On Virtual Evidence and Soft Evidence in Bayesian Networks
We provide an in-depth description of virtual evidence and its application to Bayesian networks. As we will see, virtual evidence significantly extends the power of Bayesia n networks, and makes them much more widely applicable. It does this by giving Bayesian networks the ability to represent aspects from both directed and undirected graphical models. We describe how both evidence and virtual evidence can be seen as having the evidence nodes in the Bayesian network possess virtual children who are always observed to have value unity, and where the conditional probability table of these children imbue their parents either with a sin gle value (hard evidence) or with a collection of values (soft evidenced), the latter case allowing each such value possessing a weight which gets applied to the probability score. This soft evidence is seen as a straightforward gener alization of evidence, where the soft evidence phenomena is interpreted as information provided from outside the context of the process modeled by the Bayesian network (or alternatively, as an extension to the event space that is par titioned normally by the collection of random variables in the Bayesian network). We discuss Pearl’s example of soft ev idence, interpret hybrid ANN/HMM (artificial-neural network/hidden Markov model) systems as soft evidence, and conclude that while the form of soft evidence depends only on ratios of scores and not on the scores’ absolute value s, the actual score values may be obtained from any information source so desired. We find that some information sources, however, might be more intuitively justifiable than others.