ABSTRACT

Differentiable programming has recently received much interest as a paradigm that facilitates taking gradients of computer programs. While the corresponding flexible gradient-based optimization approaches so far have been used predominantly for deep learning or enriching the latter with modeling components, we want to demonstrate that they can also be useful for statistical modeling per se, for example, for quick prototyping when classical maximum likelihood approaches are challenging or not feasible. In an application from a COVID-19 setting, we use differentiable programming to quickly build and optimize a flexible prediction model adapted to the data quality challenges at hand. Specifically, we develop a regression model, inspired by delay differential equations, that can bridge temporal gaps of observations in the central German registry of COVID-19 intensive care cases for predicting future demand. With this exemplary modeling challenge, we illustrate how differentiable programming can enable simple gradient-based optimization of the model by automatic differentiation. This allowed us to quickly prototype a model under time pressure that outperforms simpler benchmark models. We thus exemplify the potential of differentiable programming also outside deep learning applications to provide more options for flexible applied statistical modeling.

摘要

可微分编程最近作为一种有助于对计算机程序进行梯度处理的范式引起了极大的兴趣。虽然迄今为止相应的灵活的基于梯度的优化方法主要用于深度学习或通过建模组件丰富后者，但我们希望证明它们本身也可用于统计建模，例如，在经典时用于快速原型设计最大似然方法具有挑战性或不可行。在来自 COVID-19 设置的应用程序中，我们使用可微分编程来快速构建和优化适应手头数据质量挑战的灵活预测模型。具体来说，我们开发了一个回归模型，灵感来自延迟微分方程，这可以弥合德国中央 COVID-19 重症监护病例登记处的观察时间差距，以预测未来需求。通过这个示例性建模挑战，我们说明了可微分编程如何通过自动微分实现简单的基于梯度的模型优化。这使我们能够在时间压力下快速制作模型原型，该模型的性能优于简单的基准模型。因此，我们在深度学习应用程序之外举例说明了可微编程的潜力，为灵活的应用统计建模提供更多选择。这使我们能够在时间压力下快速制作模型原型，该模型的性能优于简单的基准模型。因此，我们在深度学习应用程序之外举例说明了可微编程的潜力，为灵活的应用统计建模提供更多选择。这使我们能够在时间压力下快速制作模型原型，该模型的性能优于简单的基准模型。因此，我们在深度学习应用程序之外举例说明了可微编程的潜力，为灵活的应用统计建模提供更多选择。