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：简单模型（如线性回归）的神经网络表示正被日益广泛地研究，以深入理解深度学习算法的基本原理。然而，诸如Cox模型等分布回归模型的神经网络表示迄今鲜受关注。我们通过提出基于逆流变换的分布回归框架（DRIFT）填补了这一空白，该框架包含了前述模型的神经网络表示。我们通过实验证明，在处理连续型、有序型、时间序列及生存结局的多种应用中，DRIFT中的模型神经网络表示可作为其经典统计对应物的有效替代。我们确认DRIFT中的模型在偏效应估计、预测及偶然不确定性量化方面，与多种统计方法的性能实际相当。DRIFT涵盖了可解释统计模型与灵活神经网络，为统计建模与深度学习领域开辟了新方向。