w, h, s respectively denote the sequence of For the example sentence in Figure 1 We define the joint probability distribution of the sentiment polarities of dependency subtrees s, given a subjective sentence w and its dependency tree h, using loglinear models: where is the feature function of the i-th phrase, and is classified to node feature which considers only the corresponding node, or edge feature which considers both the corresponding node and its head, as follows: where K n and K e respectively represent the sets of indices of node features and edge features.
let us consider how to infer the sentiment polarity p ∈ {+1, −1}, given a subjective sentence w and its dependency tree h. The polarity of the root node (s 0 ) is regarded as the polarity of the whole sentence, and p can be calculated as follows: the polarity of the subjective sentence is obtained as the marginal probability of the root node polarity, by summing the probabilities for all the possible configurations of hidden variables.