In this manuscript, we consider structured machine learning problems and consider more precisely the ones involving sequential structure. In a first part, we consider the problem of similarity measure learning for two tasks where sequential structure is at stake: (i) the multivariate change-point detection and (ii) the time warping of pairs of time series. The methods generally used to solve these tasks rely on a similarity measure to compare timestamps. We propose to learn a similarity measure from fully labelled data, i.e., signals already segmented or pairs of signals for which the optimal time warping is known. Using standard structured prediction methods, we present algorithmically efficient ways for learning. We propose to use loss functions specifically designed for the tasks. We validate our approach on real-world data. In a second part, we focus on the problem of weak supervision, in which sequen tial data are not totally labeled. We conduct our study on the problem of aligning a time series to its symbolic representation, using as a leading example the problem of aligning an audio recording with the score. We consider the symbolic representation as two fold: (i) a complete information about the order of events or notes played and (ii) an approximate idea about the expected shape of the alignment. We propose to learn a classifier for each note using these two kinds of information. Our learning problem is based on the optimization of a convex function that takes advantage of the weak supervision and of the sequential structure of data. Our approach is validated through experiments on the task of audio-to-score on real musical data.