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We present ShoppingAdvisor, a novel recommender system that helps users in shopping for technical products. ShoppingAdvisor leverages both user preferences and technical product attributes in order to generate its suggestions. The system elicits user preferences via a tree-shaped flowchart, where each node is a question to the user. At each node, ShoppingAdvisor suggests a ranking of products matching the preferences of the user, and that gets progressively refined along the path from the tree's root to one of its leafs. In this paper we show (i) how to learn the structure of the tree, i.e., which questions to ask at each node, and (ii) how to produce a suitable ranking at each node. First, we adapt the classical top-down strategy for building decision trees in order to find the best user attribute to ask at each node. Differently from decision trees, ShoppingAdvisor partitions the user space rather than the product space. Second, we show how to employ a learning-to-rank approach in order to learn, for each node of the tree, a ranking of products appropriate to the users who reach that node. We experiment with two real-world datasets for cars and cameras, and a synthetic one. We use mean reciprocal rank to evaluate ShoppingAdvisor, and show how the performance increases by more than 50% along the path from root to leaf. We also show how collaborative recommendation algorithms such as k-nearest neighbor benefits from feature selection done by the ShoppingAdvisor tree. Our experiments show that ShoppingAdvisor produces good quality interpretable recommendations, while requiring less input from users and being able to handle the cold-start problem.