A0360
Title: Extremes of structural causal models
Authors: Sebastian Engelke - University of Geneva (Switzerland)
Nicola Gnecco - Imperial College London (United Kingdom) [presenting]
Frank Roettger - TU Eindhoven (Netherlands)
Abstract: The behavior of extreme observations is well-understood for time series or spatial data, but little is known about whether the data-generating process is a structural causal model (SCM). The behavior of extremes is studied in this model class, both for the observational distribution and under extremal interventions. It is shown that under suitable regularity conditions on the structure functions, the extremal behavior is described by a multivariate Pareto distribution, which can be represented as a new SCM on an extremal graph. Importantly, the latter is a sub-graph of the graph in the original SCM, which means that causal links can disappear in the tails. A directed version of extremal graphical models is further introduced, and it is shown that an extremal SCM satisfies the corresponding Markov properties. Based on a new test of extremal conditional independence, two algorithms are proposed for learning the extremal causal structure from data. The first is an extremal version of the PC-algorithm, and the second is a pruning algorithm that removes edges from the original graph to consistently recover the extremal graph. The methods are illustrated on river data with known causal ground truth.
