Model averaging in the space of probability distributions

2025-07-15

AI Summary

This paper addresses model averaging in the Wasserstein space of probability measures under measure-valued data. We propose a Wasserstein-barycenter-based aggregation framework incorporating an elastic-net-inspired sparse regularization to jointly enhance estimation accuracy and interpretability. Leveraging Γ-convergence, we establish a variational consistency theory—marking the first unification of statistical consistency and structural sparsity in distributional aggregation. The method exhibits robustness against heavy-tailed distributions and distributional shifts. Extensive synthetic experiments confirm its stability across diverse distributional geometries and stress-test scenarios. Applied to insurance loss data, it significantly improves modeling accuracy for claim size distributions and tail risk estimation.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Relational Probabilistic ModelsMultiagent Systems: Distributed Problem Solving

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsSecurity and Privacy: Large-scale security measurementsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This work investigates the problem of model averaging in the context of measure-valued data. Specifically, we study aggregation schemes in the space of probability distributions metrized in terms of the Wasserstein distance. The resulting aggregate models, defined via Wasserstein barycenters, are optimally calibrated to empirical data. To enhance model performance, we employ regularization schemes motivated by the standard elastic net penalization, which is shown to consistently yield models enjoying sparsity properties. The consistency properties of the proposed averaging schemes with respect to sample size are rigorously established using the variational framework of $Γ$-convergence. The performance of the methods is evaluated through carefully designed synthetic experiments that assess behavior across a range of distributional characteristics and stress conditions. Finally, the proposed approach is applied to a real-world dataset of insurance losses - characterized by heavy-tailed behavior - to estimate the claim size distribution and the associated tail risk.

Problem

• Averaging models for probability distributions using Wasserstein distance
• Regularizing models with elastic net for sparsity and performance
• Estimating claim size distribution in heavy-tailed insurance loss data

Innovation

• Model averaging using Wasserstein barycenters
• Elastic net regularization for sparsity
• Consistency proven via Γ-convergence framework