 # Naive Bayes

## What is Naive Bayes?

Naive Bayes is a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features. It is a classification technique based on Bayes' Theorem with an assumption of independence among predictors. In simple terms, a Naive Bayes classifier assumes that the presence of a particular feature in a class is unrelated to the presence of any other feature.

Naive Bayes models are easy to build and particularly useful for very large datasets. Along with simplicity, Naive Bayes is known to outperform even highly sophisticated classification methods. It is one of the most practical approaches for certain types of problems, including document classification and spam filtering.

## Bayes' Theorem

Naive Bayes classifiers are built on Bayes' Theorem, which is an equation describing the relationship of conditional probabilities of statistical quantities. In Bayesian classification, we're interested in finding the probability of a label given some observed features, which can be written as P(Label | Features). Bayes' Theorem tells us how we can express this in terms of quantities we can compute more directly:

P(Label | Features) = P(Features | Label) * P(Label) / P(Features)

Here, P(Label) is the prior probability of the class (Label), P(Features | Label) is the likelihood which is the probability of the predictor given class, and P(Features) is the prior probability of the predictor.

## Naive Bayes' Independence Assumption

The naive aspect of the algorithm comes from the assumption that the features used to predict the class are independent of each other. This is a strong assumption and is rarely true in real-world applications. However, the approach still performs very well under this assumption, especially in cases where the independence is approximately true.

## Types of Naive Bayes Model

There are multiple types of Naive Bayes models, and the choice of model depends on the data distribution:

• Gaussian:

It assumes that features follow a normal distribution. This is used in cases where features are continuous.

• Multinomial: It is used for discrete counts. For example, let’s say we have text classification problems. Here we can consider the frequency of the word as the feature.
• Bernoulli:

The binomial model is useful if your feature vectors are binary (i.e., zeros and ones). An example could be text classification with a 'bag of words' model where the 1s & 0s are "word occurs in the document" and "word does not occur in the document" respectively.

• It is easy and fast to predict the class of the test data set. It also performs well in multi-class prediction.
• When the assumption of independence holds, a Naive Bayes classifier performs better compared to other models like logistic regression and you need less training data.

• It performs well in the case of categorical input variables compared to numerical variables. For numerical variable, a normal distribution is assumed (bell curve, which is a strong assumption).

• If the categorical variable has a category in the test data set, which was not observed in the training data set, the model will assign a 0 (zero) probability and will be unable to make a prediction. This is often known as “Zero Frequency”. To solve this, we can use the smoothing technique, like Laplace estimation.

• On the other side naive Bayes is also known as a bad estimator, so the probability outputs from predict_proba are not to be taken too seriously.
• Another limitation of Naive Bayes is the assumption of independent predictors. In real life, it is almost impossible that we get a set of predictors that are completely independent.

## Applications of Naive Bayes Algorithms

Naive Bayes is widely used for text classification purposes. Some of the areas it is commonly used include:

• Spam filtering: Naive Bayes classifiers were one of the first systems used to identify and filter spam. They are still used as a baseline for more complex methods.
• Document categorization: It is used for automated document classification into predefined categories.
• Sentiment analysis:

Naive Bayes is often used for sentiment analysis, to identify if a given text implies a positive, negative or neutral sentiment.

• Recommendation systems: Naive Bayes, along with collaborative filtering, is used by some recommendation systems to predict if a user would like a given resource or not.

## Conclusion

Despite its simplicity, Naive Bayes can yield very accurate models, especially for the size of the dataset it can handle and the speed at which it operates. While it may not be the best performing model in all situations, its performance, ease of implementation, and speed make Naive Bayes a practical algorithm for many situations where a quick solution is needed, or where the data aligns well with the independence assumptions.