Reconstructibility Analysis as an Order Theoretical Knowledge Discovery Technique
Cliff Joslyn
Los Alamos National Laboratory
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Last modified: May 24, 2006
Abstract
Reconstructibility analysis (RA) [1] is a multivariate knowledge
discovery technology similar to hierarchical loglinear modeling [3],
and geared towards the abduction of complex systems models. Given a
multivariate dataset, RA proceeds by examining the structural
hypotheses amongst those variables, each one being an irredundant
cover (set of subsets with no subsethood between them) of the variable
space, and thus representing one possible model of their
interactions. Since each block of variables within a model determines a
marginal distribution, the model as a whole determines a set of
marginals, and thus a canonical reconstructed joint distribution. In
this way the information distance of each model from the original
dataset can be calculated.
In this talk we will introduce the rudiments of RA. But our primary
interest is in casting RA as a significant technique within an overall
family of methods we have called Order Theoretical Knowledge Discovery
(OTKD) [2]. The point is that reconstruction hypotheses sit in a
lattice whose operations are coarsening and refinment, and containing
the classical partition lattice as a small subset. Information
distance is then an additive, monotonic valuation on that lattice, and
thus suggests a metric. Model discovery can then be cast as a
multicriteria optimization problem on a quantified lattice, balancing
model complexity as lattice rank against model accuracy as information
distance. We will discuss how RA exemplifies the OTKD paradigm of
metric traversal of quantified ordered sets. We will conclude by
drawing on other examples of related OTKD methods, in ontology
quantification, anomaly detection in concept lattices, and
multidimensional link analysis.
[1] Klir, George and Elias, Doug: (2003) The Architecture of Systems
Problem Solving, Plenum, New York, 2nd edition
[2] Joslyn, Cliff; Oliverira, Joseph; and Scherrer, Chad: (2004)
"Order Theoretical Knowledge Discovery: A White Paper", Los Alamos
Technical Report LAUR 045812,
ftp://ftp.c3.lanl.gov/pub/users/joslyn/white.pdf
[3] Malvestuto, FM: (1996) "Testing Implication of Hierarchical
LogLinear Models for Probability Distributions", Statistics and
Computing, v. 6, pp. 169176


