Author Summary The low costs of sequencing and other high-throughput technologies have made available large amounts of data to address molecular biology problems. However, often this means thousands of measurements, for example on gene expression, are assayed for a much smaller number of samples. The imbalance complicates the identification of genes that generalize to new samples and in finding a collection of genes that suggest a theme for interpreting the data. Pathway and network-based approaches have proven their worth in these situations. They force solutions onto known biology and they produce more robust predictors. In this manuscript, we describe a new formulation of statistical learning approaches that naturally incorporates gene-gene relationships, like those found in gene network databases. The theory we present helps unify and codify an explicit formulation for gene pathway-informed machine-learning that should have wide reach.
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