Causal Inference for Extremes via Tropical Geometry

University Of Texas At Austin, Austin TX

Investigators

Abstract

Monitoring and predicting extreme events such as flooding, financial collapses or engineering risks are of huge importance to societies. However, extreme events by definition are rare and concern large, unlikely values, while traditional statistical techniques are based on averages and large numbers of observations. This project will create new, fast methodologies to uncover the causes and potential cascading failures when an extreme event hits a system, such as a river, computer network, or financial network. Concrete applications include flood risks predictions, tracing the source of contaminants in underground waterways, and modeling risks of airplanes runway overrun. This research will advance society’s ability to monitor, predict and prevent such adverse events. Extreme value statistics concerns the maxima of random variables and relations between the tails of distributions rather than averages and correlations. Unique challenges to this field are lack of data and lack of smoothness in the likelihood, which severely limits statistical learning and inference. Goal A of this research aims to advance causal inference for extreme value statistics with provably accurate algorithms that can handle datasets with thousands of variables and missing data.Goal B of this research aims to solve the Identification Challenge for deep neural networks with rectified linear (ReLU) activation, a difficult variant of the reverse-engineering problem. These problems are intimately connected and both will be tackled in this proposal via tropical algebraic and convex geometry. Preliminary work by the PI and co-authors on hydrology data have shown that the proposed methods achieve the state-of-the-art in the Hidden River Network, the benchmark problem in causal inference for extremes. The proposed research will advance society’s ability to monitor and predict extreme events in finance, engineering, and natural disasters. It will simultaneously advance both extreme value statistics and tropical geometry, widening their applications and create new interdisciplinary, data-driven research at their intersections. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.