提出无偏随机优化方法，实现有限维核空间高斯过程的精确推断。
Unbiased Stochastic Optimization for Gaussian Processes on Finite Dimensional RKHS
- 基于有限维再生核希尔伯特空间，设计无偏随机梯度算法
- 在内存受限时性能优于现有方法，尤其在小批量场景下更优
- 适用于需精确推断且资源受限的高斯过程建模任务
高斯过程的随机超参数学习当前依赖近似方法，如有偏随机梯度或使用诱导点的随机变分推断，但无法保证收敛到真实边缘似然的驻点。本文提出针对诱导有限维再生核希尔伯特空间（RKHS）的高斯过程的精确随机推断算法。该方法可扩展至无限维RKHS，但会牺牲精确性。在有限与无限维情形下，当内存限制导致可处理的批大小和诱导点数量较小时，本方法均表现出优于现有方法的实验效果。
原文摘要 · Abstract (English)
Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such methods we are not guaranteed to converge to a stationary point of the true marginal likelihood. In this work, we propose algorithms for exact stochastic inference of GPs with kernels that induce a Reproducing Kernel Hilbert Space (RKHS) of moderate finite dimension. Our approach can also be extended to infinite dimensional RKHSs at the cost of forgoing exactness. Both for finite and infinite dimensional RKHSs, our method achieves better experimental results than existing methods when memory resources limit the feasible batch size and the possible number of inducing points.
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