We present a novel stochastic variational Gaussian process ($\mathcal{GP}$) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for $\mathcal{GP}$s (CVTGP) is defined in terms of the $\mathcal{GP}$ prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent $\mathcal{GP}$ coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to $\mathcal{O}(M)$, enjoys numerical stability, and maintains $\mathcal{O}(M^3)$ time- and $\mathcal{O}(M^2)$ space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic $\mathcal{GP}$ inference methods.

基于核心集的变分温和高斯过程的随机推理方法，在核心集的后验概率基础上，降低参数规模、提高数值稳定性和节省时间和空间复杂度的情况下，验证了其在模拟和实际回归问题中表现出更好的证据低限估计和预测均方根误差。

基于Coreset的、温和的变分后验的准确和可扩展性的随机高斯过程推断