Naïve Bayes Machine Learning: Basics to Advanced Algorithm Concepts

4 min readMay 27, 2024

The Naive Bayes classifier is a simple but effective probabilistic learning algorithm based on the Bayes theorem with strong independence assumptions among the features. Despite the naive in its name, Naive Bayes has been proved a great classifier not only for text related tasks like spam filtering, and sport events classification but also to predict medical diagnosis. This article will give you an overview as well as more advanced use and implementation of Naive Bayes in machine learning.

Naïve Bayes is a classification algorithm for categorical variables, which is based on the well-known Bayes theorem.
Used mostly in high-dimensional text classification
The Naïve Bayes Classifier is a simple probabilistic classifier and it has very few number of parameters which are used to build the ML models that can predict at a faster speed than other classification algorithms.
It is a probabilistic classifier i.e., it predicts based on the likelihood of an object.
Naïve Bayes Algorithm: It is used in spam filtration, Sentimental analysis, classifying articles and many more.

Why is it called Naïve Bayes?

Naïve Bayes is a classification algorithm based on Bayes Theorem that assumes independent predictors.

Naïve: Named as Naïve because it assumes the presence of one feature does not affect other features. For example if the fruit is classified on color shape and taste basis, then red round tailing sweet like fruit identified as apple. Which is why every single feature helps in identifying that it is an apple without relying on the other feature.
Bayes: Named Bayes for the basis in Bayes’ Theorem.

Bayes’ Theorem

Types of Naïve Bayes Model:

Three types of Naive Bayes Model are –

Gaussian : The Gaussian naive Bayes assumes that features follow a normal distribution. This assumes that the predictors X are continuous and have been sampled from a Gaussian distribution.
Multinomial : Multinomial Naïve Bayes classifier is used when the data has multinomial distribution. It is basically used for document classification, like a particular document which deals with what category like Sports, Politics or education etc.
A great Frequency of words is a predictor, and that is used as the feature for The classifier
Bernoulli : The Bernoulli classifier functions the same as the Multinomial classifier, but its predictor variables are Booleans that refer to independent. For example if some word exists in a document or not so. This model is also one of the most popular for document classification tasks.

Practical Applications

Email Filtering: In email filtering, we use the naive Bayes algorithm to classify emails as spam or not.
Text Classification: Document categorization, sentiment analysis, language detection
Medical Diagnosis: helps to diagnose diseases according to patient’s symptoms and past data.

Advanced Concepts in Naive Bayes

Handling Continued Features

The fact that Gaussian Naive Bayes is designed for continues characteristics and for such characteristic s a suitable solution it may be but there are other ways:

Kernel Density Estimation (KDE): A non-parametric means of estimating the probability density function random variable. It affords much better flexibility than the Gaussian assumption.
Discretization: This involves transforming continuous characteristics into discrete bins and placing them within each bin as a separate feature to be treated by Multinomial Naive Bayes. (A revised method has been given but it appears the effects are much less than when originally proposed.)

Handling Missing Values

Naive Bayes Naive Bayes can deal with missing values. That is, the missing nature of the characteristics will not affect the product of probabilities and can be ignored.

Feature Selection

Noise reduction and independency assumption improvement, features selection could help increase the performance of Naive Bayes classifiers greatly. Techniques include:

Mutual Information: This selects features that have a high mutual information with the class labels.
Chi-Square Test: It correspond to selecting the categorical features which have been proven highly significant, with respect to the class labels.

Laplace Smoothing

The training set may contain zero probabilities, and so we need to apply Laplace smoothing (or additive smoothing).

Computational Complexity

As Naive Bayes classifier is fast in nature, so both training and prediction takes one of the lowest time among all algorithm( only Support Vector Machine has similar kind of speed to it). Its training complexity is 𝑂(𝑛𝑑), with 𝑛 the number of instance to train, and 𝑑 the number of features. Prediction complexity is O(d).

Advantages:

Simple and easy to implement.
Requires only a small amount of training data.
Works well with high-dimensional data.

Disadvantages:

Assuming feature independence. This assumption doesn’t hold in any actual data.
If the independent assumption isn’t met, it can be not as accurate as more-complicated models.

Conclusion

Naive Bayes is a foundational algorithm in machine learning, providing a balance between simplicity and effectiveness. By leveraging Bayes’ theorem and assuming feature independence, it offers a straightforward approach to classification tasks. While the basic form is powerful, understanding and applying advanced techniques like handling continuous features, feature selection, and Laplace smoothing can further enhance its performance. Whether you’re dealing with text classification, spam filtering, or medical diagnosis, Naive Bayes remains a robust tool in the machine learning arsenal.

I hope this gives you a comprehensive understanding of Naive Bayes algorithm, from the mathematical intuition , next article you can read Practical Implementation in Python. Follow me

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