Multivariate Bernoulli classification

So far, our investigation of the Naïve Bayes has focused on features that are essentially binary {UP=1, DOWN=0}. The mean value is computed as the ratio of the number of observations for which x_i = UP over the total number of observations.

As stated in the first section, the Gaussian distribution is more appropriate for either continuous features or binary features in the case of very large labeled datasets. The example is the perfect candidate for the Bernoulli model.

Model

The Bernoulli model differs from the Naïve Bayes classifier in that it penalizes the features x, which does not have any observation; the Naïve Bayes classifier ignores them [5:10].

Note

The Bernoulli mixture model

M8: For a feature function f_k with fk = 1 if the feature is observed, 0 otherwise, and the probability p of the observed feature x_k belongs to the class C_j, the posterior probability is computed as follows:

Implementation

The implementation of the Bernoulli model consists of...