Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning

Probabilistic parsing

Postprin

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

Machine Learning and the Cognitive Basis of Natural Language

Articl

Exploring the N-th Dimension of Language

This paper is aimed at exploring the hidden fundamental\ud computational property of natural language that has been so elusive that it has made all attempts to characterize its real computational property ultimately fail. Earlier natural language was thought to be context-free. However, it was gradually realized that this does not hold much water given that a range of natural language phenomena have been found as being of non-context-free character that they have almost scuttled plans to brand natural language contextfree. So it has been suggested that natural language is mildly context-sensitive and to some extent context-free. In all, it seems that the issue over the exact computational property has not yet been solved. Against this background it will be proposed that this exact computational property of natural language is perhaps the N-th dimension of language, if what we mean by dimension is\ud nothing but universal (computational) property of natural language

Probabilistic Programming Concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been developed since more than 20 years