This paper concerns preference elicitation and learning of decision models in the context of multicriteria decision making. We propose an approach to learn a compact representation of preferences using a decomposable bi-polar Choquet integral. Our aim is to show how we can successively learn marginal utilities and then sparse representations of capacities involved in the decision model from preference data. We first present a preference elicitation method to learn spline representations of marginal utilities on every point of view. Then we propose a sparse learning approach for determining a compact representation of capacities fitted to the observed preferences. Finally, we present numerical tests showing the advantages of our approach compared to basic methods that do not seek sparsity or that force sparsity a priori by requiring kadditivity. We also apply our approach in the context of preferences over sets.