BayesBlend：在 Python 中使用伪贝叶斯模型平均、堆叠与分层堆叠进行便捷模型融合
BayesBlend: Easy Model Blending using Pseudo-Bayesian Model Averaging, Stacking and Hierarchical Stacking in Python
AI总结：
本文提出 BayesBlend Python 包，集成伪贝叶斯模型平均、堆叠及独有的分层贝叶斯堆叠方法，用于估计模型权重并将多个贝叶斯模型的预测分布融合为统一的预测分布，以提升预测性能。
摘要：
对多个相互竞争的推断模型的预测进行平均，通常优于任何单一模型的预测，前提是模型权重经过最优加权以最大化预测性能。在所谓的 $\mathcal{M}$-open 设置中尤其如此，此时真实模型不在候选模型集合中，且可能既无法在数学上具体化，也无法被精确知晓。这种模型平均的实践在统计学和机器学习中有着悠久的历史，目前已有多种方法可用于估计权重以构建模型平均的预测分布。然而，现有软件包中很少有能够从全部可用方法中估计模型权重的，更没有一个能根据估计出的权重将多个模型的预测融合为一个连贯的预测分布。在本文中，我们介绍了 BayesBlend Python 包，它提供了一个用户友好的编程接口，用于估计权重并融合多个（贝叶斯）模型的预测分布。BayesBlend 实现了伪贝叶斯模型平均、堆叠，以及其独有的分层贝叶斯堆叠来估计模型权重。我们通过保险损失建模的示例演示了 BayesBlend 的用法。
英文摘要：
Averaging predictions from multiple competing inferential models frequently outperforms predictions from any single model, providing that models are optimally weighted to maximize predictive performance. This is particularly the case in so-called $\mathcal{M}$-open settings where the true model is not in the set of candidate models, and may be neither mathematically reifiable nor known precisely. This practice of model averaging has a rich history in statistics and machine learning, and there are currently a number of methods to estimate the weights for constructing model-averaged predictive distributions. Nonetheless, there are few existing software packages that can estimate model weights from the full variety of methods available, and none that blend model predictions into a coherent predictive distribution according to the estimated weights. In this paper, we introduce the BayesBlend Python package, which provides a user-friendly programming interface to estimate weights and blend multiple (Bayesian) models' predictive distributions. BayesBlend implements pseudo-Bayesian model averaging, stacking and, uniquely, hierarchical Bayesian stacking to estimate model weights. We demonstrate the usage of BayesBlend with examples of insurance loss modeling.
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