Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional regression models, such as the Cox model, have received little attention so far. We close this gap by proposing a framework for distributional regression using inverse flow transformations (DRIFT), which includes neural representations of the aforementioned models. We empirically demonstrate that the neural representations of models in DRIFT can serve as a substitute for their classical statistical counterparts in several applications involving continuous, ordered, time-series, and survival outcomes. We confirm that models in DRIFT empirically match the performance of several statistical methods in terms of estimation of partial effects, prediction, and aleatoric uncertainty quantification. DRIFT covers both interpretable statistical models and flexible neural networks opening up new avenues in both statistical modeling and deep learning.

使用逆流转换（DRIFT）的神经网络表示，对分布回归模型提供了框架，证明其在多个应用中能替代传统统计模型，而且与统计方法在效果估计、预测和不确定性量化方面的性能相匹配，一方面涵盖了可解释的统计模型，另一方面打开了统计建模和深度学习的新途径。

如何利用逆条件流作为分布回归的替代方案