  Compositional data sets are ubiquitous in science, including geology,
ecology, and microbiology. In microbiome research, compositional data primarily
arise from high-throughput sequence-based profiling experiments. These data
comprise microbial compositions in their natural habitat and are often paired
with covariate measurements that characterize physicochemical habitat
properties or the physiology of the host. Inferring parsimonious statistical
associations between microbial compositions and habitat- or host-specific
covariate data is an important step in exploratory data analysis. A standard
statistical model linking compositional covariates to continuous outcomes is
the linear log-contrast model. This model describes the response as a linear
combination of log-ratios of the original compositions and has been extended to
the high-dimensional setting via regularization. In this contribution, we
propose a general convex optimization model for linear log-contrast regression
which includes many previous proposals as special cases. We introduce a
proximal algorithm that solves the resulting constrained optimization problem
exactly with rigorous convergence guarantees. We illustrate the versatility of
our approach by investigating the performance of several model instances on
soil and gut microbiome data analysis tasks.
