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Training

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Probability Distributions

Bayes' Theorem Step-by-Step Breakdown

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Bayes' Theorem Formula

P(Class|Features) =
P(Class) × P(Features|Class)
P(Features)
Click "Play Step-by-Step" to see how each component is calculated
1

Prior Probabilities P(Class)

Pending

The prior probability represents our initial belief about the class distribution based on the training data.

2

Likelihood P(Features|Class)

Pending

The likelihood measures how probable the observed features are, given each class. We calculate this for each feature using Gaussian distributions.

3

Combining: Prior × Likelihood

Pending

We multiply the prior probabilities by the likelihoods to get unnormalized posterior probabilities.

P(Spam) × P(Features|Spam) =
P(Ham) × P(Features|Ham) =
4

Normalization: Posterior Probabilities

Pending

We normalize by dividing by P(Features), which is the sum of all unnormalized posteriors, ensuring probabilities sum to 1.

P(Features) = Sum of all unnormalized posteriors =
P(Spam|Features) =
P(Ham|Features) =
5

Final Prediction

Pending

The class with the highest posterior probability is selected as the prediction.

Extracted Features

Dataset Statistics

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