文档介绍：Bayesian Regression and Classification Using
Mixtures of Gaussian Processes £
. Shi, R. Murray-Smith,
Depts. p. Science & Statistics. Dept. puting Science,
University of Glasgow, University of Glasgow,
Glasgow G12 8QQ, & Hamilton Institute,
Scotland, UK. National University of Ireland Maynooth.
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. Titterington,
Dept. of Statistics
University of Glasgow.
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Abstract
For a large data-set with groups of repeated measurements, a mixture model
of Gaussian process priors is proposed for modelling the heterogeneity among
the different replications. A hybrid Markov chain Monte Carlo (MCMC) al-
gorithm is developed for the implementation of the model for regression and
classification. The regression model and its implementation are illustrated
by modelling observed Functional Electrical Stimulation experimental re-
sults. The classification model is illustrated on a synthetic example.
Keywords: Classification; Gaussian process; Heterogeneity; Hybrid Markov
chain Monte Carlo; Mixture models; Nonlinear regression; Multiple mod-
els.
£ Technical Report TR-2002-114, Department puting Science, University of Glasgow,
Glasgow G12 8QQ, Scotland. June 2002
1 Introduction
Multiple model approaches to the empirical modelling of nonlinear systems have
been of interest for many years, and have seen more widespread use in the last ten
years. We reviewed the literature in (Johansen and Murray-Smith 1997), and re-
cent years have seen a number of applications of the theory. However, subsequent
work such as (Shorten et al. 1999, Leith and Leithead 1999) showed that there
were problems with identification of parameters for off-equilibrium models, and
that interpretation of local model parameters could often be misleading. This was
generalised to the fuzzy modelling literature in (Johansen et al. 2000, Johansen
and Babuska 2002). Sparseness of data in off-equilibrium regions of a nonl