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Introduction to Self

This is blog is simply a public account of my personal learning process, experimentation and self-discovery in developing ways to process human discourse to better understand human behavior in politics, financial markets. That said, this blog will likely be a collection of notes rather than a massive brain dump.

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Notes on defining a language model

Wikipedia defines "Language Model" as " a  probability distribution  over sequences of words.  Given such a sequence, say of length  m , it assigns a probability   to the whole sequence."    The Stanford NLP Group similarly implies this definition through the description of the language modeling in the context of Information Retrieval .  The equation above refers to the chain rule defined by:  See chain-rule definition in the  NLP Review of Basic Probability Theory .  Generating a probability distribution is one part of building a usable language processing infrastructure. A  useful statistical language model typically depends on the specific need, or problem you want to solve, and of course the domain of your problem. Thus the ability to cluster and partition sequences of words based on their likely occurrence given a query as input can serve as the starting point for connecting probability distri...
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Q-Analysis of Natural Language

Q-Analysis is a methodological perspective and language that can be applied to study system structure, and its dynamics. Indeed, q-analysis has been dubbed the “language of structure” ( Legrand 2002 ), because it provides both a mathematical framework and particular vocabulary for defining system features and relationships ( Atkin & Casti, 1977 ; Gould 1980 ). The mathematical framework of q-analysis is built on algebraic topology , a branch of abstract mathematics that is interested in space and shape under continuous deformation (e.g. the bending, compressing, stretching of shapes). In topology, and specifically q-analysis, shape is defined by the relationships between elements in open sets. The relationship between these sets produce new sets representing edges, faces and simplicial complexes that form as a result of the relational mapping λ     from some set A and some set B to a new set C.   The relation  λ represents a rule for defining the condit...
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Defining "lenses" for a Q-Language Topology

I n my previous post,  Q-Analysis of Natural Language  I started to describe a path for applying q-analysis in the study of natural language. One of the particularly interesting aspects of q-analysis is the ability to connect hierarchical data in a rather straightforward (although non-trivial) manner. The process of connecting data are described through the definition of a relational mapping and the rules defined for that mapping.  The relational mappings result in a new subset consisting of the combinations of the two input sets. The resulting new combinatorial set serves as a cover for constructing q-connected simplicies. Thus allowing for inspection of the q-connectivity of sets across hierarchical scales. The below example described in Beaumont and Gatrell , shows the mappings between elements at different hierarchical levels of N. The structure is the resulting mapping between three interrelated sets defined by the relation. In the language of q-analysis, ...
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