Robust Distributed Learning of Functional Data From Simulators through Data Sketching

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.