The Echo State Gaussian Process

Echo state networks (ESNs) constitute a novel approach to recurrent neural network (RNN) training, with an RNN (the reservoir) being generated randomly, and only a readout being trained using a simple, computationally efficient algorithm. ESNs have greatly facilitated the practical application of RNNs, outperforming classical approaches on a number of benchmark tasks. In this paper, we introduce a novel Bayesian approach towards ESNs, the echo state Gaussian process (ESGP). The ESGP combines the merits of ESNs and Gaussian processes to provide a more robust to noise and outliers alternative to conventional RC networks, while also offering a measure of confidence on the generated predictions (in the form of a predictive distribution). We exhibit the merits of our approach in a number of applications, considering both benchmark datasets and real-world applications, where we show that our method offers a significant enhancement in the dynamical data modeling capabilities of ESNs. Additionally, we also show that our method is orders of magnitude more computationally efficient compared to existing Gaussian process-based methods for dynamical data modeling, without compromises in the obtained predictive performance.