published: Feb. 25, 2007, recorded: May 2005, views: 41427
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Bayes Rule provides a simple and powerful framework for machine learning. This tutorial will be organised as follows:
1. I will give motivation for the Bayesian framework from the point of view of rational coherent inference, and highlight the important role of the marginal likelihood in Bayesian Occam's Razor.
2. I will discuss the question of how one should choose a sensible prior. When Bayesian methods fail it is often because no thought has gone into choosing a reasonable prior.
3. Bayesian inference usually involves solving high dimensional integrals and sums. I will give an overview of numerical approximation techniques (e.g. Laplace, BIC, variational bounds, MCMC, EP...).
4. I will talk about more recent work in non-parametric Bayesian inference such as Gaussian processes (i.e. Bayesian kernel "machines"), Dirichlet process mixtures, etc.
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