Naive Bayes Cheat Sheet

A reference for Naive Bayes covering Gaussian, Multinomial, and Bernoulli variants in scikit-learn, Bayes' theorem, and Laplace smoothing.

1 PageBeginnerMar 15, 2026

GaussianNB

For continuous, normally distributed features.

python

from sklearn.naive_bayes import GaussianNBmodel = GaussianNB()model.fit(X_train, y_train)y_pred = model.predict(X_test)proba = model.predict_proba(X_test)   # assumes features are normal per class

MultinomialNB for Text

A classic pipeline for text classification.

python

from sklearn.feature_extraction.text import CountVectorizerfrom sklearn.naive_bayes import MultinomialNBfrom sklearn.pipeline import make_pipelinetext_clf = make_pipeline(    CountVectorizer(stop_words='english'),    MultinomialNB(alpha=1.0)   # alpha: Laplace/Lidstone smoothing)text_clf.fit(train_texts, train_labels)predictions = text_clf.predict(test_texts)

BernoulliNB

For binary/boolean feature vectors.

python

from sklearn.naive_bayes import BernoulliNBmodel = BernoulliNB(alpha=1.0, binarize=0.0)   # binary/boolean feature presencemodel.fit(X_train, y_train)

Key Concepts

Core theory behind Naive Bayes.

Bayes' theorem- P(y given x) is proportional to P(x given y) times P(y): combines likelihood and prior into a posterior
Conditional independence- The 'naive' assumption that features are independent given the class; rarely true but works well in practice
Laplace smoothing (alpha)- Prevents zero probabilities for feature/class combinations unseen during training
GaussianNB- Assumes continuous features follow a normal distribution within each class
MultinomialNB- Best for discrete counts, such as word frequencies in text classification
BernoulliNB- Best for binary/boolean features, such as word presence or absence

Pro Tip

Naive Bayes is a fast, strong baseline for text classification despite its unrealistic independence assumption — but its predicted probabilities are often poorly calibrated even when the predicted class label is correct, so don't trust predict_proba() outputs at face value.

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