Gaussian Discriminant
Overview
The Gaussian discriminant is a form of
Bayes Classifier
where the conditional probabilities are assumed to follow
normal distributions.
Simplication
The log likelihood of the probability given by a Bayes classifier takes the following form when the conditional
probabilities are normal
{% log \; p(y=c|\vec{x};\vec{\theta}) = log \; \pi_c - \frac{1}{2} log |2 \pi \Sigma_c| - \frac{1}{2}(\vec{x}-\vec{\mu_c})^T \Sigma_c^{-1}(\vec{x}-\vec{\mu_c}) + const %}
where
{% \pi_c = p(y=c;\vec{\theta}) = \frac{N_c}{N} %}
Note the constant in the expression which can be ignored when only trying to find the most probable category.
