications in algebraic statistics, emphasizing models with latent variables and illustrating key concepts with examples.

Contribution

It offers a comprehensive high-level overview of tensor applications in algebraic statistics, supported by numerous examples and literature review.

Findings

Tensor theory is central to algebraic statistics.

Models with latent variables are key applications.

Extensive literature review guides further study.

Abstract

Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on its applications in algebraic statistics. This high-level treatment is supported by numerous examples to illustrate key concepts. Additionally, an extensive literature review is included to guide readers toward more detailed studies on the subject.