# Estimating an Extreme Bayesian Network via Scalings

arXiv: https://arxiv.org/abs/1912.03968 · HTML: https://mlsanity.com/paper/1912.03968/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 2 of 2)

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

## Abstract (arXiv)

Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme value theory, innovations are assumed to have regularly varying distribution tails. We propose a scaling technique in order to determine a causal order of the node variables. All dependence parameters are then estimated from the estimated scalings. Furthermore, we prove asymptotic normality of the estimated scalings and dependence parameters based on asymptotic normality of the empirical spectral measure. Finally, we apply our structure learning and estimation algorithm to financial data and food dietary interview data.