改进稀疏高斯过程近似，提升精度且不增加计算开销
Tighter sparse variational Gaussian processes
- 放宽诱导点后验与先验匹配的假设，允许更小方差
- 在回归、分类和潜变量模型上均优于标准方法
- 适合需要高精度稀疏高斯过程的应用场景
基于诱导点的稀疏变分高斯过程近似已成为大规模数据集上扩展高斯过程的主流方法，因其理论优雅性、计算效率和实现简便性。本文提出一种可证明更紧的变分近似，通过放松标准假设——即给定诱导点的条件后验必须与先验一致——实现改进。核心创新在于调整条件后验，使其在训练点处方差小于先验。我们推导了回归情形下的压缩边界，说明如何在大数据场景中使用该近似，并讨论其在正交结构诱导点及高斯过程潜变量模型中的应用。在回归基准、分类和潜变量模型上的大量实验表明，所提近似在保持相同计算成本的前提下，性能始终不低于或优于标准稀疏变分高斯过程。代码将集成至所有主流高斯过程工具包。
原文摘要 · Abstract (English)
Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation. This paper introduces a provably tighter variational approximation by relaxing the standard assumption that the conditional approximate posterior given the inducing points must match that in the prior. The key innovation is to modify the conditional posterior to have smaller variances than that of the prior at the training points. We derive the collapsed bound for the regression case, describe how to use the proposed approximation in large data settings, and discuss its application to handle orthogonally structured inducing points and GP latent variable models. Extensive experiments on regression benchmarks, classification, and latent variable models demonstrate that the proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining the same computational cost. An implementation will be made available in all popular GP packages.
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