# Inference for max-linear Bayesian networks with noise

arXiv: https://arxiv.org/abs/2505.00229 · HTML: https://mlsanity.com/paper/2505.00229/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 5 of 5)

- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Estimating a Directed Tree for Extremes](https://mlsanity.com/paper/2102.06197/) (2021)
- [A continuous updating weighted least squares estimator of tail dependence in high dimensions](https://mlsanity.com/paper/1601.04826/) (2016)
- [Bayesian Networks for Max-linear Models](https://mlsanity.com/paper/1901.03948/) (2019)
- [Estimating an Extreme Bayesian Network via Scalings](https://mlsanity.com/paper/1912.03968/) (2019)

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

- [A PC Algorithm for Max-Linear Bayesian Networks](https://mlsanity.com/paper/2508.13967/) (2025)

## Abstract (arXiv)

Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then, we show that an estimator of a parameter for each edge in a directed acyclic graph (DAG) is distributed normally. We end this paper with computational experiments with the expectation and maximization (EM) algorithm and quadratic optimization.