1 research outputs found
What are the Differences between Bayesian Classifiers and Mutual-Information Classifiers?
In this study, both Bayesian classifiers and mutual information classifiers
are examined for binary classifications with or without a reject option. The
general decision rules in terms of distinctions on error types and reject types
are derived for Bayesian classifiers. A formal analysis is conducted to reveal
the parameter redundancy of cost terms when abstaining classifications are
enforced. The redundancy implies an intrinsic problem of "non-consistency" for
interpreting cost terms. If no data is given to the cost terms, we demonstrate
the weakness of Bayesian classifiers in class-imbalanced classifications. On
the contrary, mutual-information classifiers are able to provide an objective
solution from the given data, which shows a reasonable balance among error
types and reject types. Numerical examples of using two types of classifiers
are given for confirming the theoretical differences, including the
extremely-class-imbalanced cases. Finally, we briefly summarize the Bayesian
classifiers and mutual-information classifiers in terms of their application
advantages, respectively.Comment: (2nd version: 19 pages, 5 figures, 7 tables. Theorems on Bayesian
classifiers are extended to multiple variables. Appendix B for "Tighter
bounds between the conditional entropy and Bayesian error in binary
classifications" are added, in which Fano's bound is shown numerically to be
very tight