用于具有可解释边缘分布的灵活多元密度回归的混合伯恩斯坦归一化流
Hybrid Bernstein Normalizing Flows for Flexible Multivariate Density Regression with Interpretable Marginals
AI总结：
针对多元密度回归中模型灵活性与可解释性难以兼顾的问题，提出结合多元条件变换模型（MCTM）与自回归归一化流（NF）的混合方法，兼顾边缘分布可解释性与联合分布建模灵活性，经实验验证性能优于现有方法。
摘要：
密度回归模型通过对完整条件概率分布建模，可实现对数据的全面理解。尽管归一化流（NF）等灵活估计方法在多维场景中表现尤为出色，但由于深度学习模型的黑箱特性，这类模型的输入-输出关系通常难以解释。相比之下，现有的多元结果统计方法，如多元条件变换模型（MCTM），灵活性受限，通常不足以表达复杂的多元概率分布。本文将MCTM与最先进的自回归NF相结合，第一步利用MCTM的透明性对边缘分布上的可解释特征效应建模，再借助基于神经网络的NF技术的灵活性处理联合数据分布中的复杂非线性关系。我们在多项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将其与MCTM及其他NF模型进行了对比。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
