scikit-extremes

Sparse Structures for Multivariate Extremes

Summary

Core Concept:

The package scikit-extremes is for sparse multivariate extreme value analysis, structure learning, and robust spectral measure estimation

Key Approaches:

1. Unsupervised Learning for Extremes: Adapting clustering and PCA specifically for the geometry of "extremal angles".
2. Extremal Graphical Models: Constructing graphs where nodes are variables and edges represent "extremal dependence".
3. Concomitant Extremes: Automatically detecting subgroups of variables likely to be extreme at the same time.

Installation

pip install scikit-extremes

For development:

git clone https://github.com/yourusername/scikit-extremes.git
cd scikit-extremes
pip install -e .

Features

A. Data Preprocessing & Marginal Transformation

• to_unit_pareto: Transform arbitrary data to standard Unit Pareto scale.
• threshold_selection: Tools for selecting the threshold $u$.

B. Empirical Estimation

• SpectralMeasureEstimator: Fit the empirical spectral measure using Maximum Empirical Likelihood Estimation (MELE).
• ExtremalCoefficient: Compute $\chi$ and $\eta$ coefficients.

C. Unsupervised Learning for Extremes

• ExtremalClustering: Spherical K-Means for extremal angles.
• ExtremalPCA: Dimensionality reduction for extremal angles.

D. Extremal Graphical Models

• HuslerReissGraph: Estimate the Hüsler-Reiss variogram matrix and infer graph structure.

Usage

(Example usage would go here - refer to documentation for details)

Requirements

• CPU: Modern dual-core processor.
• RAM: 8 GB+ recommended.
• Python: 3.8+
• Dependencies: numpy, scipy

References

This project incorporates research from the following papers:

• Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution John H. J. Einmahl, Johan Segers arXiv:0812.3485

• Sparse Structures for Multivariate Extremes Sebastian Engelke, Jevgenijs Ivanovs arXiv:2004.12182