pared: Model selection using multi-objective optimization

Motivation: Model selection is a ubiquitous challenge in statistics. For penalized models, model selection typically entails tuning hyperparameters to maximize a measure of fit or minimize out-of-sample prediction error. However, these criteria fail to reflect other desirable characteristics, such as model sparsity, interpretability, or smoothness. Results: We present the R package pared to enable the use of multi-objective optimization for model selection. Our approach entails the use of Gaussian process-based optimization to efficiently identify solutions that represent desirable trade-offs. Our implementation includes popular models with multiple objectives including the elastic net, fused lasso, fused graphical lasso, and group graphical lasso. Our R package generates interactive graphics that allow the user to identify hyperparameter values that result in fitted models which lie on the Pareto frontier. Availability: We provide the R package pared and vignettes illustrating its application to both simulated and real data at https://github.com/priyamdas2/pared.

Latent Network Estimation and Variable Selection for Compositional Data via Variational EM

Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to simultaneously estimate network interactions and associations to relevant covariates for count data, and specifically for compositional data, which have a fixed sum constraint. We use a hierarchical Bayesian model with latent layers and employ spike-and-slab priors for both edge and covariate selection. For posterior inference, we develop a variational inference scheme with an expectation maximization step, to enable efficient estimation. Through simulation studies, we demonstrate that the proposed model outperforms existing methods in its accuracy of network recovery. We show the practical utility of our model via an application to microbiome data. The human microbiome has been shown to contribute to many of the functions of the human body, and also to be linked with a number of diseases. In our application, we seek to better understand the interaction between microbes and relevant covariates, as well as the interaction of microbes with each other. We provide a Python implementation of our algorithm, called SINC (Simultaneous Inference for Networks and Covariates), available online.