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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 $p(c|d_1,d_2;\theta)$.

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This is already multivariate. For $p$ features:

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

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  • $\begingroup$ So how to solve $p(c|d1,d2)$? $\endgroup$
    – MAZDAK
    Jun 23, 2016 at 5:36

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