  Despite substantial progress in deep learning approaches to time-series
reconstruction, no existing methods are designed to uncover local activities
with minute signal strength due to their negligible contribution to the
optimization loss. Such local activities however can signify important abnormal
events in physiological systems, such as an extra foci triggering an abnormal
propagation of electrical waves in the heart. We discuss a novel technique for
reconstructing such local activity that, while small in signal strength, is the
cause of subsequent global activities that have larger signal strength. Our
central innovation is to approach this by explicitly modeling and disentangling
how the latent state of a system is influenced by potential hidden internal
interventions. In a novel neural formulation of state-space models (SSMs), we
first introduce causal-effect modeling of the latent dynamics via a system of
interacting neural ODEs that separately describes 1) the continuous-time
dynamics of the internal intervention, and 2) its effect on the trajectory of
the system's native state. Because the intervention can not be directly
observed but have to be disentangled from the observed subsequent effect, we
integrate knowledge of the native intervention-free dynamics of a system, and
infer the hidden intervention by assuming it to be responsible for differences
observed between the actual and hypothetical intervention-free dynamics. We
demonstrated a proof-of-concept of the presented framework on reconstructing
ectopic foci disrupting the course of normal cardiac electrical propagation
from remote observations.
