Fast computation of latent correlations

TL;DR

This paper introduces a fast computational method for estimating latent Gaussian correlations in copula models, enabling efficient analysis of high-dimensional multi-view data with mixed variable types.

Contribution

A novel hybrid interpolation and optimization scheme that significantly accelerates latent correlation estimation in Gaussian copula models.

Findings

Speeds up computation by several orders of magnitude.

Provides theoretical guarantees for approximation error.

Demonstrates effectiveness on microbiome and cancer genomics data.

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 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.