[Verse 1]
Thomas Bayes dropped knowledge in seventeen-sixty-three
Posterior equals prior times the likelihood, you see
Independence assumption, features don't collide
Multiply probabilities, let the math decide
Start with prior knowledge, what we think we know
Evidence updates beliefs, watch the numbers grow
Conditional probability, flip the script around
Given class, find feature chance, wisdom can be found
[Chorus]
Naive Bayes, features independent, that's the game
Prior times likelihood, posterior's the name
Argmax classification, highest probability wins
Naive Bayes, features independent, that's where learning begins
[Verse 2]
Gaussian for continuous, multinomial discrete
Bernoulli for binary, make the model complete
Training phase computes the stats, means and variance stored
Count the frequencies up, build that knowledge hoard
Laplace smoothing saves the day when zero counts appear
Add-one to numerator, keep the math sincere
Curse of dimensionality? Naive Bayes don't care
Linear decision boundary slices through the air
[Chorus]
Naive Bayes, features independent, that's the game
Prior times likelihood, posterior's the name
Argmax classification, highest probability wins
Naive Bayes, features independent, that's where learning begins
[Bridge]
Spam detection, document classification tool
Medical diagnosis, following Bayes' rule
Fast to train, fast to predict, computational dream
Log probabilities prevent the underflow scheme
[Verse 3]
Maximum a posteriori, MAP estimation clean
Compare the products, pick the highest scene
Generative model learns the joint distribution well
Discriminative counterparts got stories to tell
Text analysis champion, bag of words supreme
Sentiment classification, living the dream
Despite naive assumptions, performance stays strong
Real-world applications prove the theory's not wrong
[Chorus]
Naive Bayes, features independent, that's the game
Prior times likelihood, posterior's the name
Argmax classification, highest probability wins
Naive Bayes, features independent, that's where learning begins
[Outro]
Probabilistic framework, uncertainty embraced
Bayesian inference, elegantly placed
When features truly independent, performance peaks high
Naive Bayes classifier, mathematics that fly