## The Multivariate Bernoulli classification

The previous example uses the Gaussian distribution for features that are essentially binary (*UP = 1* and *DOWN = 0*) to represent the change in value. 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 for 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 such a way that it penalizes the feature *x* that does not have any observation; the Naïve Bayes classifier ignores it [5:10].

### Note

**The Bernoulli mixture model**

M8: For a feature function *f _{k}* with

*f*

_{k}*= 1*, if the feature is observed, and a value of 0 otherwise, and the probability

*p*of the observed feature

*x*belongs to the class

_{k}*C*, then the posterior probability is computed as follows:

_{j}