We propose a hybrid model combining a generative model and a discriminative model for signal labelling and classification tasks, aiming at taking the best from each world. The idea is to focus the learning of the discriminative model on most likely state sequences as output by the generative model. This allows taking advantage of the usual increased accuracy of generative models on small training datasets and of discriminative models on large training datasets. We instantiate this framework with Hidden Markov Models and Hidden Conditional Random Fields. We validate our model on financial time series and on handwriting data.