标题： 多维成员混合模型 显示英文标题

标题： Multidimensional Membership Mixture Models

摘要： 我们提出了多维成员混合（M3）模型，其中每个维度的成员表示一个独立的混合模型，并且每个数据点是从所选的混合成分联合生成的。 当数据具有一定的共享结构时，这非常有帮助。 例如，三个独特的均值和三个独特的方差可以有效地形成一个具有九个成分的高斯混合模型，同时只需要六个参数即可完全描述它。 在本文中，我们提出了三种M3模型的实例化（连同学习和推理算法）：无限、有限和混合，具体取决于混合的数量是否固定。 它们分别基于狄利克雷过程混合模型、潜在狄利克雷分配模型以及两者的组合构建。 然后，我们考虑了两个应用：主题建模和学习3D对象排列。 我们的实验表明，与许多经典主题模型相比，我们的M3模型使用更少的主题实现了更好的性能。 我们还观察到，来自M3模型不同维度的主题是有意义的并且彼此正交。 显示英文摘要

摘要： We present the multidimensional membership mixture (M3) models where every dimension of the membership represents an independent mixture model and each data point is generated from the selected mixture components jointly. This is helpful when the data has a certain shared structure. For example, three unique means and three unique variances can effectively form a Gaussian mixture model with nine components, while requiring only six parameters to fully describe it. In this paper, we present three instantiations of M3 models (together with the learning and inference algorithms): infinite, finite, and hybrid, depending on whether the number of mixtures is fixed or not. They are built upon Dirichlet process mixture models, latent Dirichlet allocation, and a combination respectively. We then consider two applications: topic modeling and learning 3D object arrangements. Our experiments show that our M3 models achieve better performance using fewer topics than many classic topic models. We also observe that topics from the different dimensions of M3 models are meaningful and orthogonal to each other.