A Dynamic Neural ODE Model for Nonlinear Time Series

• Activity Number: 501 - Time Series Methods
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Yijia Liu* and Lexin Li and Xiao Wang
• Companies: Purdue University and University of California, Berkeley and Purdue University
• Keywords: Deep Neural Networks; Ordinary Differential Equations; Brain Mapping; Gradient Descent; Regularization

Abstract

Motivated by many nonlinear dynamic interactions in applied domains such as neuroscience and genomics, we propose a novel neural ordinary differential equation (ODE) model to analyze the nonlinear relationships between multiple time series. The latent states of these time series are described by a set of differential equations and observed equations linking the latent states to observed data. In particular, we model the dynamic changes of the latent states by a set of deep neural networks (DNNs), and the flexibility of DNNs enables us to efficiently capture the nonlinear dependence among time series. Combined with sparsity-inducing regularization on the weights, we can further capture the casual structure among these series. Efficient algorithms are developed to estimate the unknown weights for DNNs. Simulated data are used to illustrate the effectiveness of both our model and the algorithm. The methods are also applied to identifying effective brain connectivity.