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
翻译:我们建议了一种方法,用于建模和比较巴伊西亚非参数框架内的概率分布。基于依赖性正常随机测量,我们考虑先分配一套离散随机测量的集集,其中每种测量都是一组潜在测量的线性组合,可解释为不同分布所共有的特征特征,具有正随机加权数。该模型未经确定,是处理后后后后后后后后后后后后后后后后后继样本实现确定推断的方法。这使用里曼尼亚优化解决一个非三边优化问题,而不是一组测谎矩阵。我们的方法的有效性在模拟数据上得到验证,在两个真实世界数据集的两个应用中得到验证:加利福尼亚的学校学生测试分数和个人收入。我们的方法为人口带来有趣的洞察力,并且容易解释的后世推断。