Simultaneous Predictive Gaussian Classifiers

YQ Cui, J Siren, T Koski, Jukka Corander

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    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.
    Original languageUndefined/Unknown
    Pages (from-to)73–102
    Number of pages30
    JournalJournal of Classification
    Volume33
    Issue number1
    DOIs
    Publication statusPublished - 2016
    MoE publication typeA1 Journal article-refereed

    Keywords

    • Bayesian modeling
    • Discriminant analysis
    • Inductive learning
    • Predictive inference
    • Probabilistic classification

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