  Vertical federated learning (VFL) considers the case that the features of
data samples are partitioned over different participants. VFL consists of two
main steps, i.e., identify the common data samples for all participants
(alignment) and train model using the aligned data samples (training). However,
when there are many participants and data samples, both alignment and training
become slow. As such, we propose TreeCSS as an efficient VFL framework that
accelerates the two main steps. In particular, for sample alignment, we design
an efficient multi-party private set intersection (MPSI) protocol called
Tree-MPSI, which adopts a tree-based structure and a data-volume-aware
scheduling strategy to parallelize alignment among the participants. As model
training time scales with the number of data samples, we conduct coreset
selection (CSS) to choose some representative data samples for training. Our
CCS method adopts a clustering-based scheme for security and generality, which
first clusters the features locally on each participant and then merges the
local clustering results to select representative samples. In addition, we
weight the samples according to their distances to the centroids to reflect
their importance to model training. We evaluate the effectiveness and
efficiency of our TreeCSS framework on various datasets and models. The results
show that compared with vanilla VFL, TreeCSS accelerates training by up to
2.93x and achieves comparable model accuracy.
