Understanding by Implementing: Gaussian Naive Bayes

To illustrate everything, let us use a toy dataset with two real features x₁, x₂, and three classes c₁, c₂, c₃ in the following. Let us start with the class probability p(c), the probability that some class c is observed in the labeled dataset. The simplest way to estimate this is to just compute the relative frequencies of the classes and use them as the probabilities. We can use our dataset to see what this means exactly. There are 7 out of 20 points labeled class c₁ (blue) in the dataset, therefore we say p(c₁) 7/20.