Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential fashion. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $O(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently recycle computations for constant-time $O(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting. Code is available at https://github.com/wjmaddox/online_gp.
翻译:Gaussian process(GPs)为在线环境中的性能提供了一个黄金标准,例如样本高效控制和黑盒优化,我们需要在以相继方式获取数据时更新后端分布,然而,在观测到一美元点后,更新GP postior,以适应哪怕是一次新的观测,在准确的环境下至少要花费O(n)美元计算。我们展示了如何使用结构化内核内插来高效回收计算,以进行关于点数($)的固定时间(O(1)美元)在线更新,同时保留精确的推断。我们在一系列在线回归和分类设置、Bayesian 优化和积极抽样中展示了我们做法的希望,以减少疟疾发病率预测中的错误。 代码见https://github.com/wjmaddox/online_gp。