Gated Bayesian Networks

Abstract: Bayesian networks have grown to become a dominant type of model within the domain of probabilistic graphical models. Not only do they empower users with a graphical means for describing the relationships among random variables, but they also allow for (potentially) fewer parameters to estimate, and enable more efficient inference. The random variables and the relationships among them decide the structure of the directed acyclic graph that represents the Bayesian network. It is the stasis over time of these two components that we question in this thesis.By introducing a new type of probabilistic graphical model, which we call gated Bayesian networks, we allow for the variables that we include in our model, and the relationships among them, to change overtime. We introduce algorithms that can learn gated Bayesian networks that use different variables at different times, required due to the process which we are modelling going through distinct phases. We evaluate the efficacy of these algorithms within the domain of algorithmic trading, showing how the learnt gated Bayesian networks can improve upon a passive approach to trading. We also introduce algorithms that detect changes in the relationships among the random variables, allowing us to create a model that consists of several Bayesian networks, thereby revealing changes and the structure by which these changes occur. The resulting models can be used to detect the currently most appropriate Bayesian network, and we show their use in real-world examples from both the domain of sports analytics and finance.