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5.3 Bayesian Classifiers (Bayes theorem \( P( Y|X) = \frac {P(X|Y)*P(Y)}…

- - - - for Categorical Attributes
        fraction
      - for Continuous Attributes
        
        Discretization
        fraction of intervals
        
        Assuming Distribution
        example, Gaussian distribution:
        \( P(X_i = x_i|Y = y_i) = \frac {1} { \sqrt{2 \pi} \sigma_{ij}}exp^- \frac{(x_i- \mu_{ij})^2 } { 2 \sigma_{ij}^2} \)
        where: \( \mu - mean; \sigma^2 - variance \)
      - M-estimate of Conditional Probability
        
        to avoid the problem \( P(Xi|Y) = 0 \) .
        
        more robust when training examples is small.
        
        \( P(X_i|Y_i) = \frac {n_c + mp} {n+m} \)
        n: total number of instances from class \( y_i \)
        \( n_c \): the number of \( X=x_i \) and \(Y=y_i \)
        m: the equivalent sample size
        p: user-specified parameter;