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Hybrid smoothing for surfaces and anomaly detection
Hofkes, Matthew
Hofkes, Matthew
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2024
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Abstract
Many natural and industrial processes exhibit a combination of smooth and rough features. Motivated by real world data from large-scale water filtration and the Community Earth System Model Large Ensemble (CESM-LE), this works introduces a novel approach called ``hybrid smoothing”. By combining a Gaussian process with a rough function, hybrid smoothing can separate a smooth trend or spatial process from rough features, which may be due to anomalous behavior or unknown covariates. Initially implemented using basis functions, the rough function is re-proposed as a non-Gaussian process, specifically in the form of a scaled Gaussian mixture. This adaptation introduces flexibility into the model by permitting a range of priors on the rough process. Among these, the Normal Jeffrey’s prior proves particularly robust and effective in distinguishing between smooth and rough features.
The preferred implementation of hybrid smoothing is via an MCMC with a full Gibbs sampler. This is made possible by the Gaussian mixture representation of the sparse rough function. Several strategies, including orthogonalization and adaptive sampling, are employed to aid convergence, and computational efficiency is enhanced through partial updates. While
"roughness" is primarily modeled as stepwise linear behavior, the methodology extends easily to other discrete differences in the data.
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