标题： 概率分布空间中的模型平均 显示英文标题

标题： Model averaging in the space of probability distributions

摘要： 这项工作研究了在测度值数据背景下模型平均的问题。 具体而言，我们研究了在 Wasserstein 距离度量下的概率分布空间中的聚合方案。 通过 Wasserstein 中心定义的聚合模型，能够最优地校准实证数据。 为了提高模型性能，我们采用了由标准弹性网络惩罚提出的正则化方案，该方案被证明可以一致地产生具有稀疏性特性的模型。 使用$\Gamma$-收敛的变分框架，严格建立了所提出平均方案在样本量方面的相容性性质。 通过精心设计的合成实验评估了方法的性能，这些实验评估了在各种分布特征和压力条件下的行为。 最后，将所提出的方法应用于一个具有重尾行为的真实世界保险损失数据集，以估计索赔规模分布及其相关的尾部风险。 显示英文摘要

摘要： 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 $\Gamma$-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.