连续时间贝叶斯网络的均值场变分逼近
Mean Field Variational Approximation for Continuous-Time Bayesian Networks
摘要：
连续时间贝叶斯网络是一种自然的结构化表示语言，用于描述随时间连续演化的多组分随机过程。尽管有紧凑的表示，但即使在相对简单的结构化网络中，这种模型中的推理也是难以处理的。在这里，我们介绍了一个平均场变分近似，我们使用的产品的非齐次马尔可夫过程近似分布的轨迹。这种变分方法导致全局一致的分布，可以有效地查询。此外，它提供了一个观察概率的下限，从而使其对学习任务具有吸引力。我们提供的理论基础的近似，一个有效的实现，利用广泛的高度优化的常微分方程（ODE）求解器，实验探索这种近似是合适的过程的特征，并显示应用程序的大规模现实世界的推理问题。
英文摘要：
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even in relatively simple structured networks. Here we introduce a mean field variational approximation in which we use a product of inhomogeneous Markov processes to approximate a distribution over trajectories. This variational approach leads to a globally consistent distribution, which can be efficiently queried. Additionally, it provides a lower bound on the probability of observations, thus making it attractive for learning tasks. We provide the theoretical foundations for the approximation, an efficient implementation that exploits the wide range of highly optimized ordinary differential equations (ODE) solvers, experimentally explore characterizations of processes for which this approximation is suitable, and show applications to a large-scale realworld inference problem.
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