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.
Highlights
Time series prediction is a major task within the realm of statistics and machine learning algorithms, with plentiful applications in economy, biomedicine, engineering, and astronomy, to cite just a few fields.In view of the limitations of linear methods such as the classical ARIMA family of algorithms, techniques borrowed from computational intelligence have been applied to the forecasting of time series for decades
This paper focuses on the paradigm of reservoir computing, which leads to this kind of constant-weights recurrent neural networks (RNNs)
We study a discretization of the Mackey–Glass equation with delay τ = 17, which has often been used to test the performance of nonlinear time series prediction algorithms [9]
Summary
Time series prediction is a major task within the realm of statistics and machine learning algorithms, with plentiful applications in economy, biomedicine, engineering, and astronomy, to cite just a few fields.In view of the limitations of linear methods such as the classical ARIMA family of algorithms, techniques borrowed from computational intelligence have been applied to the forecasting of time series for decades (see [1] for a recent review). Time series prediction is a major task within the realm of statistics and machine learning algorithms, with plentiful applications in economy, biomedicine, engineering, and astronomy, to cite just a few fields. Recurrent neural networks (RNNs) seem at first to be well-suited to deal with the complexities of long-term temporal dependencies of time series, even though learning in RNNs usually presents a high computational cost for large-size applications. RNNs with fixed weights that do not require complex learning algorithms have been proposed as an alternative method for time series prediction, with satisfactory results. Echo state networks (ESNs) are a model of neural network with recurrent connections within the paradigm of reservoir computing, which have often been applied to tasks related to time series, in particular classification and prediction. It would be desirable to include some
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