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.

翻译：神经网络对简单模型（如线性回归）的表征正日益受到研究，以更好地理解深度学习算法的基本原理。然而，分布回归模型（如Cox模型）的神经表征迄今鲜受关注。我们通过提出一种基于逆流变换的分布回归框架（DRIFT）来填补这一空白，该框架包含了上述模型的神经表征。我们通过实验证明，在涉及连续、有序、时间序列和生存结果的若干应用中，DRIFT中模型的神经表征可以替代其经典统计对应方法。我们证实，在部分效应估计、预测和偶然不确定性量化方面，DRIFT中的模型在经验上与多种统计方法的性能相当。DRIFT同时涵盖了可解释的统计模型和灵活的神经网络，为统计建模和深度学习开辟了新途径。