A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

翻译：一个观测杂乱的复杂系统可能由多个对应于潜在实体的简单子系统耦合混合而成。这些子系统在连续时间域中可能具有不同的动力学特性；同时，子系统间复杂的相互作用也随时间演化。这种设置在实际世界中相当常见，但此前较少被研究。在本文中，我们提出一种针对该设置的序列学习方法，通过解耦复杂系统来处理不规则采样且杂乱的序列观测。这种解耦不仅带来了描述每个潜在实体动力学的子系统，还产生了一个随时间捕获实体间交互的元系统。具体而言，我们论证了在单纯形上演化的元系统受投影微分方程（ProjDEs）支配。我们进一步分析了基于Bregman散度的投影算子，并提供了神经网络的友好实现。在合成数据集和真实世界数据集上的实验结果表明，与现有最先进方法相比，我们的方法在处理复杂且杂乱的序列数据时具有优势。