Estimating a Latent Tree for Extremes

The Latent River Problem has emerged as a flagship problem for causal discovery in extreme value statistics. This paper gives QTree, a simple and efficient algorithm to solve the Latent River Problem that outperforms existing methods. QTree returns a directed graph and achieves almost perfect recovery on the Upper Danube, the existing benchmark dataset, as well as on new data from the Lower Colorado River in Texas. It can handle missing data, has an automated parameter tuning procedure, and runs in time $O(n |V|^2)$, where $n$ is the number of observations and $|V|$ the number of nodes in the graph. In addition, under a Bayesian network model for extreme values with propagating noise, we show that the QTree estimator returns for $n\to\infty$ a.s. the correct tree.