基于数据草图（Data Sketching）的模拟器函数数据鲁棒分布式学习
Robust Distributed Learning of Functional Data From Simulators through Data Sketching
AI总结：
针对模拟器函数数据分布式推断对数据分片选择敏感的问题，提出基于随机数据草图的鲁棒分布式贝叶斯学习方法，在保护隐私的同时实现跨机器推断聚合，并在SLOSH模拟器替代模型上验证了性能。
摘要：
在环境研究中，真实的模拟对于理解复杂系统至关重要。使用高斯过程（Gaussian processes, GPs）进行函数数据模型的统计仿真已成为实现这一目的的标准工具。此类模型的传统集中式处理需要大量的计算和存储资源，促使新兴的分布式贝叶斯学习算法将数据划分为分片以进行分布式计算。然而，分布式推断对分片选择的敏感性引发了担忧。我们的方法不使用数据分片，而是采用多个随机矩阵来创建数据集的随机线性投影，即草图（sketches）。各机器并行使用随机数据草图对函数数据模型进行后验推断。这些单独的推断在中央服务器上跨机器进行合并。跨随机矩阵的推断聚合使我们的方法对数据草图的选择具有鲁棒性，从而实现鲁棒的分布式贝叶斯学习。一个重要优势是其能够维持采样单元的隐私，因为随机草图可防止原始数据的恢复。我们通过模拟示例突显了该方法的重要性，并使用飓风海、湖和陆上涌浪（Sea, Lake, and Overland Surges from Hurricanes, SLOSH）模拟器的替代模型展示了其作为仿真器的性能，该模拟器是政府机构的重要模拟器。
英文摘要：
In environmental studies, realistic simulations are essential for understanding complex systems. Statistical emulation with Gaussian processes (GPs) in functional data models have become a standard tool for this purpose. Traditional centralized processing of such models requires substantial computational and storage resources, leading to emerging distributed Bayesian learning algorithms that partition data into shards for distributed computations. However, concerns about the sensitivity of distributed inference to shard selection arise. Instead of using data shards, our approach employs multiple random matrices to create random linear projections, or sketches, of the dataset. Posterior inference on functional data models is conducted using random data sketches on various machines in parallel. These individual inferences are combined across machines at a central server. The aggregation of inference across random matrices makes our approach resilient to the selection of data sketches, resulting in robust distributed Bayesian learning. An important advantage is its ability to maintain the privacy of sampling units, as random sketches prevent the recovery of raw data. We highlight the significance of our approach through simulation examples and showcase the performance of our approach as an emulator using surrogates of the Sea, Lake, and Overland Surges from Hurricanes (SLOSH) simulator - an important simulator for government agencies.
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