  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.

Machine Learning