We review the principles of Minimum Description Length and Stochastic Complexity as used in data compression and statistical modeling. Stochastic complexity is formulated as the solution to optimum universal coding problems extending Shannon’s basic source coding theorem. The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to ...

Binary decision trees based on univariate splits have traditionally employed so-called impurity functions as a means of searching for the best node splits. Such functions use estimates of the class distributions. In the present paper we introduce a new concept to binary tree design: instead of working with the class distributions of the data we work directly with the distribution of the errors ...

Context Free Grammars (CFGs) are widely used in programming language descriptions, natural language processing, compilers, and other areas of software engineering where there is a need for describing the syntactic structures of programs. Grammar inference (GI) is the induction of CFGs from sample programs and is a challenging problem. We describe an unsupervised GI approach which uses simplicit...