Gaussian naive Bayes is useful when working with continuous values whose probabilities can be modeled using a Gaussian distribution:
The conditional probabilities P(xi|y) are also Gaussian distributed; therefore, it's necessary to estimate the mean and variance of each of them using the maximum likelihood approach. This quite easy; in fact, considering the property of a Gaussian, we get:
Here, the k index refers to the samples in our dataset and P(xi|y) is a Gaussian itself. By minimizing the inverse of this expression ...
