Statistical heterogeneity of clients' local data is an important
characteristic in federated learning, motivating personalized algorithms
tailored to the local data statistics. Though there has been a plethora of
algorithms proposed for personalized supervised learning, discovering the
structure of local data through personalized unsupervised learning is less
explored. We initiate a systematic study of such personalized unsupervised
learning by developing algorithms based on optimization criteria inspired by a
hierarchical Bayesian statistical framework. We develop adaptive algorithms
that discover the balance between using limited local data and collaborative
information. We do this in the context of two unsupervised learning tasks:
personalized dimensionality reduction and personalized diffusion models. We
develop convergence analyses for our adaptive algorithms which illustrate the
dependence on problem parameters (e.g., heterogeneity, local sample size). We
also develop a theoretical framework for personalized diffusion models, which
shows the benefits of collaboration even under heterogeneity. We finally
evaluate our proposed algorithms using synthetic and real data, demonstrating
the effective sample amplification for personalized tasks, induced through
collaboration, despite data heterogeneity.

我们开启了对个性化无监督学习的系统研究，通过基于层次贝叶斯统计框架的优化准则，开发了一种自适应算法，在使用有限的本地数据和协作信息之间寻找平衡。我们在个性化降维和个性化扩散模型的背景下开发了我们的自适应算法，并对其进行了收敛性分析，揭示了问题参数（例如，异质性，本地样本大小）的依赖关系。我们还为个性化扩散模型开发了一个理论框架，展示了即使在异质性下也能从协作中获益。最后，我们使用合成和真实数据评估了我们提出的算法，展示了通过协作诱发的针对个性化任务的有效样本放大，尽管数据异质性存在。