E-health allows smart devices and medical institutions to collaboratively
collect patients' data, which is trained by Artificial Intelligence (AI)
technologies to help doctors make diagnosis. By allowing multiple devices to
train models collaboratively, federated learning is a promising solution to
address the communication and privacy issues in e-health. However, applying
federated learning in e-health faces many challenges. First, medical data is
both horizontally and vertically partitioned. Since single Horizontal Federated
Learning (HFL) or Vertical Federated Learning (VFL) techniques cannot deal with
both types of data partitioning, directly applying them may consume excessive
communication cost due to transmitting a part of raw data when requiring high
modeling accuracy. Second, a naive combination of HFL and VFL has limitations
including low training efficiency, unsound convergence analysis, and lack of
parameter tuning strategies. In this paper, we provide a thorough study on an
effective integration of HFL and VFL, to achieve communication efficiency and
overcome the above limitations when data is both horizontally and vertically
partitioned. Specifically, we propose a hybrid federated learning framework
with one intermediate result exchange and two aggregation phases. Based on this
framework, we develop a Hybrid Stochastic Gradient Descent (HSGD) algorithm to
train models. Then, we theoretically analyze the convergence upper bound of the
proposed algorithm. Using the convergence results, we design adaptive
strategies to adjust the training parameters and shrink the size of transmitted
data. Experimental results validate that the proposed HSGD algorithm can
achieve the desired accuracy while reducing communication cost, and they also
verify the effectiveness of the adaptive strategies.

电子健康允许智能设备和医疗机构协作收集患者数据，通过人工智能技术进行训练，以帮助医生进行诊断。我们提出了一个混合联邦学习框架，包括水平和垂直分区的数据，并开发了一种适应性策略来调整训练参数和缩小发送的数据大小。实验证明，所提出的算法可以实现所需的准确性，同时减少通信成本，也验证了适应性策略的有效性。