Non-exchangeable feature allocation models with sublinear growth of the feature sizes
Non-exchangeable feature allocation models with sublinear growth of the feature sizes
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发表时间：
2020-03
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通讯作者：
G. Benedetto;F. Caron;Y. Teh
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作者：
G. Benedetto;F. Caron;Y. Teh
特征分配模型是常用的模型，用于不同的应用，如无监督学习或网络建模。其中，印度自助餐过程是一种灵活、简单的单参数特征分配模型，其特征数量随对象数量无界增长。印度自助餐过程与大多数特征分配模型一样，满足可交换性的对称性质：在对象置换下，分布是不变的。虽然这个属性在某些情况下是可取的，但它有一些强烈的含义。重要的是，共享特定特征的对象的数量与对象的数量呈线性增长。在本文中，我们描述了一类不可交换的特征分配模型，其中共享给定特征的对象数量呈次线性增长，其速率可以通过调优参数来控制。我们推导了该模型的渐近性质，并证明了该模型在各种数据集上具有较好的拟合和预测性能。
Feature allocation models are popular models used in different applications such as unsupervised learning or network modeling. In particular, the Indian buffet process is a flexible and simple one-parameter feature allocation model where the number of features grows unboundedly with the number of objects. The Indian buffet process, like most feature allocation models, satisfies a symmetry property of exchangeability: the distribution is invariant under permutation of the objects. While this property is desirable in some cases, it has some strong implications. Importantly, the number of objects sharing a particular feature grows linearly with the number of objects. In this article, we describe a class of non-exchangeable feature allocation models where the number of objects sharing a given feature grows sublinearly, where the rate can be controlled by a tuning parameter. We derive the asymptotic properties of the model, and show that such model provides a better fit and better predictive performances on various datasets.