Naive Bayes

Naive Bayes is a popular classification algorithm that assumes independence between features. It’s particularly useful for text classification and spam filtering, but it may not always hold true in practice due to its simplistic assumption. Before diving into naive Bayes, let’s understand the Bayes’ theorem, upon which naive Bayes is based.

Bayes’ Theorem

Bayes’ theorem is a fundamental concept in probability theory and statistics that describes how to update the probability for a hypothesis (or event) based on new evidence or data. It’s named after the Reverend Thomas Bayes, an 18th-century statistician and theologian.

Bayes’ Theorem mathematically expresses this relationship as follows:

Where:

• $P(A∣B)$ is the posterior probability, the probability of event A occurring given that event B has occurred. This is what we want to calculate—the updated probability of event A being true after taking into account the new evidence B. It’s essentially our new belief about A based on the observed evidence. In practice, this could be the equivalent of the probability of a person buying our services, given that they live in a certain region. It’s essentially the probability of something happening, given that something else happened.

• $P(B∣A)$ is the likelihood, the probability of event B occurring given that event A has occurred. In other words, it quantifies how likely our observed data is under the assumption that our prior belief is correct. To continue our example, this would be the equivalent of the probability of a person living in a certain region, given that they bought our services.

• $P(A)$ is the prior probability, the probability of event A occurring before considering any new evidence. It represents what we believe about the event based on our prior knowledge or assumptions. In our example, this would be the probability of someone buying our services.

• $P(B)$ ...