Irregularly measured time series are common in many of the applied settings in which time series modelling is a key statistical tool, including medicine. This provides challenges in model choice, often necessitating imputation or similar strategies. Continuous time autoregressive recurrent neural networks (CTRNNs) are a deep learning model that account for irregular observations through incorporating continuous evolution of the hidden states between observations. This is achieved using a neural ordinary differential equation (ODE) or neural flow layer. In this manuscript, we give an overview of these models, including the varying architectures that have been proposed to account for issues such as ongoing medical interventions. Further, we demonstrate the application of these models to probabilistic forecasting of blood glucose in a critical care setting using electronic medical record and simulated data. The experiments confirm that addition of a neural ODE or neural flow layer generally improves the performance of autoregressive recurrent neural networks in the irregular measurement setting. However, several CTRNN architecture are outperformed by an autoregressive gradient boosted tree model (Catboost), with only a long short-term memory (LSTM) and neural ODE based architecture (ODE-LSTM) achieving comparable performance on probabilistic forecasting metrics such as the continuous ranked probability score (ODE-LSTM: 0.118$\pm$0.001; Catboost: 0.118$\pm$0.001), ignorance score (0.152$\pm$0.008; 0.149$\pm$0.002) and interval score (175$\pm$1; 176$\pm$1).
翻译:在许多应用场景中,如医学领域,不规则测量的时间序列是常见的,而这提供了在选择模型时的挑战,通常需要插值或类似的策略。连续时间自回归递归神经网络(CTRNN)是深度学习模型,通过在观测之间合并连续的隐藏状态,从而解决了不规则观测的问题。这是通过神经常微分方程(ODE)或神经流层来实现的。在本文中,我们概述了这些模型,包括已经被提出来解决问题的各种体系结构,如持续的医疗干预。此外,我们使用电子医疗记录和模拟数据展示了这些模型在临床监测和预测血糖水平时的应用。实验证实,在不规则测量设置中,添加神经ODE或神经流层通常可以提高自回归递归神经网络的性能。然而,仅有长短期记忆(LSTM)和神经ODE模型(ODE-LSTM)的性能达到了可比性,与基于树的自回归渐变算法模型(catboost)相当。衡量预测指标时,如持续等级概率得分(ODE-LSTM: 0.118±0.001; Catboost: 0.118±0.001),忽略率(0.152±0.008; 0.149±0.002)和区间得分(175±1; 176±1)等等。