Abstract

Latent Gaussian copula models provide a powerful means to perform multi-view data integration since these models can seamlessly express dependencies between mixed variable types (binary, continuous, zero-inflated) via latent Gaussian correlations. The estimation of these latent correlations, however, comes at considerable computational cost, having prevented the routine use of these models on high-dimensional data. Here, we propose a new computational approach for estimating latent correlations via a hybrid multilinear interpolation and optimization scheme. Our approach speeds up the current state of the art computation by several orders of magnitude, thus allowing fast computation of latent Gaussian copula models even when the number of variables p is large. We provide theoretical guarantees for the approximation error of our numerical scheme and support its excellent performance on simulated and real-world data. We illustrate the practical advantages of our method on high-dimensional sparse quantitative and relative abundance microbiome data as well as multi-view data from The Cancer Genome Atlas Project. Our method is implemented in the R package mixedCCA, available at https://github.com/irinagain/mixedCCA.

摘要

潜在高斯 copula 模型提供了执行多视图数据集成的强大方法，因为这些模型可以通过潜在高斯相关性无缝表达混合变量类型（二进制、连续、零膨胀）之间的依赖关系。然而，对这些潜在相关性的估计需要相当大的计算成本，这阻碍了这些模型在高维数据上的常规使用。在这里，我们提出了一种新的计算方法，用于通过混合多线性插值和优化方案来估计潜在相关性。我们的方法将当前最先进的计算速度提高了几个数量级，因此即使变量 p 的数量很大，也可以快速计算潜在的高斯 copula 模型。我们为我们的数值方案的近似误差提供了理论保证，并支持其在模拟和真实数据上的出色表现。我们说明了我们的方法在高维稀疏定量和相对丰度微生物组数据以及来自癌症基因组图谱项目的多视图数据上的实际优势。我们的方法在 R 包混合CCA 中实现，可在 https://github.com/irinagain/mixedCCA 获得。