Logistic Probabilistic Models

Definition

Given $\beta \in \R , \theta \in \R ^d$ the logistic model (the logistic probabilistic model) corresponding to the parameters $\beta $ and $\theta $ is the function $p: X \to [0, 1]$ defined by

\[ p(x) = \frac{1}{1 + \exp(-\theta ^\top x - \beta )} \]