The general sequence labelling problem consists in processing an input sequence (xi) and producing an output sequence (yi) of discrete labels. Since the space of the possible output sequences is discrete, this can be viewed as a massive classification problem.
The notion of structured output prediction arises when one makes strong modelling assumption in order to learn the association with a reasonable number of examples. The conditional independence assumption states that a label it can be modelled as a function of the inputs (xt+i), i 2 I and the labels (yt+j), j 2 J for suitable choice of the sets I and J . The invariance assumption states that this function does not depend on t. The choice of sets I and J has a non trivial impact on the generalization performance and on the training and testing times.