Neural Structure Learning with Stochastic Differential Equations
Benjie Wang Joel Jennings Wenbo Gong
Discovering the underlying relationships among variables from temporal
observations has been a longstanding challenge in numerous scientific
disciplines, including biology, finance, and climate science. The dynamics of
such systems are often best described using continuous-time stochastic
processes. Unfortunately, most existing structure learning approaches assume
that the underlying process evolves in discrete-time and/or observations occur
at regular time intervals. These mismatched assumptions can often lead to
incorrect learned structures and models. In this work, we introduce a novel
structure learning method, SCOTCH, which combines neural stochastic
differential equations (SDE) with variational inference to infer a posterior
distribution over possible structures. This continuous-time approach can
naturally handle both learning from and predicting observations at arbitrary
time points. Theoretically, we establish sufficient conditions for an SDE and
SCOTCH to be structurally identifiable, and prove its consistency under
infinite data limits. Empirically, we demonstrate that our approach leads to
improved structure learning performance on both synthetic and real-world
datasets compared to relevant baselines under regular and irregular sampling
intervals.