Iterative Temporal Learning and Prediction with the Sparse Online Echo State Gaussian Process

Abstract—In this work, we contribute the online echo state gaussian process (OESGP), a novel Bayesian-based online method that is capable of iteratively learning complex temporal dy-namics and producing predictive distributions (instead of point predictions). Our method can be seen as a combination of the echo state network with a sparse approximation of Gaussian processes (GPs). Extensive experiments on the one-step prediction task on well-known benchmark problems show that OESGP produced statistically superior results to current online ESNs and state-of-the-art regression methods. In addition, we characterise the benefits (and drawbacks) associated with the considered online methods, specifically with regards to the trade-off between computational cost and accuracy. For a high-dimensional action recognition task, we demonstrate that OESGP produces high accuracies comparable to a recently published graphical model, while being fast enough for real-time interactive scenarios. I

Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes

Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair

Technical report on hierarchical reservoir computing architectures

One approach for building architectures (of which an overview was given in D.6.1) in AMARSi is to use reservoir computing. Here, untrained (or unsupervised trained) recurrent neural networks are used for motion control by learning simple readouts on the dynamic representation generated by the dynamic RNN system. Although single reservoirs are able to generate rich and tunable control patterns (as demonstrated in D.4.1), to allow composition of motion or high-level control, these modules need to be built in an architecture. An active research area in reservoir computing is to build hierarchical reservoir systems. The main reason for this is that reservoirs basically are band-pass systems and can only represent information in a limited frequency band. If information at both fast and slow timescales needs to be integrated, a natural approach is to build a hierarchical system where each layer operates at a different time scale. The big challenge in these hierarchies is how to learn intermediate representations that link the various layers, and especially how bottom-up and top-down information flows need to be organized. We believe that these hierarchical reservoir computing systems are good candidates to build (at least part of) architectures required in AMARSi for rich motor control. In this short deliverable we give an overview of and references to current approaches in hierarchical reservoir computing, several of which have been investigated on speech and handwriting recognition problems in the sister EU project ORGANIC (http://reservoir- computing.org/organic). Many of these hierarchical systems can be used to not only generate dynamical feature hierarchies, but are also able to learn a hierarchy of pattern controller, of special interest to the AMARSi project