The topic of this thesis is the analysis of the contextual independencies in probabilistic models. Contextual independency can be thought of as a value-specific extension of conditional independency.
To represent contextual independencies, I use the generalisation of Bayesian networks, a fundamental approach in probabilistic modelling. I summarize earlier approaches in this field, some of which I examine in greater depth. The examined studies all share the concept of using parent-child (local) structures to represent these kind of independencies.
By using local structures not only the representational ability increases, but the modification and extension of the learning methods are also needed. To do so, I overview known methods and propose extensions to utilize special local structures to infer contextual independecies from statisical data.
I introduce the definition of the contextual Markov blanket and boundary, which are value-specific extensions of the standard concept. Their significance follows from the fact that one can use the various possible value configurations of stochastic variables to represent the contexts where a given variable is independent of all others. I examine and characterize the properties of these value configurations. I describe an algorithm to generate contextual Markov boundaries from a contextual Bayesian network. Finally, I evaluate this implementation using artificial and real-world data sets.