# Estimating an extreme Bayesian network via scalings

@article{Klppelberg2021EstimatingAE, title={Estimating an extreme Bayesian network via scalings}, author={Claudia Kl{\"u}ppelberg and Mario Krali}, journal={J. Multivar. Anal.}, year={2021}, volume={181}, pages={104672} }

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…

## 8 Citations

Recursive max-linear models with propagating noise

- MathematicsElectronic Journal of Statistics
- 2021

Recursive max-linear vectors model causal dependence between node variables by a structural equation model, expressing each node variable as a max-linear function of its parental nodes in a directed…

Markov equivalence of max-linear Bayesian networks

- Computer Science, MathematicsUAI
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The parallel between the two theories via tropicalization is established, and the surprising result that the Markov equivalence classes for max-linear Bayesian networks coincide with the ones obtained by regular CI is established.

Fe b 20 20 CONDITIONAL INDEPENDENCE IN MAX-LINEAR BAYESIAN NETWORKS

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Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the…

Estimating a Latent Tree for Extremes

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QTree is given, a simple and efficient algorithm to solve the Latent River Problem that outperforms existing methods, and under a Bayesian network model for extreme values with propagating noise, it is shown that the QTree estimator returns for n → ∞ a.s. the correct tree.

Causal Discovery of a River Network from its Extremes

- Computer ScienceArXiv
- 2021

QTree is provided, a new and simple algorithm to solve the Hidden River Problem that outperforms existing methods and relies on qualitative aspects of the max-linear Bayesian network model.

Causal Modelling of Heavy-Tailed Variables and Confounders with Application to River Flow

- Mathematics
- 2021

Confounding variables are a recurrent challenge for causal discovery and inference. In many situations, complex causal mechanisms only manifest themselves in extreme events, or take simpler forms in…

Detection of causality in time series using extreme values

- Mathematics
- 2021

Consider two stationary time series with heavy-tailed marginal distributions. We want to detect whether they have a causal relation, that is, if a change in one of them causes a change in the other.…

Conditional Independence in Max-linear Bayesian Networks

- Mathematics
- 2020

Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the…

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