Naive Bayes › Advantages

The first advantage is speed. Training a Gaussian naive Bayes classifier requires only class counts, per-class feature means, and per-class feature variances. That is $O(nd)$ work for $n$ observations and $d$ features, with no iterative optimization. Multinomial naive Bayes is similarly cheap: it accumulates word counts per class and then normalizes them. Prediction is also fast because each class score is a sum of $d$ terms. For high-dimensional text data, where the number of features can be tens or hundreds of thousands, this matters.

The second advantage is behavior with small samples and many features. A full multivariate Gaussian model would need to estimate a $d \times d$ covariance matrix for each class, whose unregularized sample estimate is singular when a class has at most $d$ observations. Regularized full-covariance models remain possible. Naive Bayes replaces that matrix with $d$ separate variances per class. The number of parameters grows linearly in $d$, not quadratically. This is why naive Bayes often works as a strong baseline for document classification, spam filtering, and other sparse count problems.

The third advantage is interpretability. Each class score is a sum of contributions from the prior and from individual features. We can inspect which words or measurements push an observation toward a class. The model also handles multiclass problems without modification: we compute one score per class and normalize.

Finally, naive Bayes is a natural online learner. With count data, we can update class counts and feature counts as new observations arrive. With Gaussian data, we can update means and variances incrementally. This makes the model useful in streaming settings where retraining a more complex classifier would be expensive.