The naive Bayes classifier is a probabilistic classifier based on the Bayes theorem. Let’s say we have a dataset with features X = [x₁, x₂, …, x_n]. And we need to determine the output label y based on these n features. Now, as per Bayes’ theorem:

Here, P(Y|X) = Probability of event Y given event X
P(X|Y) = Probability of event X given event Y
P(X) and P(Y) are the probabilities of events X and Y, respectively.

Now, if a dataset has n features X = [x₁, x₂, …, x_n] and the output label is y, then we can say:

In other words, if we know the probabilities P(y), P(x_i|y), and P(x_i), for 1 ≤ i ≤ n, then we can calculate P(y|X).

There are different types of naive Bayes classifiers:

• Gaussian Naive Bayes Classifier: We use it when the predictor values are continuous and they follow Gaussian distribution.
• Bernoulli Naive Bayes Classifier: We use it when the predictors are boolean in nature and follow the Bernoulli distribution
• Multinomial Naive Bayes Classifier: This classifier uses a multinomial distribution.

Please note that the naive Bayes classifier uses the term “naive” because we assume the features are strongly independent of each other.

How to solve classification problems using the Gaussian Naive Bayes Classifier in sklearn?

In this example, we will solve a classification problem using the Gaussian naive Bayes classifier. We will assume that the features are continuous and they follow Gaussian distribution.

Let’s read the breast cancer dataset using the sklearn library. The dataset contains various features based on which we can predict whether a patient has breast cancer. We can use the following Python code for this classification problem…