融合统计模型与神经网络，实现可解释的多变量密度回归。
Hybrid Bernstein Normalizing Flows for Flexible Multivariate Density Regression with Interpretable Marginals
- 先用可解释的MCTM建模边际分布，再用NF捕捉联合分布复杂关系。
- 在模拟与真实数据上均优于传统MCTM和普通NF模型。
- 适合需要理解变量影响且处理复杂多维数据的研究者。
密度回归模型通过建模完整的条件概率分布，提供对数据的全面理解。尽管灵活的归一化流（NF）方法在高维场景中表现优异，但其深层学习的黑箱特性使其输入输出关系难以解释。相比之下，现有的多变量统计方法如多变量条件变换模型（MCTM）虽具可解释性，但灵活性不足，难以表达复杂的多变量分布。本文将MCTM与先进的自回归型归一化流结合，在第一步利用MCTM构建可解释的边际分布，第二步通过基于神经网络的NF技术捕捉联合分布中的非线性复杂关系。我们在多种数值实验中验证了该方法的通用性，并在模拟数据和真实数据上与MCTM及其他NF模型进行了对比，结果表明其兼具解释性与灵活性。
原文摘要 · Abstract (English)
Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple dimensions, interpreting the input-output relationship of such models is often difficult, due to the black-box character of deep learning models. In contrast, existing statistical methods for multivariate outcomes such as multivariate conditional transformation models (MCTM) are restricted in flexibility and are often not expressive enough to represent complex multivariate probability distributions. In this paper, we combine MCTM with state-of-the-art and autoregressive NF to leverage the transparency of MCTM for modeling interpretable feature effects on the marginal distributions in the first step and the flexibility of neural-network-based NF techniques to account for complex and non-linear relationships in the joint data distribution. We demonstrate our method's versatility in various numerical experiments and compare it with MCTM and other NF models on both simulated and real-world data.
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