I. Introduction
With the increasing concerns for data privacy in machine learning, federated learning (FL) [1] has received a lot of attention as a privacy-preserving machine learning framework to enable multiple clients (e.g., hospitals) to collaboratively train a model without sharing raw data. Existing FL approaches mainly focus on the scenario where each client has homogeneous data, i.e., the data with the same feature space. This setting is called horizontal federated learning (HFL) [2]. However, in many real world applications, the feature spaces of the data owned by different clients may not be completely the same. Their data may differ in the feature space except for some common features. Consider the following example [3]. A hospital may share common features of patients such as age, blood pressure, etc. with nursing homes and physical examination centers. However, each medical institution also holds additional unique features such as prescription and diet information, as well. Applying existing HFL approaches to this setting is not efficient in terms of the performance because they can only use the common features and leaves the unique features unutilized. We need more efficient approaches to address this problem.