We develop an envelope model for joint mean and covariance regression in the large p, small n setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we focus on identifying covariance heterogeneity by incorporating information about mean-level differences. We use a Monte Carlo EM algorithm to identify a low-dimensional subspace that explains differences in both means and covariances as a function of covariates, and then use MCMC to estimate the posterior uncertainty conditional on the inferred low-dimensional subspace. We demonstrate the utility of our model on a motivating application on the metabolomics of aging. We also provide R code that can be used to develop and test other generalizations of the response envelope model.

中文翻译：

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减少大规模协方差回归的子空间模型

我们为大p、小n的联合均值和协方差回归开发了一个包络模型环境。与通过结合协方差结构的估计来改进均值估计的现有包络方法相比，我们专注于通过结合关于均值水平差异的信息来识别协方差异质性。我们使用 Monte Carlo EM 算法来识别低维子空间，该子空间将均值和协方差的差异解释为协变量的函数，然后使用 MCMC 来估计以推断的低维子空间为条件的后验不确定性。我们展示了我们的模型在衰老代谢组学激励应用中的实用性。我们还提供了 R 代码，可用于开发和测试响应包络模型的其他概括。