  Federated learning has emerged as a promising distributed learning paradigm
that facilitates collaborative learning among multiple parties without
transferring raw data. However, most existing federated learning studies focus
on either horizontal or vertical data settings, where the data of different
parties are assumed to be from the same feature or sample space. In practice, a
common scenario is the hybrid data setting, where data from different parties
may differ both in the features and samples. To address this, we propose
HybridTree, a novel federated learning approach that enables federated tree
learning on hybrid data. We observe the existence of consistent split rules in
trees. With the help of these split rules, we theoretically show that the
knowledge of parties can be incorporated into the lower layers of a tree. Based
on our theoretical analysis, we propose a layer-level solution that does not
need frequent communication traffic to train a tree. Our experiments
demonstrate that HybridTree can achieve comparable accuracy to the centralized
setting with low computational and communication overhead. HybridTree can
achieve up to 8 times speedup compared with the other baselines.
