Title: Linearized Binary Regression,
Abstract: Probit regression was first proposed by Bliss in 1934 to study mortality
rates of insects. Since then, an extensive body of work has analyzed and used
probit or related binary regression methods (such as logistic regression) in
numerous applications and fields. This paper provides a fresh angle to such
well-established binary regression methods. Concretely, we demonstrate that
linearizing the probit model in combination with linear estimators performs on
par with state-of-the-art nonlinear regression methods, such as posterior mean
or maximum aposteriori estimation, for a broad range of real-world regression
problems. We derive exact, closed-form, and nonasymptotic expressions for the
mean-squared error of our linearized estimators, which clearly separates them
from nonlinear regression methods that are typically difficult to analyze. We
showcase the efficacy of our methods and results for a number of synthetic and
real-world datasets, which demonstrates that linearized binary regression finds
potential use in a variety of inference, estimation, signal processing, and
machine learning applications that deal with binary-valued observations or
measurements.