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How does Gaussian Naïve Bayes handle continuous variables mathematically?
Updated May 17, 2026
Short answer
Gaussian Naïve Bayes assumes features follow a normal distribution within each class.
Deep explanation
Gaussian NB models likelihood as P(x|C) using Gaussian density: (1 / √(2πσ²)) exp(-(x-μ)² / 2σ²). It estimates mean and variance per class for each feature. During prediction, it multiplies probabilities across features under independence assumption.
Real-world example
Medical diagnosis using patient vitals like blood pressure and temperature.
Common mistakes
- Assuming real-world data strictly follows normal distribution.
Follow-up questions
- What if data is not Gaussian?
- Can we mix distributions?