论文标题
归一化潜在测量因子模型
Normalized Latent Measure Factor Models
论文作者
论文摘要
我们提出了一种建模和比较贝叶斯非参数框架内的概率分布的方法。在依赖归一化的随机度量的基础上，我们考虑了一系列离散随机度量集合的先验分布，其中每种度量是一组潜在测量的线性组合，可以解释为具有不同分布的特征性状，并具有正随机重量。该模型是未识别的，并且开发了一种后处理后样品确定推理的方法。这使用riemannian优化来解决一组矩阵的非平凡优化问题。在模拟数据和两个现实世界数据集的两个应用程序中，我们的方法的有效性得到了验证：在加利福尼亚州的学校学生考试成绩和个人收入。我们的方法导致人们对人群的有趣见解，并易于解释后推断
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random measures where each measure is a linear combination of a set of latent measures, interpretable as characteristic traits shared by different distributions, with positive random weights. The model is non-identified and a method for post-processing posterior samples to achieve identified inference is developed. This uses Riemannian optimization to solve a non-trivial optimization problem over a Lie group of matrices. The effectiveness of our approach is validated on simulated data and in two applications to two real-world data sets: school student test scores and personal incomes in California. Our approach leads to interesting insights for populations and easily interpretable posterior inference
