Seminar: Causal Discovery for Max-Linear Bayesian Networks

We are pleased to announce an upcoming talk by Francesco Nowell from TU Berlin, who will be presenting on August 20, 2025, at 15:00.

Abstract:

Max-linear Bayesian Networks (MLBNs) are a class of directed acyclic graphical (DAG) models which are of interest to statistics and data science due to their relevance to causality and probabilistic inference, particularly of extreme events. They differ from Gaussian Bayesian Networks in that the structural equations governing the model are tropical linear forms in the random variables. This difference leads to several novel challenges in the task of causal discovery, i.e. the reconstruction of the true DAG underlying a given empirical distribution. Most notably, the combinatorial criteria for separation in the graph corresponding to conditional independence in the distribution are such that there is no longer a well-defined notion of Markov equivalence. 

This talk explains how the traditional PC algorithm for causal discovery in linear structural equation models fails for MLBNs, and discusses how it may be modified such as to output a well-defined subgraph of the true DAG which encodes its most significant causal relationships. Furthermore, our modified PC algorithm contains an extra edge orientation rule for induced cycles of a specific kind. This allows for additional identifiability in MLBNs compared to the Gaussian setting.