Bayesian regression filters and the issue of priors |
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Authors: | Huaiyu Zhu Richard Rohwer |
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Affiliation: | (1) Neural Computing Research Group, Department of Computer Science and Applied Mathematics, Aston University, B4 7ET Birmingham, UK |
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Abstract: | We propose a Bayesian framework for regression problems, which covers areas usually dealt with by function approximation. An online learning algorithm is derived which solves regression problems with a Kalman filter. Its solution always improves with increasing model complexity, without the risk of over-fitting. In the infinite dimension limit it approaches the true Bayesian posterior. The issues of prior selection and over-fitting are also discussed, showing that some of the commonly held beliefs are misleading. The practical implementation is summarised. Simulations using 13 popular publicly available data sets are used to demonstrate the method and highlight important issues concerning the choice of priors. |
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Keywords: | Approximation Bayesian method Kalman filter Online learning Prior selection Radial Basis Functions Regression |
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