We are now in an information era and the volume of data is growing explosively. However, due to privacy issues, it is very common that data cannot be freely shared among the data generating. Federated analytics was recently proposed aiming at deriving analytical insights among data-generating devices without exposing the raw data, but the intermediate analytics results. Note that the computing resources at the data generating devices are limited, thus making on-device execution of computing-intensive tasks challenging. We thus propose to apply the digital twin technique, which emulates the resource-limited physical/end side, while utilizing the rich resource at the virtual/computing side. Nevertheless, how to use the digital twin technique to assist federated analytics while preserving distributed data privacy is challenging. To address such a challenge, this work first formulates a problem on digital twin-assisted federated distribution discovery. Then, we propose a federated Markov chain Monte Carlo with a delayed rejection (FMCMC-DR) method to estimate the representative parameters of the global distribution. We combine a rejection–acceptance sampling technique and a delayed rejection technique, allowing our method to be able to explore the full state space. Finally, we evaluate FMCMC-DR against the Metropolis–Hastings (MH) algorithm and random walk Markov chain Monte Carlo method (RW-MCMC) using numerical experiments. The results show our algorithm outperforms the other two methods by 50% and 95% contour accuracy, respectively, and has a better convergence rate.

中文翻译：

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使用贝叶斯方法进行联合分析的数字孪生

我们现在处于信息时代，数据量呈爆炸式增长。然而，由于隐私问题，数据不能在数据生成之间自由共享是很常见的。最近提出了联合分析，旨在在不暴露原始数据但不暴露中间分析结果的情况下在数据生成设备中获得分析见解。请注意，数据生成设备的计算资源是有限的，因此计算密集型任务的设备上执行具有挑战性。因此，我们建议应用数字孪生技术，模拟资源有限的物理/端侧，同时利用虚拟/计算侧的丰富资源。然而，如何使用数字孪生技术来协助联合分析同时保护分布式数据隐私具有挑战性。为了应对这样的挑战，这项工作首先提出了一个关于数字孪生辅助联合分布发现的问题。然后，我们提出了一种带有延迟拒绝（FMCMC-DR）方法的联合马尔可夫链蒙特卡罗来估计全局分布的代表性参数。我们结合了拒绝接受采样技术和延迟拒绝技术，使我们的方法能够探索完整的状态空间。最后，我们使用数值实验评估 FMCMC-DR 与 Metropolis-Hastings (MH) 算法和随机游走马尔可夫链蒙特卡罗方法 (RW-MCMC)。结果表明，我们的算法在轮廓精度上分别优于其他两种方法 50% 和 95%，并且具有更好的收敛速度。最后，我们使用数值实验评估 FMCMC-DR 与 Metropolis-Hastings (MH) 算法和随机游走马尔可夫链蒙特卡罗方法 (RW-MCMC)。结果表明，我们的算法在轮廓精度上分别优于其他两种方法 50% 和 95%，并且具有更好的收敛速度。最后，我们使用数值实验评估 FMCMC-DR 与 Metropolis-Hastings (MH) 算法和随机游走马尔可夫链蒙特卡罗方法 (RW-MCMC)。结果表明，我们的算法在轮廓精度上分别优于其他两种方法 50% 和 95%，并且具有更好的收敛速度。