A Bayesian Hierarchical Framework for Non-linear and Iterative Transfer Learning of Gaussian Process

Zhiyong Hu; Jianguo Wu; Chao Wang

doi:10.1109/TPAMI.2026.3696225

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A Bayesian Hierarchical Framework for Non-linear and Iterative Transfer Learning of Gaussian Process

Journal article

Open access

Peer reviewed

A Bayesian Hierarchical Framework for Non-linear and Iterative Transfer Learning of Gaussian Process

Zhiyong Hu, Jianguo Wu and Chao Wang

IEEE transactions on pattern analysis and machine intelligence, Vol.48(10), pp.12506-12517

05/22/2026

DOI: 10.1109/TPAMI.2026.3696225

PMID: 42172164

Appears in UI Libraries Support Open Access

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Abstract

Classical multi-output GP (MGP) models often suffer from limitations such as the assumption of linear inter-process correlations, sensitivity to data imbalance, and lack of support for online updates. This paper proposes a novel Bayesian hierarchical framework to address these challenges. Specifically, we introduce a three-layer architecture that models shared hyper-parameters as random variables and updates them asymmetrically through a hierarchical structure. The proposed framework treats source data as historical information to form informative priors and uses target data for posterior update, which facilitates a flexible and process-specific knowledge transfer. We theoretically establish that this treatment induces nonlinear inference for the target process and allows efficient, iterative updates without re-optimizing the entire model. Comprehensive evaluations on synthetic data and real-world case studies in battery diagnostics and nano-sensor design demonstrate that our method significantly outperforms existing single-output and hierarchical MGP baselines in both accuracy and computational efficiency. The results suggest that our approach offers a principled and scalable solution for transfer learning under data-scarce and heterogeneous conditions.

Bayesian updating

Gaussian Process

Multi-output modeling

nonlinear correlation

transfer learning

UIOWA OA Agreement

Details

Title: Subtitle: A Bayesian Hierarchical Framework for Non-linear and Iterative Transfer Learning of Gaussian Process
Creators: Zhiyong Hu - Anhui University
Jianguo Wu - Peking University
Chao Wang - University of Iowa
Resource Type: Journal article
Publication Details: IEEE transactions on pattern analysis and machine intelligence, Vol.48(10), pp.12506-12517
DOI: 10.1109/TPAMI.2026.3696225
PMID: 42172164
NLM abbreviation: IEEE Trans Pattern Anal Mach Intell
ISSN: 0162-8828
eISSN: 1939-3539
Publisher: IEEE
Number of pages: 12
Grant note: National Natural Science Foundation of China (NSFC): 52305142 National Science Foundation (NSF): CMMI-2436025
The work of Zhiyong Hu was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 52305142. The work of Chao Wang was supported in part by National Science Foundation (NSF) under Grant CMMI-2436025.
Language: English
Date published: 05/22/2026
Academic Unit: Industrial and Systems Engineering
Record Identifier: 9985166963002771

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