Logistic Regression (Probabilistic Discriminative Model)

Here, the Posterior is modeled directly as a function of $x$. The posterior probability is specified using a sigmoid function applied to a linear function of the input (Logistic Regression)

$$p(C_k|x_n)=y(x_n)=\sigma (w^T{x}_n)$$

where,

• $y(x_n)\to$ This is the Model Prediction.
• $\sigma \to$ Sigmoid Function that squashes it’s input values into a value between $0$ and $1$
• $w^T{x}_n\to$ Linear Model