  Vertical Federated Learning (vFL) allows multiple parties that own different
attributes (e.g. features and labels) of the same data entity (e.g. a person)
to jointly train a model. To prepare the training data, vFL needs to identify
the common data entities shared by all parties. It is usually achieved by
Private Set Intersection (PSI) which identifies the intersection of training
samples from all parties by using personal identifiable information (e.g.
email) as sample IDs to align data instances. As a result, PSI would make
sample IDs of the intersection visible to all parties, and therefore each party
can know that the data entities shown in the intersection also appear in the
other parties, i.e. intersection membership. However, in many real-world
privacy-sensitive organizations, e.g. banks and hospitals, revealing membership
of their data entities is prohibited. In this paper, we propose a vFL framework
based on Private Set Union (PSU) that allows each party to keep sensitive
membership information to itself. Instead of identifying the intersection of
all training samples, our PSU protocol generates the union of samples as
training instances. In addition, we propose strategies to generate synthetic
features and labels to handle samples that belong to the union but not the
intersection. Through extensive experiments on two real-world datasets, we show
our framework can protect the privacy of the intersection membership while
maintaining the model utility.
