/naɪˈiːv ˈbeɪz/
noun … “probabilities, simplified and fast.”
Naive Bayes is a probabilistic machine learning algorithm based on Bayes’ theorem that assumes conditional independence between features given the class label. Despite this “naive” assumption, it performs remarkably well for classification tasks, particularly in text analysis, spam detection, sentiment analysis, and document categorization. The algorithm calculates the posterior probability of each class given the observed features and assigns the class with the highest probability.
Formally, given a set of features X = {x₁, x₂, ..., xₙ} and a class variable Y, the Naive Bayes classifier predicts the class ŷ as:
ŷ = argmax_y P(Y = y) Π P(xᵢ | Y = y)Here, P(Y = y) is the prior probability of class y, and P(xᵢ | Y = y) is the likelihood of feature xᵢ given class y. The algorithm works efficiently with high-dimensional data due to the independence assumption, which reduces computational complexity and allows rapid estimation of probabilities.
Naive Bayes is connected to several key concepts in statistics and machine learning. It leverages Probability Distributions to model feature likelihoods, uses Expectation Values and Variance to analyze estimator reliability, and often integrates with text preprocessing techniques like tokenization, term frequency, and feature extraction in natural language processing. It can also serve as a baseline model to compare with more complex classifiers such as Support Vector Machines or ensemble methods like Random Forest.
Example conceptual workflow for Naive Bayes classification:
collect labeled dataset with features and target classes
preprocess features (e.g., encode categorical variables, normalize)
estimate prior probabilities P(Y) for each class
compute likelihoods P(xᵢ | Y) for all features and classes
calculate posterior probabilities for new observations
assign class with highest posterior probabilityIntuitively, Naive Bayes is like assuming each clue in a mystery works independently: even if the assumption is not entirely true, combining the individual probabilities often leads to a surprisingly accurate conclusion. It converts simple probabilistic reasoning into a fast, scalable, and interpretable classifier.