Probability tables or conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and may become intractable by conventional methods of statistical inference in Bayesian networks and in other areas because of their dimensionality. In may cases, however, these probability tables constitute tensors of relatively low rank. Such tensors can be written in so called Kruskal form as a sum of rank-one components. Such representation need not be unique and several (sometimes many) equivalent representations of the same tensor may co-exist.

How to work with these Kruskal form representations instead of working with full form of the tensors will be suggested. Particular elements of the tensor are evaluated only when they are needed. It will be shown how standard operations with probability tables can be done through the Kruskal form of tensors. In this way it is possible to work with probability tables that are intractable otherwise because of their large size.

Institute of Information Theory and Automation