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

Author

Listed:
  • Gonzalo Perez-de-la-Cruz

    (National Institute of Statistics and Geography (INEGI) of Mexico)

  • Guillermina Eslava-Gomez

    (UNAM)

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.

Suggested Citation

  • Gonzalo Perez-de-la-Cruz & Guillermina Eslava-Gomez, 2019. "Discriminant analysis for discrete variables derived from a tree-structured graphical model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 855-876, December.
    • Handle: RePEc:spr:advdac:v:13:y:2019:i:4:d:10.1007_s11634-019-00352-z
    DOI: 10.1007/s11634-019-00352-z
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    References listed on IDEAS

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    1. Abreu, Gabriel C. G. & Labouriau, Rodrigo & Edwards, David, 2010. "High-Dimensional Graphical Model Search with the gRapHD R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 37(i01).
    2. Asparoukhov, Ognian K. & Krzanowski, Wojtek J., 2001. "A comparison of discriminant procedures for binary variables," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 139-160, December.
    3. Kim, Ji-Hyun, 2009. "Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3735-3745, September.
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