Dimension Reduction in Multivariate Extremes via Latent Linear Factor Models

TL;DR

This paper introduces a new high-dimensional tail dependence model using latent linear factors, enabling interpretable dimension reduction and scalable estimation, demonstrated through a spatial wind energy application.

Contribution

It proposes a novel latent factor model for multivariate extremes with identifiable parameters and practical estimation methods, enhancing interpretability and scalability.

Findings

Model captures extremal dependence via low-dimensional latent factors.

Estimation method based on tail pairwise dependence matrix.

Application to wind energy demonstrates practical utility.

Abstract

We propose a new and interpretable class of high-dimensional tail dependence models based on latent linear factor structures. Specifically, extremal dependence of an observable vector is assumed to be driven by a lower-dimensional latent $K$-factor model, where $K \ll d$, thereby inducing an explicit form of dimension reduction. Geometrically, this is reflected in the support of the associated spectral dependence measure, whose intrinsic dimension is at most $K-1$. The loading structure may additionally exhibit sparsity, meaning that each component is influenced by only a small number of latent factors, which further enhances interpretability and scalability. Under mild structural assumptions, we establish identifiability of the model parameters and provide a constructive recovery procedure based on a margin-free tail pairwise dependence matrix, which also yields practical rank-based estimation methods. The framework combines naturally with marginal tail models and is particularly well suited to high-dimensional settings. We illustrate its applicability in a spatial wind energy application, where the latent factor structure enables tractable estimation of the risk that a large proportion of turbines simultaneously fall below their cut-in wind speed thresholds.