MML, hybrid Bayesian network graphical models, statistical consistency, invarianc

Publisher Summary The problem of statistical—or inductive—inference pervades a large number of human activities and a large number of (human and non-human) actions requiring “intelligence.” The Minimum Message Length (MML) approach to machine learning (within artificial intelligence) and statistical (or inductive) inference gives a trade-off between simplicity of hypothesis and goodness of fit to the data. There are several different and intuitively appealing ways of thinking of MML. There are many measures of predictive accuracy. The most common form of prediction seems to be a prediction without a probability or anything else to quantify it. MML is also discussed in terms of algorithmic information theory, the shortest input to a (Universal) Turing Machine [(U)TM] or computer program which yields the original data string. This chapter sheds light on information theory, turing machines and algorithmic information theory—and relates all of these to MML. It then moves on to Ockham's razor and the distinction between inference (or induction, or explanation) and prediction.