BACKGROUND: The ability to confidently predict health outcomes from gene expression would catalyze a revolution in molecular diagnostics. Yet, the goal of developing actionable, robust, and reproducible predictive signatures of phenotypes such as clinical outcome has not been attained in almost any disease area. Here, we report a comprehensive analysis spanning prediction tasks from ulcerative colitis, atopic dermatitis, diabetes, to many cancer subtypes for a total of 24 binary and multiclass prediction problems and 26 survival analysis tasks. We systematically investigate the influence of gene subsets, normalization methods and prediction algorithms. Crucially, we also explore the novel use of deep representation learning methods on large transcriptomics compendia, such as GTEx and TCGA, to boost the performance of state-of-the-art methods. The resources and findings in this work should serve as both an up-to-date reference on attainable performance, and as a benchmarking resource for further research. RESULTS: -regularized regression methods applied to centered log-ratio transformed transcript abundances provide the best predictive analyses overall. CONCLUSIONS: Transcriptomics-based phenotype prediction benefits from proper normalization techniques and state-of-the-art regularized regression approaches. In our view, breakthrough performance is likely contingent on factors which are independent of normalization and general modeling techniques; these factors might include reduction of systematic errors in sequencing data, incorporation of other data types such as single-cell sequencing and proteomics, and improved use of prior knowledge.

Two species with similar resource requirements respond in a characteristic way to variations in their habitat-their abundances rise and fall in concert. We use this idea to learn how bacterial populations in the microbiota respond to habitat conditions that vary from person-to-person across the human population. Our mathematical framework shows that habitat fluctuations are sufficient for explaining intra-bodysite correlations in relative species abundances from the Human Microbiome Project. We explicitly show that the relative abundances of closely related species are positively correlated and can be predicted from taxonomic relationships. We identify a small set of functional pathways related to metabolism and maintenance of the cell wall that form the basis of a common resource sharing niche space of the human microbiota.

MOTIVATION: Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. RESULTS: Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. AVAILABILITY AND IMPLEMENTATION: An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode.

Identifying small subsets of features that are relevant for prediction and classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult, for modern data sets where the number of features can be comparable to or even exceed the number of samples. Here, we show that feature selection with Bayesian inference takes a universal form and reduces to calculating the magnetizations of an Ising model under some mild conditions. Our results exploit the observation that the evidence takes a universal form for strongly regularizing priors--priors that have a large effect on the posterior probability even in the infinite data limit. We derive explicit expressions for feature selection for generalized linear models, a large class of statistical techniques that includes linear and logistic regression. We illustrate the power of our approach by analyzing feature selection in a logistic regression-based classifier trained to distinguish between the letters B and D in the notMNIST data set.