# On Information (pseudo) Metric

arXiv: https://arxiv.org/abs/2103.02008 · HTML: https://mlsanity.com/paper/2103.02008/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Relation between the Kantorovich-Wasserstein metric and the Kullback-Leibler divergence](https://mlsanity.com/paper/1908.09211/) (2019)
- [Topological Information Data Analysis](https://mlsanity.com/paper/1907.04242/) (2019)

## Abstract (arXiv)

This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and conditional independence condition. Pythagorean theorem is given, providing in special case potentially interesting natural integer triplets. This metric is computed for illustration on Diabetes dataset using infotopo package.