Bayesian methods for learning to learn

Contains fulltext : 72783.pdf (publisher's version ) (Open Access)This thesis describes Bayesian approaches to the fields of survival analysis, hierarchical (time series) modelling and model clustering. The application areas serve as playing grounds to introduce new methods and approximations to make calculations on large databases that would otherwise be unfeasible, doable in reasonable time. After a general introduction on the use of Bayesian statistics the second chapter describes how the over-fitting problems that are generally encountered in survival analysis are averted through the use of Bayesian priors. The resulting (complicated) posterior is approximated through a variational approach and through hybrid Markov chain Monte Carlo sampling. The Bayes factor is used to eliminate irrelevant inputs to the model, and improve its accuracy. The third chapter describes a hierarchical method to model parallel tasks (with the same type of inputs/outputs). The tasks 'learn from each other' both through explicitly sharedmodel parameters and through parameters that are subject to the same prior. A multi-modal prior is shown to produce a meaningful clustering of the regarded tasks. The fourth chapter describes parallel time series, that use the same philosophy as the previous parallel tasks to improve prediction. The exact (dynamic linear) model here implies numerous inversions of high-dimensional matrices, and is therefore approximated through a variational approach and through 'expectation propagation'. The last chapter regards collections of similar models (obtained e.g. through bootstrapping) and introduces a clustering method that produces a small number of representative models. These models are shown to have the same predictive power as the full collection. Model clustering is also used as an analysis tool to study the bootstrapping process143 p