## What is it about?

We are all familiar with the calculation of Kullback-Leibler (and similar) divergences. We need probability density functions (pdfs). But what can we do if we do not have them or if they do not exist? Especially in high dimensional (10-300) cases? Can we use probability characteristic functions (pcfs) instead? Moreover, if we cannot even store high-dimensional probability density functions, how can we perform calculations with them? We suggest using low-rank tensor data formats and low-rank calculus.

## Featured Image

Photo by Agence Olloweb on Unsplash

## Why is it important?

The representation as a low-rank element of a high order tensor space allows to reduce the computational complexity and storage cost from exponential in the dimension to almost linear. This will reduce the computing time from years to minutes (for certain class of problems).

## Perspectives

## Read the Original

This page is a summary of: Computing f‐divergences and distances of high‐dimensional probability density functions, Numerical Linear Algebra with Applications, September 2022, Wiley,

DOI: 10.1002/nla.2467.

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