Neural Differential Recurrent Neural Network with Adaptive Time Steps
This work addresses forecasting challenges for time series with spikes, such as in medical or financial data, but is incremental as it builds on existing neural ODE and RNN methods.
The authors tackled the problem of modeling and forecasting non-stationary time series with sharp changes like spikes by proposing RNN-ODE-Adap, an RNN-based model that uses neural ODEs with adaptive time steps, achieving higher prediction accuracy and reduced computational cost on simulated and real datasets such as electrocardiography.
The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that are non-stationary and may have sharp changes like spikes. We propose an RNN-based model, called RNN-ODE-Adap, that uses a neural ODE to represent the time development of the hidden states, and we adaptively select time steps based on the steepness of changes of the data over time so as to train the model more efficiently for the "spike-like" time series. Theoretically, RNN-ODE-Adap yields provably a consistent estimation of the intensity function for the Hawkes-type time series data. We also provide an approximation analysis of the RNN-ODE model showing the benefit of adaptive steps. The proposed model is demonstrated to achieve higher prediction accuracy with reduced computational cost on simulated dynamic system data and point process data and on a real electrocardiography dataset.