发表机构
University of Washington; Zhejiang University; Inria; École Normale Supérieure; PSL Research University（华盛顿大学; 浙江大学; 法国国家信息与自动化研究所; 巴黎高等师范学院; 巴黎文理研究大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多元混合类型结果的联合条件分布估计问题，提出广义engression模型，一种基于评分规则的统一非参数分布回归框架，通过数据类型特定链接函数和随机扰动平滑损失，实现梯度训练，并在模拟和实际应用中优于或匹配现有方法。
AI 中文摘要
我们考虑在给定协变量的情况下，估计多元结果的联合条件分布，其中结果坐标可以是连续的、二元的、分类的、有序的或排名的，并且它们之间条件依赖。针对每种结果类型，已有不同的统计方法被开发出来，且大多数方法针对条件分布的某个汇总统计量，如每个坐标的均值，而非结果向量的联合分布。我们开发了广义engression模型，这是一个适用于任何类型结果的统一非参数分布回归框架。所提出的方法建立在engression（一种基于评分规则的深度生成模型）之上，并引入了特定于数据类型的链接函数和一种随机扰动来平滑损失，使得即使使用不连续的链接函数也能进行基于梯度的训练。我们为连续、离散和混合结果建立了通用表示结果。在模拟和两个应用中——一个群落生态学基准中的242个物种和一个17维混合类型的健康结果——该方法在边际得分上与特定类型的模型相匹配，在联合分布上优于它们，并达到或超过专门构建的最先进的联合物种分布模型。软件可在Python中获取。
英文摘要
We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.
