潜在相关的快速计算
Fast computation of latent correlations
摘要：
潜在高斯copula模型提供了一种强大的手段来执行多视图数据集成，因为这些模型可以通过潜在高斯相关性无缝地表达混合变量类型（二进制，连续，零膨胀）之间的依赖关系。然而，这些潜在的相关性的估计，来在相当大的计算成本，阻止了这些模型的高维数据的常规使用。在这里，我们提出了一种新的计算方法，通过混合多线性插值和优化方案估计潜在的相关性。我们的方法加快了几个数量级的当前最先进的计算，从而允许快速计算的潜在高斯copula模型，即使当变量的数量$p$是大的。我们提供了理论保证我们的数值方案的近似误差，并支持其模拟和真实世界的数据的优异性能。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mixedCCA中实现，可在https://github.com/irinagain/mixedCCA上获得。
英文摘要：
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 multi-linear 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.
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