Bayesian estimation of parameters in the Dirichlet mixture process of the Beta-Liouville distribution (i.e., the infinite Beta-Liouville mixture model) has recently gained considerable attention due to its modeling capability for proportional data. However, applying the conventional variational inference (VI) framework cannot derive an analytically tractable solution since the variational objective function cannot be explicitly calculated. In this paper, we adopt the recently proposed extended VI framework to derive the closed-form solution by further lower bounding the original variational objective function in the VI framework. This method is capable of simultaneously determining the model's complexity and estimating the model's parameters. Moreover, due to the nature of Bayesian nonparametric approaches, it can also avoid the problems of underfitting and overfitting. Extensive experiments were conducted on both synthetic and real data, generated from two real-world challenging applications, namely, object detection and text categorization, and its superior performance and effectiveness of the proposed method have been demonstrated.

中文翻译：

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用于比例数据建模的 Beta-Liouville 分布的 Dirichlet 过程混合的扩展变分推理

Beta-Liouville 分布的Dirichlet 混合过程（即无限Beta-Liouville 混合模型）中参数的贝叶斯估计由于其对比例数据的建模能力而最近引起了相当大的关注。然而，由于无法明确计算变分目标函数，因此应用传统的变分推理 (VI) 框架无法得出易于分析的解决方案。在本文中，我们采用最近提出的扩展 VI 框架，通过进一步降低 VI 框架中的原始变分目标函数的边界来推导出封闭形式的解决方案。该方法能够同时确定模型的复杂性和估计模型的参数。此外，由于贝叶斯非参数方法的性质，它还可以避免欠拟合和过拟合的问题。对从两个现实世界具有挑战性的应用程序（即对象检测和文本分类）生成的合成数据和真实数据进行了广泛的实验，并证明了所提出方法的优越性能和有效性。