9. Linear Discriminant Analysis

We consider classification models of the form:

where $p(y=c,x)$ is the prior over the class labels, and $p(x|y=c,\theta)$ is the class conditional density for $c$.

• The overall model is a generative model since it specifies the distribution over the feature $x$, $p(x|y=c,\theta)$

• By contrast, a discriminative model directly estimates the class posterior $p(y=c|\theta,x)$