Parameter learning for high-dimensional, partially observed, and nonlinear stochastic processes is a methodological challenge. Spatiotemporal disease transmission systems provide examples of such processes giving rise to open inference problems. We propose the iterated block particle filter (IBPF) algorithm for learning high-dimensional parameters over graphical state space models with general state spaces, measures, transition densities and graph structure. Theoretical performance guarantees are obtained on beating the curse of dimensionality (COD), algorithm convergence, and likelihood maximization. Experiments on a highly nonlinear and non-Gaussian spatiotemporal model for measles transmission reveal that the iterated ensemble Kalman filter algorithm (Li et al. (2020)) is ineffective and the iterated filtering algorithm (Ionides et al. (2015)) suffers from the COD, while our IBPF algorithm beats COD consistently across various experiments with different metrics.

翻译：针对高维、部分可观测且非线性的随机过程进行参数学习是方法论上的重大挑战。时空疾病传播系统为此类过程提供了实例，并衍生出开放的推断问题。我们提出迭代分块粒子滤波器（IBPF）算法，用于在具有一般状态空间、测度、转移密度和图结构的图状态空间模型上进行高维参数学习。在克服维度灾难（COD）、算法收敛性及似然最大化方面，我们获得了理论性能保证。针对麻疹传播的高度非线性且非高斯时空模型的实验表明，迭代集成卡尔曼滤波算法（Li et al., 2020）失效，迭代滤波算法（Ionides et al., 2015）受困于维度灾难，而我们的IBPF算法在不同指标的多组实验中持续克服了维度灾难。