Usually, the most efficient solutions are the easiest, and Naïve Bayes is a clear example of that. It has proven to be not only easy, but also fast, accurate, and reliable, considering the advances in machine learning in the last few years. In this article we will learn about, what is naive Bayes classifier, a Bayes classifier example, and what naive Bayes algorithm is useful for?

  1. What is Naïve Bayes Classifier?
  2. How does Naive Bayes work
  3. Why do we use Naive Bayes Classifier?
  4. Naive Bayes classifier in Python
  5. Naive Bayes Probability

1) What is Naïve Bayes Classifier?

A Naive Bayes classifier assumes, in simple terms, that the existence in a class of a certain function is irrelevant to the presence of some other function.

Naive Bayes classifiers in statistics are a family of simple “probabilistic classifiers” based on applying the Bayes theorem with clear assumptions of independence between the features. They are among the simplest Bayesian network models but combined with kernel density estimation, they can reach higher levels of precision.

For instance, if it is red, round, and around 3 inches in diameter, a fruit may be considered to be an apple. Even if these characteristics depend on each other or the presence of the other characteristics, all of these characteristics independently lead to the possibility that this fruit is an apple and that’s why it’s known as ‘Naive.’

For very large data sets, the Naive Bayes model is easy to construct and particularly helpful. Also, very complex classification approaches are considered to outperform Naive Bayes, along with simplicity.

The Bayes theorem provides a way for P(c|x) posterior likelihood to be determined from P(c), P(x), and P(x|c).

Using the Bayes theorem, provided that B has occurred, we can find the likelihood of A occurring. Here, the proof is B and the hypothesis is A. The assumption made here is the independence of the predictors/features. That is, the presence of one unique characteristic does not influence the other. It is thus called naive.

Other common classifiers for Naive Bayes are:

  • Naive Bayes multinomial: Function vectors reflect the frequencies at which a multinomial distribution has produced some events. Usually used for document classification, this is the event model.
  • Bernoulli Naive Bayes: The attributes are separate Booleans representing Inputs into the case model of the multivariate Bernoulli. This model is popular for tasks of text classification, like the multinomial model, where functions are used instead of term frequencies, where binary term frequency.

2) How does Naive Bayes work

With the aid of the example below, you can understand the work of Naïve Bayes’ Classifier:

Suppose we have a weather conditions dataset and the required “Play” target variable. So we need to determine, using this dataset, whether we should play according to the weather conditions on a specific day or not. So, we need to follow the steps below to solve this issue:

Convert the given dataset into tables of frequency.

Generate a table of probability by finding the probabilities of the characteristics given.

To measure the posterior likelihood, use the Bayes theorem.

3) Why do we use Naive Bayes Classifier?

Predicting the class of the test data set is simple and quick. In multi-class prediction, it also performs well.

When assuming freedom, a Naive Bayes classifier performs well relative to other methods, such as logistic regression, and you need fewer data from preparation.

Compared to the numerical variable, it performs well in categorical input variables (s). Standard distribution is considered for numerical variable distributions (bell curve, which is a strong assumption).


  • Prediction in real-time: Naive Bayes is an enthusiastic learning classifier, and it’s quick for sure. Therefore, it could be used for making forecasts in real-time.
  • Multi-Class Prediction: For multi-class prediction functions, Also, this algorithm is well known. We will estimate the probabilities of several target variable groups here.
  • Text classification: Compared to other algorithms, Naive Bayes classifiers, commonly used in text classification, have higher performance rates. (due to better performance in multi-class problems and the law of independence).

4) Naive Bayes classifier in Python

  • The implementation of the Naive Bayes scratch algorithm in python is uploaded to my Github repository with a description for each move.
  • In the Github repository, implementation of Naive Bayes with Scikit learning is also added.

5) Naive Bayes Probability

The Naive Bayes classifier assumes that the effect on a given class (c) The predictor value (x) is separate from the values of other predictors. Class conditional independence is called this assumption.

  • The posterior probability of the class (target) given predictor is P(c|x) (attribute).
  • P(c) is the class’s prior likelihood.
  • P(x|c) is the likelihood of the class defined by the predictor.
  • P(x) is the predictor’s prior likelihood.


The basic hypothesis of Naive Bayes is that each attribute makes one:

  • Self-contained
  • Equally Equal

The contribution to the performance.

Concerning our dataset, it is possible to understand this notion as:

  • We presume that there are no dependent pairs of features. For eg, the ‘warm’ weather has nothing to do with the humidity, or the ‘rainy’ forecast doesn’t change the winds. Hence, it is presumed that the features are separate.
  • Secondly, the same weight is given to every element (or importance). Knowing only the temperature and humidity alone, for example, does not forecast the outcome correctly. None of the attributes is trivial and is considered to contribute equally to the result.


In sentiment analysis, spam filtering, recommendation systems, etc, Naive Bayes algorithms are often used. They are simple and easy to introduce, but their main drawback is that predictors need to be autonomous. In most real-life situations, the predictors are dependent, which hinders the classifier’s efficiency. Compared to more advanced methods, Naive Bayes learners and classifiers can be extremely swift.

The decoupling of the distributions of the class conditional function implies that each distribution can be calculated as a one-dimensional distribution independently. In effect, this helps to mitigate issues arising from the curse of dimensionality. Despite their seemingly over-simplified assumptions, in many real-world scenarios, including document classification and spam filtering, naive Bayes classifiers have performed very well. To estimate the required parameters, they need a small amount of training data.

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