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Simultaneous Predictive Gaussian Classifiers

Author

Listed:
  • Yaqiong Cui

    (University of Helsinki)

  • Jukka Sirén

    (University of Helsinki)

  • Timo Koski

    (KTH Royal Institute of Technology)

  • Jukka Corander

    (University of Helsinki
    Åbo Akademi University
    University of Helsinki
    Åbo Akademi University)

Abstract

Gaussian distribution has for several decades been ubiquitous in the theory and practice of statistical classification. Despite the early proposals motivating the use of predictive inference to design a classifier, this approach has gained relatively little attention apart from certain specific applications, such as speech recognition where its optimality has been widely acknowledged. Here we examine statistical properties of different inductive classification rules under a generic Gaussian model and demonstrate the optimality of considering simultaneous classification of multiple samples under an attractive loss function. It is shown that the simpler independent classification of samples leads asymptotically to the same optimal rule as the simultaneous classifier when the amount of training data increases, if the dimensionality of the feature space is bounded in an appropriate manner. Numerical investigations suggest that the simultaneous predictive classifier can lead to higher classification accuracy than the independent rule in the low-dimensional case, whereas the simultaneous approach suffers more from noise when the dimensionality increases.

Suggested Citation

  • Yaqiong Cui & Jukka Sirén & Timo Koski & Jukka Corander, 2016. "Simultaneous Predictive Gaussian Classifiers," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 73-102, April.
  • Handle: RePEc:spr:jclass:v:33:y:2016:i:1:d:10.1007_s00357-016-9197-3
    DOI: 10.1007/s00357-016-9197-3
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    References listed on IDEAS

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    1. Jukka Corander & Mats Gyllenberg & Timo Koski, 2009. "Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy," 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. 3(1), pages 3-24, June.
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