Naive Bayes Probability Calculator
Calculate class probabilities for a Naive Bayes classifier given feature likelihoods.
Inputs
Comma-separated probabilities per feature
Comma-separated probabilities per feature
P(Class 1 | features)
0.939130
P(Class 2 | features)
0.060870
Predicted Class
1
Step by step
Score C₁: prior × Π likelihoods
0.6 × 0.8 × 0.6 × 0.9
= 0.25920000
Score C₂: prior × Π likelihoods
0.40 × 0.3 × 0.7 × 0.2
= 0.01680000
Normalized P(C₁|features)
0.259200 ÷ (0.259200 + 0.016800)
= 0.939130
How it works
Naive Bayes classification computes P(C|features) ∝ P(C) × Π P(fᵢ|C) for each class, then normalizes. The 'naive' assumption is that features are conditionally independent given the class, which greatly simplifies computation and works surprisingly well for text classification, spam filtering, and sentiment analysis.
Formula
Naive Bayes
P(C|f1,...,fn) = P(C) * product(P(fi|C)) / P(f1,...,fn)
- P(C)
- Prior probability of class C
- P(fi|C)
- Likelihood of feature i given class C
Frequently Asked Questions
Why is it called 'naive'?
It assumes all features are conditionally independent given the class — a strong and usually unrealistic assumption. Despite this, Naive Bayes often performs well in practice, especially for text classification where the feature space is very high-dimensional.
How do you handle zero probabilities?
Laplace smoothing (adding a small constant to all counts) prevents any likelihood from being exactly zero, which would otherwise zero out the entire product for that class.