Entropy Estimation Using a Linguistic Zipf-Mandelbrot-Li Model for Natural Sequences

Estimating Sentence-like Structure in Synthetic Languages Using Information Topology

Estimating sentence-like units and sentence boundaries in human language is an important task in the context of natural language understanding. While this topic has been considered using a range of techniques, including rule-based approaches and supervised and unsupervised algorithms, a common aspect of these methods is that they inherently rely on a priori knowledge of human language in one form or another. Recently we have been exploring synthetic languages based on the concept of modeling behaviors using emergent languages. These synthetic languages are characterized by a small alphabet and limited vocabulary and grammatical structure. A particular challenge for synthetic languages is that there is generally no a priori language model available, which limits the use of many natural language processing methods. In this paper, we are interested in exploring how it may be possible to discover natural ‘chunks’ in synthetic language sequences in terms of sentence-like units. The problem is how to do this with no linguistic or semantic language model. Our approach is to consider the problem from the perspective of information theory. We extend the basis of information geometry and propose a new concept, which we term information topology, to model the incremental flow of information in natural sequences. We introduce an information topology view of the incremental information and incremental tangent angle of the Wasserstein-1 distance of the probabilistic symbolic language input. It is not suggested as a fully viable alternative for sentence boundary detection per se but provides a new conceptual method for estimating the structure and natural limits of information flow in language sequences but without any semantic knowledge. We consider relevant existing performance metrics such as the F-measure and indicate limitations, leading to the introduction of a new information-theoretic global performance based on modeled distributions. Although the methodology is not proposed for human language sentence detection, we provide some examples using human language corpora where potentially useful results are shown. The proposed model shows potential advantages for overcoming difficulties due to the disambiguation of complex language and potential improvements for human language methods.

An Information Theoretic Approach to Symbolic Learning in Synthetic Languages

An important aspect of using entropy-based models and proposed “synthetic languages”, is the seemingly simple task of knowing how to identify the probabilistic symbols. If the system has discrete features, then this task may be trivial; however, for observed analog behaviors described by continuous values, this raises the question of how we should determine such symbols. This task of symbolization extends the concept of scalar and vector quantization to consider explicit linguistic properties. Unlike previous quantization algorithms where the aim is primarily data compression and fidelity, the goal in this case is to produce a symbolic output sequence which incorporates some linguistic properties and hence is useful in forming language-based models. Hence, in this paper, we present methods for symbolization which take into account such properties in the form of probabilistic constraints. In particular, we propose new symbolization algorithms which constrain the symbols to have a Zipf–Mandelbrot–Li distribution which approximates the behavior of language elements. We introduce a novel constrained EM algorithm which is shown to effectively learn to produce symbols which approximate a Zipfian distribution. We demonstrate the efficacy of the proposed approaches on some examples using real world data in different tasks, including the translation of animal behavior into a possible human language understandable equivalent.