Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

翻译：马尔可夫跳跃过程是一类连续时间随机过程，在自然科学和社会科学中具有广泛应用。尽管应用广泛，但这类模型的推断极为复杂，通常需借助蒙特卡洛方法或期望最大化算法。本文提出一种替代性变分推断算法，该算法基于神经常微分方程，可通过反向传播进行训练。我们的方法学习观测数据的神经连续时间表征，进而近似后验马尔可夫跳跃过程的初始分布与时变转移概率速率。先验过程的时间不变速率则采用类似生成对抗网络的训练方式。我们在从真实马尔可夫跳跃过程生成的合成数据、实验性离子通道开关数据以及分子动力学模拟上测试了该方法。重现实验的源代码已在线公开。