On Posterior Consistency of Bayesian Factor Models in High Dimensions
On Posterior Consistency of Bayesian Factor Models in High Dimensions
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DOI：
10.1214/21-ba1281
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发表时间：
2020-06
影响因子：
4.4
通讯作者：
Yucong Ma;Jun S. Liu
中科院分区：
文献类型：
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作者：
Yucong Ma;Jun S. Liu
因子模型作为一种原则性的降维技术，在社会科学、经济学、生物信息学等领域得到了广泛的应用。然而，在高维环境中，进行“正确的”贝叶斯因子分析可能是微妙的，因为它需要仔细规定的先验分布和合适的计算策略。特别是，我们分析的问题有关的尝试是“非信息”的因素加载矩阵的元素，特别是稀疏贝叶斯因子模型在高维，并提出解决方案。我们在这里说明了为什么采用正交因子假设是适当的，并且可以根据真实的特质方差和真实加载矩阵中非零元素的分配对加载矩阵进行一致的后验推断。我们还提供了一个有效的吉布斯采样器，根据Rockova和乔治（2016）的先验设置和因子矩阵上的均匀正交因子假设进行完整的后验推断。
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.