Discriminative Sequence Labeling

In a classification problem, we are given the input x and want to find out which category it belongs to in a given label set Π. Information from the input x is often represented as a feature vector φ(x). The basic idea of linear classifiers, then, is to have a weight vector wz for each class label z, in the same dimension as φ(x), to distinguish input from different categories. The label for an input is predicted to be the one whose weight vector gives the highest inner product value with φ(x), i.e. a linear classifier predicts the label ẑ by letting