ABSTRACT

While Bayesian functional mixed models have been shown effective to model functional data with various complex structures, their application to extremely high-dimensional data is limited due to computational challenges involved in posterior sampling. We introduce a new computational framework that enables ultra-fast approximate inference for high-dimensional data in functional form. This framework adopts parsimonious basis to represent functional observations, which facilitates efficient compression and parallel computing in basis space. Instead of performing expensive Markov chain Monte Carlo sampling, we approximate the posterior distribution using variational Bayes and adopt a fast iterative algorithm to estimate parameters of the approximate distribution. Our approach facilitates a fast multiple testing procedure in basis space, which can be used to identify significant local regions that reflect differences across groups of samples. We perform two simulation studies to assess the performance of approximate inference, and demonstrate applications of the proposed approach by using a proteomic mass spectrometry dataset and a brain imaging dataset. Supplementary materials for this article are available online.

摘要

虽然贝叶斯函数混合模型已被证明可以有效地对具有各种复杂结构的函数数据进行建模，但由于后采样中涉及的计算挑战，它们在极高维数据上的应用受到限制。我们引入了一种新的计算框架，可以对函数形式的高维数据进行超快速近似推理。该框架采用简约基来表示函数观测值，有利于基空间的高效压缩和并行计算。我们没有执行昂贵的马尔可夫链蒙特卡罗采样，而是使用变分贝叶斯近似后验分布，并采用快速迭代算法来估计近似分布的参数。我们的方法促进了基础空间中的快速多重测试过程，可用于识别反映样本组之间差异的重要局部区域。我们进行了两项模拟研究来评估近似推理的性能，并通过使用蛋白质组质谱数据集和脑成像数据集来演示所提出的方法的应用。本文的补充材料可在线获取。