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Many biological high-throughput data sets, such as targeted amplicon-based and metagenomic sequencing data, are compositional in nature. A common exploratory data analysis task is to infer statistical associations between the high-dimensional microbial compositions and habitat- or host-related covariates. We propose a general robust statistical regression framework, RobRegCC (Robust Regression with Compositional Covariates), which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for parsimonious model estimation, a data-driven robust initialization procedure, and a novel robust cross-validation model selection scheme. We show RobRegCC's ability to perform simultaneous sparse log-contrast regression and outlier detection over a wide range of simulation settings and provide theoretical non-asymptotic guarantees for the underlying estimators. To demonstrate the seamless applicability of the workflow on real data, we consider a gut microbiome data set from HIV patients and infer robust associations between a sparse set of microbial species and host immune response from soluble CD14 measurements. All experiments are fully reproducible and available on GitHub at https://github.com/amishra-stats/robregcc., Comment: 43 pages, 12 figures

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place., Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology"