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:复杂的系统,加上各种观测,可能是与潜在实体相对应的多个简单子系统的混合体。这种分系统可能具有连续时间领域的不同动态;因此,分系统之间的复杂互动也随时间而变化。这种环境在现实世界中相当常见,但考虑较少。在本文中,我们建议在这个环境下采用顺序学习方法,将处理非常规抽样和混合顺序观测的复杂系统脱钩。这种脱钩不仅带来描述每个潜在实体动态的子系统,而且带来一个记录实体之间随时间推移相互作用的元系统。具体地说,我们认为,在一个简单x范围内演变的元系统受预测差异方程式(ProjDEs)的制约。我们在布雷格曼差异的背景下进一步分析和提供对神经友好的预测操作器。合成和现实世界数据集的实验结果显示,在面对与状态相比复杂和混合的序列数据时,我们的方法具有优势。