Multivariate Log-linear Model

Question

I know from here that a log-linear model can be used to estimate a conditional probability of class $c$ given the feature representation $d$ of datapoint $x$.

$p(c|d;\theta) = \frac{exp(\theta.d_c)}{\sum_{d_{c^\prime}}exp(\theta.d_{c^\prime}) }$

How can I generalize the above formulation of log-linear models to estimate $p(c|d_1,d_2;\theta)$.

Answer 1

This is already multivariate. For $p$ features:

\begin{equation} \theta^\top.d_c = \sum_{i=1}^p\theta_i * {d_c}_i \end{equation}