Uncertainty Quantification through Dropout in Time Series Prediction by Echo State Networks

Abstract

The application of echo state networks to time series prediction has provided notable results, favored by their reduced computational cost, since the connection weights require no learning. However, there is a need for general methods that guide the choice of parameters (particularly the reservoir size and ridge regression coefficient), improve the prediction accuracy, and provide an assessment of the uncertainty of the estimates. In this paper we propose such a mechanism for uncertainty quantification based on Monte Carlo dropout, where the output of a subset of reservoir units is zeroed before the computation of the output. Dropout is only performed at the test stage, since the immediate goal is only the computation of a measure of the goodness of the prediction. Results show that the proposal is a promising method for uncertainty quantification, providing a value that is either strongly correlated with the prediction error or reflects the prediction of qualitative features of the time series. This mechanism could eventually be included into the learning algorithm in order to obtain performance enhancements and alleviate the burden of parameter choice.

Keywords

• echo state networks
• reservoir computing
• uncertainty quantification
• dropout
• ensemble learning