# A distance function for stochastic matrices

arXiv: https://arxiv.org/abs/2410.12689 · HTML: https://mlsanity.com/paper/2410.12689/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 64 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Space-Time Correspondence as a Contrastive Random Walk](https://mlsanity.com/paper/2006.14613/) (2020)
- [Fusing Similarity Models with Markov Chains for Sparse Sequential Recommendation](https://mlsanity.com/paper/1609.09152/) (2016)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [On Computing the Total Variation Distance of Hidden Markov Models](https://mlsanity.com/paper/1804.06170/) (2018)
- [Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey](https://mlsanity.com/paper/1501.00644/) (2015)
- [Process Comparison Using Object-Centric Process Cubes](https://mlsanity.com/paper/2103.07184/) (2021)
- [Clustering in Hilbert simplex geometry](https://mlsanity.com/paper/1704.00454/) (2017)

## Built on by (most cited first, 1 of 1)

- [Resolution limits for process comparison from event data](https://mlsanity.com/paper/2609.20489/) (2026)

## Abstract (arXiv)

Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long term Markov chain runs. Bounds on the convergence of the distance and mixing times are derived. Guided by the desire to compare different Markov chain models, especially in the setting of healthcare processes, a new distance function on the space of stochastic matrices is presented. It is a true distance measure which has a closed form and is efficient to implement for numerical evaluation. In the case of ergodic Markov chains, it is shown that considering either the Bhattacharyya angle on Markov sequences or the new stochastic matrix distance leads to the same distance between models.