# Perfect Tree-Like Markovian Distributions

arXiv: https://arxiv.org/abs/1301.3834 · HTML: https://mlsanity.com/paper/1301.3834/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

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

- [Differentiable and Transportable Structure Learning](https://mlsanity.com/paper/2206.06354/) (2022)

## Abstract (arXiv)

We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probability distributions.