论文标题
关于贝叶斯因子分析模型的可识别性
On the identifiability of Bayesian factor analytic models
论文作者
论文摘要
因素分析模型中众所周知的可识别性问题是关于正交转换的不变性。这个问题负担贝叶斯设置下的推断，其中马尔可夫链蒙特卡洛（MCMC）方法用于从后分布中生成样品。我们引入了一种后处理方案，以处理MCMC样本的旋转，符号和排列不变性。该贡献算法的确切版本需要解决$ 2^q $分配问题（保留）MCMC迭代，其中$ q $表示拟合模型的因子数量。对于大量因素，还讨论了基于模拟退火的两个近似方案。我们证明了所提出的方法使用典型因素分析模型的合成和公开数据以及因子分析仪的混合物提供了可解释的后验分布。 R Package可在Cran网页上在线获得。
A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve $2^q$ assignment problems per (retained) MCMC iteration, where $q$ denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page.
