  Combining data from varied sources has considerable potential for knowledge
discovery: collaborating data parties can mine data in an expanded feature
space, allowing them to explore a larger range of scientific questions.
However, data sharing among different parties is highly restricted by legal
conditions, ethical concerns, and / or data volume. Fueled by these concerns,
the fields of cryptography and distributed learning have made great progress
towards privacy-preserving and distributed data mining. However, practical
implementations have been hampered by the limited scope or computational
complexity of these methods. In this paper, we greatly extend the range of
analyses available for vertically partitioned data, i.e., data collected by
separate parties with different features on the same subjects. To this end, we
present a novel approach for privacy-preserving generalized linear models, a
fundamental and powerful framework underlying many prediction and
classification procedures. We base our method on a distributed block coordinate
descent algorithm to obtain parameter estimates, and we develop an extension to
compute accurate standard errors without additional communication cost. We
critically evaluate the information transfer for semi-honest collaborators and
show that our protocol is secure against data reconstruction. Through both
simulated and real-world examples we illustrate the functionality of our
proposed algorithm. Without leaking information, our method performs as well on
vertically partitioned data as existing methods on combined data -- all within
mere minutes of computation time. We conclude that our method is a viable
approach for vertically partitioned data analysis with a wide range of
real-world applications.
