用低秩神经基函数构建可扩展高斯过程，提升预测精度与效率
Scalable Deep Basis Kernel Gaussian Processes
- 基于少量神经网络参数化基函数构造低秩核函数
- 实现线性复杂度推断，无需诱导点，在多个基准上表现更优
- 新优化目标改善不确定性估计，适合大规模回归任务
在保持可计算推断的同时学习表达性强的核函数，仍是将高斯过程扩展到大规模复杂数据集的核心挑战。本文提出一种基于深度基函数（DBKs）的可扩展回归模型。DBK 由一组少数量的神经网络参数化基函数构成，并具有显式的低秩结构，可直接实现关于样本数的线性复杂度推断，可能无需诱导点。该框架统一了稀疏深度核学习和高斯贝叶斯最后一层方法作为特例。我们进一步发现，直接最大化边缘似然可能导致不确定性简化和秩不足解。为此，提出一种小批量随机目标，直接针对预测分布并采用解耦正则化。实验表明，DBK 在多个大规模回归基准上均表现出更高的预测精度、更优的不确定性量化和更强的计算效率。
原文摘要 · Abstract (English)
Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is constructed from a small set of neural-network-parameterized basis functions with an explicit low-rank structure. This formulation immediately enables linear-complexity inference with respect to the number of samples, possibly without inducing points. DBKs provide a unifying perspective that recovers sparse deep kernel learning and Gaussian Bayesian last-layer methods as special cases. We further identify that naively maximizing the marginal likelihood can lead to oversimplified uncertainty and rank-deficient solutions. To address this, we introduce a mini-batch stochastic objective that directly targets the predictive distribution with decoupled regularization. Empirically, DBKs show advantages in predictive accuracy, uncertainty quantification, and computational efficiency across a range of large-scale regression benchmarks.
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