Neural graphical modelling in continuous-time: consistency guarantees and algorithms
This addresses the challenge of learning graphical models from irregularly-sampled multivariate time series in fields like complex systems, offering a novel continuous-time approach.
The paper tackles the problem of discovering structure from time series data by proving that least squares optimization with adaptive regularization consistently recovers directed graphs in stochastic differential equations, and proposes a score-based learning algorithm based on penalized Neural ODEs that outperforms state-of-the-art methods across various dynamical systems.
The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define dependencies in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider score-based structure learning for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, least squares optimization with adaptive regularization schemes consistently recovers directed graphs of local independencies in systems of stochastic differential equations. Using this insight, we propose a score-based learning algorithm based on penalized Neural Ordinary Differential Equations (modelling the mean process) that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to outperform the state of the art across a range of dynamical systems.