Neural structure learning with stochastic differential equations

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. INTRODUCTION Time-series data is ubiquitous in the real world, often comprising a series of data points recorded at varying time intervals. Understanding the underlying structures between variables associated with temporal processes is of paramount importance for numerous real-world applications (Spirtes et al., 2000; Berzuini et al., 2012; Peters et al., 2017) . Although randomised experiments are considered the gold standard for unveiling such relationships, they are frequently hindered by factors such as cost and ethical concerns. Structure learning seeks to infer hidden structures from purely observational data, offering a powerful approach for a wide array of applications (