All Naive Bayes classifiers assume that the value of a one feature is independent of the value of any other feature, on given a condition(i.e. class label). For instance, a fruit may be considered to be an apple if it is red, round, and about 10 cm in diameter.

A Naive Bayes classifier is a type of supervised learning algorithm that is used for the classification task. A Naive Bayes classifier is a simple classifier, which is an application of Bayes theorem. It is the probabilistic classification method as it uses the likelihood probability to predict the purpose of the classification task. The model used by a Naive Bayes classifier makes strong conditional independence assumptions. The conditional independence assumption is that given a class, the predictor or feature values are independent. There is no correlation between the features of a certain class.

Naive Bayes Classifier is based on the Bayes Theorem. The Bayes Theorem says the conditional probability of an outcome can be computed using the conditional probability of the cause of the result. The Naive Bayes classifier uses the input variable to choose the class with the highest posterior probability.

The algorithm is called naive because it assumes that the distribution of the data can be Gaussian or normal, Bernoulli or Multinomial distribution.

Another drawback of Naive Bayes is that continuous features have to be preprocessed and discretized by binning, which can discard useful information.

*The conditional probability purely derives Bayes theorem. Let’s define the conditional probability.*

*This orange rectangular space is known as a sample space. It is a collection of all possible outcomes of an experiment, and in circles, A and B are events. These are not disjoint events. They are just overlapping and the overlapping portion. That is the portion which is familiar to both a and b are known as A intersection b. Now, If we are asked what the conditional probability of happening A given that B has already happened is, Which is the probability that event A will occur given that B has already happened. Now simplify whenever you are dealing with the conditional probability, assume that the entire sample space has shrunk to the event which is already happened, so now our sample space becomes event b because we are only dealing with that portion of sample space where B has already happened. Now we figured out that B has already happened. Where do we find A in this portion? That is nothing but the intersection portion, so you can write the probability of A given that B as the probability of A intersection B divided by the probability of B.*

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