Active Learning for Manifold Gaussian Process Regression

TL;DR

This paper presents an active learning framework that integrates manifold learning with Gaussian Process regression, optimizing data selection to enhance accuracy in high-dimensional spaces and handling complex functions efficiently.

Contribution

It introduces a joint neural network and Gaussian process approach with an active learning criterion, improving data efficiency and performance in manifold GP regression.

Findings

Outperforms random sequential learning on synthetic data

Handles complex, discontinuous functions effectively

Maintains computational tractability in high-dimensional settings

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.