论文标题
在高维的贝叶斯因子模型的后验一致性上
On Posterior Consistency of Bayesian Factor Models in High Dimensions
论文作者
论文摘要
作为一种原则上的降低技术，因子模型在社会科学，经济学，生物信息学和许多其他领域中广泛采用。但是，在高维设置中，进行“正确”的贝叶斯因素分析可能是微妙的，因为它既需要仔细的先验分布处方，又需要适当的计算策略。特别是，我们分析了与因子加载矩阵的元素“非信息”尝试相关的问题，尤其是对于高维度中稀疏的贝叶斯因子模型，并向它们提出解决方案。我们在这里说明了为什么采用正交因子假设是合适的，并且可以导致对真实特质方差的有条件的加载矩阵的后验推断以及在真实加载矩阵中非零元素的分配。我们还提供有效的Gibbs采样器，以基于Rockova和George（2016）的先前设置以及对因子矩阵的统一正交因素假设进行完整的后推理。
As a principled dimension reduction technique, factor models have been widely adopted in social science, economics, bioinformatics, and many other fields. However, in high-dimensional settings, conducting a 'correct' Bayesianfactor analysis can be subtle since it requires both a careful prescription of the prior distribution and a suitable computational strategy. In particular, we analyze the issues related to the attempt of being "noninformative" for elements of the factor loading matrix, especially for sparse Bayesian factor models in high dimensions, and propose solutions to them. We show here why adopting the orthogonal factor assumption is appropriate and can result in a consistent posterior inference of the loading matrix conditional on the true idiosyncratic variance and the allocation of nonzero elements in the true loading matrix. We also provide an efficient Gibbs sampler to conduct the full posterior inference based on the prior setup from Rockova and George (2016)and a uniform orthogonal factor assumption on the factor matrix.
