  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.
