# Bayesian Networks for Max-linear Models

arXiv: https://arxiv.org/abs/1901.03948 · HTML: https://mlsanity.com/paper/1901.03948/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Estimating a Directed Tree for Extremes](https://mlsanity.com/paper/2102.06197/) (2021)
- [Spectral learning of multivariate extremes](https://mlsanity.com/paper/2111.07799/) (2021)
- [Inference for max-linear Bayesian networks with noise](https://mlsanity.com/paper/2505.00229/) (2025)

## Abstract (arXiv)

We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Kl"uppelberg [16] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are generally not faithful to the independence model determined by their associated directed acyclic graph. In addition, we consider some of the basic issues of estimation and discuss generalized maximum likelihood estimation of the coefficients, using the concept of a generalized likelihood ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21]. Finally we argue that the structure of a minimal network asymptotically can be identified completely from observational data.