  Asymmetric binary classification problems, in which the type I and II errors
have unequal severity, are ubiquitous in real-world applications. To handle
such asymmetry, researchers have developed the cost-sensitive and
Neyman-Pearson paradigms for training classifiers to control the more severe
type of classification error, say the type I error. The cost-sensitive paradigm
is widely used and has straightforward implementations that do not require
sample splitting; however, it demands an explicit specification of the costs of
the type I and II errors, and an open question is what specification can
guarantee a high-probability control on the population type I error. In
contrast, the Neyman-Pearson paradigm can train classifiers to achieve a
high-probability control of the population type I error, but it relies on
sample splitting that reduces the effective training sample size. Since the two
paradigms have complementary strengths, it is reasonable to combine their
strengths for classifier construction. In this work, we for the first time
study the methodological connections between the two paradigms, and we develop
the TUBE-CS algorithm to bridge the two paradigms from the perspective of
controlling the population type I error.
