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What are the differences between Bayesian classifiers and mutual-information classifiers?

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    Bayesian and mutual-information classifiers were compared for binary classification. Mutual-information classifiers offer a more objective and balanced approach, especially for imbalanced datasets, unlike Bayesian classifiers.

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    Area of Science:

    • Machine Learning
    • Statistical Classification

    Background:

    • Binary classification tasks often require decision-making with potential for abstention (reject option).
    • Bayesian and mutual-information classifiers are common approaches, each with distinct characteristics.

    Purpose of the Study:

    • To examine and compare Bayesian and mutual-information classifiers for binary classification, with and without a reject option.
    • To analyze the decision rules, error types, and reject types for both classifier types.

    Main Methods:

    • Derivation of general decision rules for Bayesian classifiers, considering error and reject types.
    • Formal analysis of parameter redundancy in Bayesian cost terms when abstention is enforced.
    • Evaluation of classifier performance using numerical examples, including extremely class-imbalanced scenarios.

    Main Results:

    • Bayesian classifiers exhibit parameter redundancy in cost terms, leading to interpretation issues and weakness in class-imbalanced problems without data.
    • Mutual-information classifiers provide objective solutions using available data, achieving a balanced trade-off between error and reject types.
    • Numerical examples confirm the distinct performance characteristics, particularly in imbalanced classification scenarios.

    Conclusions:

    • Mutual-information classifiers demonstrate superior objectivity and balance, especially for class-imbalanced data, compared to Bayesian classifiers.
    • Bayesian classifiers face challenges with cost term interpretation and performance on imbalanced datasets without explicit data input.
    • The study highlights the respective advantages and disadvantages of Bayesian and mutual-information classifiers for practical applications.