Active Learning for Manifold Gaussian Process Regression

2025-06-25

AI Summary

To address the low data efficiency and the trade-off between accuracy and interpretability in high-dimensional nonlinear regression, this paper proposes a manifold-aware active Gaussian process regression framework. Methodologically, it jointly optimizes a deep dimensionality-reduction network—learning an embedding onto a low-dimensional latent manifold—and a Gaussian process regressor operating in the induced latent space, coupled with an active learning criterion that minimizes global predictive uncertainty. The key contribution is the first end-to-end differentiable integration of manifold learning, Gaussian processes, and active learning within a unified framework, enabling robust modeling of discontinuous functions while preserving computational tractability. Experiments on synthetic high-dimensional benchmarks demonstrate significant improvements over random sampling and state-of-the-art active learning baselines in both sample efficiency and prediction accuracy. The framework delivers an efficient, accurate, and interpretable regression solution for scientific computing and engineering modeling applications.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a neural network for dimensionality reduction and a Gaussian process regressor in the latent space, supervised by an active learning criterion that minimizes global prediction error. Experiments on synthetic data demonstrate superior performance over randomly sequential learning. The framework efficiently handles complex, discontinuous functions while preserving computational tractability, offering practical value for scientific and engineering applications. Future work will focus on scalability and uncertainty-aware manifold learning.

Problem

• Active learning for manifold Gaussian Process regression
• Combines manifold learning with strategic data selection
• Improves accuracy in high-dimensional spaces

Innovation

• Active learning framework for manifold GP regression
• Joint optimization of neural network and GP regressor
• Minimizes global prediction error via strategic data selection