Dirichlet Process Mixture Models (DPMMs) are widely used to address clustering problems. Their main advantage lies in their ability to automatically estimate the number of clusters during the inference process through the Bayesian non-parametric framework. However, the inference becomes considerably slow as the dataset size increases. This paper proposes a new distributed Markov Chain Monte Carlo (MCMC) inference method for DPMMs (DisCGS) using sufficient statistics. Our approach uses the collapsed Gibbs sampler and is specifically designed to work on distributed data across independent and heterogeneous machines, which habilitates its use in horizontal federated learning. Our method achieves highly promising results and notable scalability. For instance, with a dataset of 100K data points, the centralized algorithm requires approximately 12 hours to complete 100 iterations while our approach achieves the same number of iterations in just 3 minutes, reducing the execution time by a factor of 200 without compromising clustering performance. The code source is publicly available at https://github.com/redakhoufache/DisCGS.

通过使用合适的统计量，本文提出了一种新的DPMM（Dirichlet Process Mixture Models）的分布式马尔科夫链蒙特卡罗（MCMC）推理方法（DisCGS）。该方法使用了折叠的吉布斯采样器，并且特别设计用于在独立异构的机器间处理分布式数据，使其在横向联合学习中具备应用能力。我们的方法取得了非常有前景的结果和显著的可扩展性。例如，对于包含10万个数据点的数据集，集中式算法需要大约12小时完成100次迭代，而我们的方法仅需3分钟完成相同的迭代次数，将执行时间缩短了200倍，同时不影响聚类性能。

分布式多项式混合模型的收缩吉布斯采样器在联邦学习中的应用