Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

翻译：学习真实世界动态现象（如气候、生物）的精确预测模型仍是一项具有挑战性的任务。关键问题在于，自然和人工过程生成的数据往往包含不规则采样和/或存在缺失观测的时间序列。本文提出神经连续-离散状态空间模型（NCDSSM），通过离散时间观测对时间序列进行连续时间建模。NCDSSM 利用辅助变量将识别与动态过程解耦，从而仅需对辅助变量进行摊销推理。借助连续-离散滤波理论的技术，我们展示了如何对动态状态执行精确的贝叶斯推理。我们提出了三种灵活的潜在动态参数化方法，以及一种高效的训练目标，该目标在推理过程中对动态状态进行边缘化处理。在多个基准数据集的跨领域实证结果表明，NCDSSM 在插补和预测性能上均优于现有模型。