提出更可靠的计算感知高斯过程，解决大样本时不确定性过高的问题。
Calibrated Computation-Aware Gaussian Processes
- 用高斯-赛德尔迭代构建校准的随机线性求解器
- 在低维测试集上减少迭代次数时表现优于现有方法
- 适合大规模回归且对不确定性敏感的场景
高斯过程在训练集规模增大时计算复杂度呈立方增长，难以应用于大规模回归任务。计算感知高斯过程（CAGP）通过使用概率线性求解器降低计算量，但会因计算缩减引入额外的不确定性，导致后验不确定性严重保守。本文证明：若所用概率线性求解器是统计意义下校准的，则由此生成的CAGP也必然是校准的。为此，我们提出基于高斯-赛德尔迭代的新框架CAGP-GS。在合成数据上验证了其校准性，并在大规模全球气温回归任务中与现有方法对比，结果显示当测试集维度低且迭代次数少时，该方法性能更优。
原文摘要 · Abstract (English)
Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting probabilistic linear solvers to reduce complexity, widening the posterior with additional computational uncertainty due to reduced computation. However, the most commonly used CAGP framework results in (sometimes dramatically) conservative uncertainty quantification, making the posterior unrealistic in practice. In this work, we prove that if the utilised probabilistic linear solver is calibrated, in a rigorous statistical sense, then so too is the induced CAGP. We thus propose a new CAGP framework, CAGP-GS, based on using Gauss-Seidel iterations for the underlying probabilistic linear solver. CAGP-GS performs favourably compared to existing approaches when the test set is low-dimensional and few iterations are performed. We test the calibratedness on a synthetic problem, and compare the performance to existing approaches on a large-scale global temperature regression problem.
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