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

Area of Science:

• Machine Learning
• Statistical Modeling

Background:

• Classical multi-output Gaussian process (MGP) models face challenges including linear correlation assumptions, data imbalance sensitivity, and lack of online update support.
• These limitations hinder their application in complex, real-world scenarios requiring flexible knowledge transfer.

Purpose of the Study:

• To propose a novel Bayesian hierarchical framework to address limitations of classical MGP models.
• To enable flexible, process-specific knowledge transfer and efficient online updates for MGP models.
• To provide a scalable solution for transfer learning in data-scarce and heterogeneous conditions.

Main Methods:

• A three-layer Bayesian hierarchical architecture is introduced, modeling shared hyperparameters as random variables.
• Asymmetric hyperparameter updates leverage source data for informative priors and target data for posterior updates.
• Theoretical analysis confirms nonlinear inference and efficient, iterative model updates without full re-optimization.

Main Results:

• The proposed framework significantly outperforms existing single-output and hierarchical MGP baselines.
• Demonstrated improvements in both predictive accuracy and computational efficiency.
• Successful application in synthetic data and real-world case studies in battery diagnostics and nano-sensor design.

Conclusions:

• The novel Bayesian hierarchical framework offers a principled and scalable solution for transfer learning.
• The method effectively handles data scarcity and heterogeneity in multi-output GP modeling.
• This approach advances the capabilities of MGP models for complex applications.