SYSC 551/651: Discrete Multivariate Modeling
The course focuses on information theory as a modeling framework and as a tool for discrete multivariate analysis. The course presents set- and information-theoretic methods for studying static or dynamic (time series) relations among qualitative variables or among quantitative variables having unknown nonlinear relationships. In the "general systems" literature, this is known as "reconstructability analysis" (RA). RA overlaps partially with log-linear statistical techniques widely used in the social sciences; both are especially valuable in data-rich applications (but RA is not exclusively statistical). RA is highly relevant to the many interrelated "projects" which go under the names of data-mining, machine learning, knowledge discovery and representation, etc.
Applied to data analysis, RA allows the decomposition and compression of multivariate probability distributions (contingency tables) and set-theoretic relations (and mappings), as well as the composition of multiple distributions/relations. The methods are very general. They are valuable in the natural and social sciences and in engineering, business, or other professional fields whenever categorical variables are useful or linear models are inadequate. Applied to the conceptualization of "structure" and "complexity," these set- and information-theoretic ideas are foundational for systems science.
Information on Discrete Multivariate Modeling research