# Context-Specific Independence in Graphical Models

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Abstract

The theme of this thesis is context-specific independence in graphical models. Considering a system of stochastic variables it is often the case that the variables are dependent of each other. This can, for instance, be seen by measuring the covariance between a pair of variables. Using graphical models, it is possible to visualize the dependence structure found in a set of stochastic variables. Using ordinary graphical models, such as Markov networks, Bayesian networks, and Gaussian graphical models, the type of dependencies that can be modeled is limited to marginal and conditional (in)dependencies. The models introduced in this thesis enable the graphical representation of context-specific independencies, i.e. conditional independencies that hold only in a subset of the outcome space of the conditioning variables.

In the articles included in this thesis, we introduce several types of graphical models that can represent context-specific independencies. Models for both discrete variables and continuous variables are considered. A wide range of properties are examined for the introduced models, including identifiability, robustness, scoring, and optimization. In one article, a predictive classifier which utilizes context-specific independence models is introduced. This classifier clearly demonstrates the potential benefits of the introduced models. The purpose of the material included in the thesis prior to the articles is to provide the basic theory needed to understand the articles.