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In this thesis we study a problem of searching in a space of objects using comparisons. To navigate through the space to the target object , we ask a sequence of questions of the form ``which object or is closer to ?'' for which we observe noisy answers. We propose two new probabilistic models for triplet comparisons , which fit the real world data better than the state-of-the-art. We study theoretical properties of these models and for both derive search algorithms that are scalable in the number of objects and that have convergence guarantees. Finally, we conduct two experiments with real users, in which we demonstrate the efficiency of the proposed methods.