联邦软聚类：基于广义全变差最小化
Federated Soft Clustering via Generalized Total Variation Minimization
- Aalto University（阿尔托大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对联邦学习中各设备持有私有数据并拟合个性化高斯混合模型的软聚类问题，提出广义全变差最小化框架，比较三种差异度量，并给出优化算法与收敛保证，评估了对数据异质性的鲁棒性。
AI中文摘要：
我们研究在联邦学习（FL）网络中的联邦软聚类问题，其中每个设备持有私有本地数据集，并拟合个性化的高斯混合模型（GMM）。广义全变差最小化（GTVMin）通过图正则化器耦合本地极大似然问题，该正则化器惩罚连接节点模型之间的差异。差异度量的选择是一个关键的设计决策：我们比较了模型参数之间的平方欧氏距离（需要组件匹配），与两种直接比较本地模型分布因此无需匹配的度量：蒙特卡洛近似的Kullback-Leibler（KL）散度和闭式最大均值差异（MMD）。所有三种GTVMin实例均通过同步投影梯度更新进行优化；对于平滑的MMD实例，我们提供了收敛到驻点的保证。我们刻画了它们的计算成本，并评估了它们对数据异质性的鲁棒性。
英文摘要：
We study federated soft clustering over federated learning (FL) networks of devices that each hold a private local dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.
