The following paper is now published in the Journal of Machine Learning Research (JMLR)
http://jmlr.csail.mit.edu/papers/v19/18-015.html
This contribution will be of value to all employing and developing the Gaussian Process in the statistical modelling of data and physical/natural processes as it is the first publication that provides theoretically rigorous insights into the design of Deep Structures composed of GPs. In particular Applied Mathematicians, Statisticians, Engineers (of every hue), and of course Artificial Intelligence and Machine Learning communities will find this work of particular relevance.
Title: How Deep Are Deep Gaussian Processes?
Authors: Matthew M. Dunlop, Mark A. Girolami, Andrew M. Stuart, Aretha L. Teckentrup; 19(54):1−46, 2018.
Abstract: Recent research has shown the potential utility of deep Gaussian processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current published body of work is placed in a common framework and, through recursion, several classes of deep Gaussian processes are defined. The resulting samples generated from a deep Gaussian process have a Markovian structure with respect to the depth parameter, and the effective depth of the resulting process is interpreted in terms of the ergodicity, or non-ergodicity, of the resulting Markov chain. For the classes of deep Gaussian processes introduced, we provide results concerning their ergodicity and hence their effective depth. We also demonstrate how these processes may be used for inference; in particular we show how a Metropolis-within-Gibbs construction across the levels of the hierarchy can be used to derive sampling tools which are robust to the level of resolution used to represent the functions on a computer. For illustration, we consider the effect of ergodicity in some simple numerical examples.
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Professor Mark Girolami FRSE FIET
Chair of Statistics
Lloyd’s Register Foundation / Royal Academy of Engineering Research Chair in Data Centric Engineering
EPSRC Established Career Research Fellow
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Strategic Programme Director
The Alan Turing Institute | The British Library | 96 Euston Road | London, NW1 2DB
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