The tropical geometry of causal inference for extremes

Abstract

Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new, efficient learning algorithms with leading performance on benchmark datasets in extreme value statistics. We give intuition, backed by performances on benchmark datasets, for why and when causal inference for extremes should be employed over classical methods. Finally, we list some open problems at the intersection of causal inference, tropical geometry and deep learning.and its special case, the max-linear Bayesian network [41,50] s.t.Z j ≥ 0, Z j independent, unobserved, C supported on a DAG D.