Neural Structure Learning with Stochastic Differential Equations
This addresses the challenge of discovering variable relationships in continuous-time systems for fields like biology and finance, offering a novel approach that handles irregular observations, though it is incremental in advancing structure learning methods.
The authors tackled the problem of learning underlying variable relationships from temporal observations by introducing SCOTCH, a method combining neural stochastic differential equations with variational inference, which demonstrated improved structure learning performance on synthetic and real-world datasets compared to baselines under regular and irregular sampling intervals.
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.