On selection of kernel parametes in relevance vector machines for hydrologic applications |
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| Authors: | Shivam Tripathi Rao S Govindaraju |
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| Institution: | (1) School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA |
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| Abstract: | Recent advances in statistical learning theory have yielded tools that are improving our capabilities for analyzing large
and complex datasets. Among such tools, relevance vector machines (RVMs) are finding increasing applications in hydrology
because of (1) their excellent generalization properties, and (2) the probabilistic interpretation associated with this technique
that yields prediction uncertainty. RVMs combine the strengths of kernel-based methods and Bayesian theory to establish relationships
between a set of input vectors and a desired output. However, a bias–variance analysis of RVM estimates revealed that a careful
selection of kernel parameters is of paramount importance for achieving good performance from RVMs. In this study, several
analytic methods are presented for selection of kernel parameters. These methods rely on structural properties of the data
rather than expensive re-sampling approaches commonly used in RVM applications. An analytical expression for prediction risk
in leave-one-out cross validation is derived. For brevity, the effectiveness of the proposed methods is assessed first by
data generated from the benchmark sinc function, followed by an example involving estimation of hydraulic conductivity values
over a field based on observations. It is shown that a straightforward maximization of likelihood function can lead to misleading
results. The proposed methods are found to yield robust estimates of parameters for kernel functions. |
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| Keywords: | Bayesian learning Relevance vector machines Interpolation Leave-one-out cross-validation VC dimension Bayes information criterion Power spectrum |
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