# A Geometric Reduction Approach for Identity Testing of Reversible Markov Chains

arXiv: https://arxiv.org/abs/2302.08059 · HTML: https://mlsanity.com/paper/2302.08059/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 16 Feb 2023.

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

- [Minimax Testing of Identity to a Reference Ergodic Markov Chain](https://mlsanity.com/paper/1902.00080/) (2019)
- [ℓp Testing and Learning of Discrete Distributions](https://mlsanity.com/paper/1412.2314/) (2014)
- [Identity testing of reversible Markov chains](https://mlsanity.com/paper/2105.06347/) (2021)

## Abstract (arXiv)

We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at least in a mildly restricted setting, testing identity to a reversible chain reduces to testing to a symmetric chain over a larger state space and recover state-of-the-art sample complexity for the problem.