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To enable predictive modeling of the deformation method, we propose to model the spatial deformation as a function of covariates. The spaces of diffeomorphic deformations and Euclidean covariate vectors are connected by characterizing deformations as generated by velocity fields living in a Lie algebra. To overcome the estimation instability caused by high-order interactions between multiple covariates in a general Lie algebra, we prove that those interactions can be truncated with a moderate physical assumption. Based on the theoretical results, a concise functional form of deformations driven by multiple covariates can be established, and an efficient estimation-inference algorithm is developed for out-of-sample nonstationary GP prediction with limited covariate-deformation sample pairs. The effectiveness and generalizability of the method are demonstrated on a simulation study and two case studies, in the fields of manufacturing and geostatistics, respectively.
| Subjects: | Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2604.27280 [cs.LG] |
| (or arXiv:2604.27280v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.27280 arXiv-issued DOI via DataCite (pending registration) |
From: Minghao Gu [view email]
[v1]
Thu, 30 Apr 2026 00:31:32 UTC (4,336 KB)
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