be the value of feature 2' for subtree 7“ over sentence s, and let E9 [fi|s] be the expected value of feature 2' in sentence 3, based on the current model parameters 6.

After training has been completed, we retain only the joint model’s parameters .

The first summation in this equation computes the log-likelihood of each model, using the data and parameters which correspond to that model, and the prior likelihood of that model’s parameters , based on a Gaussian prior centered around the top-level, non-model-specific parameters 6*, and with model-specific variance am.

We need to compute partial derivatives in order to optimize the model parameters .

We select the model parameters 6 by maximizing the marginal likelihood of the data, where the data D is given in the form of groups w =

When estimating the model parameters , we followed the training regime prescribed in (Liang et al., 2009).

In the supervised case, where a and m are observable, estimation of the generative model parameters is generally straightforward.