Fast Computation of Latent Correlations

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.

Keywords:

• Bridge function
• Kendall’s tau
• Latent Gaussian copula
• Multilinear interpolation

Supplementary Materials

Supplementary: Proofs of Theorems 3 and 4, derivation of bound (9), description of interpolation grid and additional approximation accuracy results for the TT, TB, BC, and BB cases (.pdf file)

Additional information

Funding

The authors gratefully acknowledge the support from the National Institutes of Health National Cancer Institute training grant T32-CA090301, the National Science Foundation grant DMS-1712943, and the Flatiron Institute of the Simons Foundation.