Estimating a Directed Tree for Extremes
This work addresses the challenge of discovering causal structures in extreme events for applications like hydrology, though it appears incremental as it builds on existing max-linear Bayesian network models.
The authors tackled the problem of estimating a root-directed spanning tree from extreme data, such as river networks from flow measurements, by proposing a new algorithm based on max-linear Bayesian networks, which they proved is consistent and performs well on benchmark and new data.
We propose a new method to estimate a root-directed spanning tree from extreme data. A prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and new data. We prove that the new estimator is consistent under a max-linear Bayesian network model with noise. We also assess its strengths and limitations in a small simulation study.