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Abstract:
The recent introduction of the `relevance vector machine' has
effectively demonstrated how sparsity may be obtained in
generalised linear models within a Bayesian framework. Using a
particular form of Gaussian parameter prior, `learning' is the
maximisation, with respect to hyperparameters, of the
marginal likelihood
of the data. This paper studies the properties of that objective
function, and demonstrates that conditioned on an individual
hyperparameter, the marginal likelihood has a unique maximum
which is computable in closed form. It is further shown that if a
derived `sparsity criterion' is satisfied, this maximum is
exactly equivalent to `pruning' the corresponding parameter from
the model.
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