Contributions of the thesis

Graphical models provide a good framework for machine learning and artificial intelligence. Graphical models are going to be extended, based on approximate Bayesian inference, into a system that can plan, infer, and interact with its environment using both discrete and continuous variables as well as structured representations. The concrete steps that have been taken in this work can be summarised as follows:

• A novel framework where Bayesian networks may include nonlinear dependencies and algorithms for variational Bayesian learning are automatically derived.
• An extension of hidden Markov models to deal with sequences of structured symbols rather than characters, with four relevant algorithms and an applications in the domain of bioinformatics.
• The first graphical model that can handle both nonlinear dependencies and relations.
• An extension of a method for learning nonlinear state-space models to control.
• A novel algorithm for inference in nonlinear state-space models that is both efficient and reliable.
• A study of methods for handling corrupted or inaccurate values in data.
• A study of some latent variable models based on their capability of reconstructing missing values in data.