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Feature allocation models are popular models used in different applicationssuch as unsupervised learning or network modeling. In particular, the Indianbuffet process is a flexible and simple one-parameter feature allocation modelwhere the number of features grows unboundedly with the number of objects. TheIndian buffet process, like most feature allocation models, satisfies asymmetry property of exchangeability: the distribution is invariant underpermutation of the objects. While this property is desirable in some cases, ithas some strong implications. Importantly, the number of objects sharing aparticular feature grows linearly with the number of objects. In this article,we describe a class of non-exchangeable feature allocation models where thenumber of objects sharing a given feature grows sublinearly, where the rate canbe controlled by a tuning parameter. We derive the asymptotic properties of themodel, and show that such model provides a better fit and better predictiveperformances on various datasets.

Non-exchangeable feature allocation models with sublinear growth of the feature sizes