  Despite the availability of numerous statistical and machine learning tools
for joint feature modeling, many scientists investigate features marginally,
i.e., one feature at a time. This is partly due to training and convention but
also roots in scientists' strong interests in simple visualization and
interpretability. As such, marginal feature ranking for some predictive tasks,
e.g., prediction of cancer driver genes, is widely practiced in the process of
scientific discoveries. In this work, we focus on marginal ranking for binary
prediction, the arguably most common predictive tasks. We argue that the most
widely used marginal ranking criteria, including the Pearson correlation, the
two-sample t test, and two-sample Wilcoxon rank-sum test, do not fully take
feature distributions and prediction objectives into account. To address this
gap in practice, we propose two ranking criteria corresponding to two
prediction objectives: the classical criterion (CC) and the Neyman-Pearson
criterion (NPC), both of which use model-free nonparametric implementations to
accommodate diverse feature distributions. Theoretically, we show that under
regularity conditions both criteria achieve sample-level ranking consistent
with their population-level counterpart with high probability. Moreover, NPC is
robust to sampling bias when the two class proportions in a sample deviate from
those in the population. This property endows NPC good potential in biomedical
research where sampling bias is common. We demonstrate the use and relative
advantages of CC and NPC in simulation and real data studies. Our model-free
objective-based ranking idea is extendable to ranking feature subsets and
generalizable to other prediction tasks and learning objectives.
