Discriminant analysis for discrete variables derived from a tree-structured graphical model

Gonzalo Perez- de-la-Cruz () and Guillermina Eslava-Gomez ()
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Gonzalo Perez- de-la-Cruz: National Institute of Statistics and Geography (INEGI) of Mexico
Guillermina Eslava-Gomez: UNAM

Advances in Data Analysis and Classification, 2019, vol. 13, issue 4, No 3, 855-876

Abstract: Abstract The purpose of this paper is to illustrate the potential use of discriminant analysis for discrete variables whose dependence structure is assumed to follow, or can be approximated by, a tree-structured graphical model. This is done by comparing its empirical performance, using estimated error rates for real and simulated data, with the well-known Naive Bayes classification rule and with linear logistic regression, both of which do not consider any interaction between variables, and with models that consider interactions like a decomposable and the saturated model. The results show that discriminant analysis based on tree-structured graphical models, a simple nonlinear method including only some of the pairwise interactions between variables, is competitive with, and sometimes superior to, other methods which assume no interactions, and has the advantage over more complex decomposable models of finding the graph structure in a fast way and exact form.

Keywords: Discrete variables; Discriminant analysis; Error rates; Minimum weight spanning tree; Multinomial distribution; Sparseness; Structure estimation; Tree-structured graphical models; 62H30; 68T10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11634-019-00352-z

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