The tropical geometry of causal inference for extremes

TL;DR

This paper explores how tropical geometry can be applied to extreme value statistics and causal inference, leading to new algorithms and insights into when to prefer causal methods over classical approaches.

Contribution

It introduces a novel application of tropical geometry to develop efficient algorithms for causal inference in extreme value statistics, with demonstrated superior performance.

Findings

Tropical geometry provides valuable insights for causal inference in extremes.

New algorithms outperform classical methods on benchmark datasets.

Causal inference for extremes is advantageous in specific scenarios.

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.