With the proliferation of data, and the increased use of Bayesian networks as
a statistical modelling technique, the expectations and demands on Bayesian
networks have increased substantially. In this text we explore novel techniques
for performing exact inference with Bayesian networks, in an efficient
stable and scalable manner. We consider not only discrete variable Bayesian
networks but also those with continuous variables, and Dynamic Bayesian
networks for modelling time series/sequential data.
We first examine how existing algorithms can be decomposed into a library
of techniques which can then be used when constructing novel algorithms
or extending existing algorithms.
We then go on to develop novel techniques, including an algorithm for
the efficient and scalable manipulation of distributions during inference and
algorithms for performing numerically stable inference.
Additionally we develop a technique for performing fixed memory inference,
which can be used to extend existing algorithms, and we also identify
an inference mechanism which has similar performance to the polytree algorithm,
but can operate on classes of networks that are not trees.
Finally, we explore how nodes with multiple variables can lead to both
graphical simplicity and performance gains.