改进高斯过程的近似方法，提升精度且不增加计算开销。
Sparse Gaussian Processes: Structured Approximations and Power-EP Revisited
- 采用分块对角缩放矩阵优化后验近似，理论证明下界更紧。
- 实验表明新方法在回归任务中表现优于或等同于现有对角方法。
- 新框架兼容多种超参数设置，适合需要灵活选择的实践者。
基于诱导点的稀疏变分高斯过程已成为扩展高斯过程模型的标准方法。近期研究显示，通过在给定诱导点的后验密度中引入对角缩放矩阵，可进一步提升该方法性能。本文首先提出一种扩展：使用分块对角结构代替原对角缩放矩阵，理论上可收紧变分下界。随后，重新审视基于幂期望传播（Power-EP）的稀疏高斯过程统一框架，并证明其可有效利用新的结构化后验近似。通过大量回归实验验证，所提出的分块对角近似在保持相近计算成本的前提下，表现始终优于或等同于现有的对角近似。此外，结合结构化后验的新型Power-EP框架在不同幂超参数设置下均表现出竞争力，为从业者提供了相比标准变分方法更灵活的替代方案。
原文摘要 · Abstract (English)
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional posterior density given the inducing points. This paper first considers an extension that employs a block-diagonal structure for the scaling matrix, provably tightening the variational lower bound. We then revisit the unifying framework of sparse GPs based on Power Expectation Propagation (PEP) and show that it can leverage and benefit from the new structured approximate posteriors. Through extensive regression experiments, we show that the proposed block-diagonal approximation consistently performs similarly to or better than existing diagonal approximations while maintaining comparable computational costs. Furthermore, the new PEP framework with structured posteriors provides competitive performance across various power hyperparameter settings, offering practitioners flexible alternatives to standard variational approaches.
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