精确聚集局部模型
Precision Aggregated Local Models
摘要：
大规模高斯过程（GP）回归对于较大的数据集是不可行的，这是由于在处理协方差阵时涉及到触发器的立方缩放和二次存储。最近文献中的补救措施侧重于分而治之，例如，划分成子问题，并诱导功能（从而计算）的独立性。这种近似可以是快速的，准确的，有时甚至比普通的GPS更灵活。然而，一个很大的缺点是分区边界处的连续性损失。像局部近似GP（LAGP）这样的现代方法实际上意味着无限划分，因此在这方面是病态的好和坏。模型平均，一个替代分治，可以保持绝对的连续性，但往往过于平滑，降低准确性。在这里，我们建议将类似LAGP的方法放入类似本地专家的框架中，将基于分区的速度与模型平均连续性相结合，作为我们称之为精确聚合本地模型（PALM）的旗舰示例。使用$K$ LAGP，每个选择$n$从$N$总的数据对，我们说明了一个计划，最多立方的$n$，二次的$K$，线性的$N$，大大减少了计算和存储的需求。大量的经验说明显示了PALM如何至少与LAGP一样准确，在速度方面可以快得多，并消除连续的预测表面。最后，我们提出了顺序更新方案，它greetly细化PALM预测的计算预算。
英文摘要：
Large scale Gaussian process (GP) regression is infeasible for larger data sets due to cubic scaling of flops and quadratic storage involved in working with covariance matrices. Remedies in recent literature focus on divide-and-conquer, e.g., partitioning into sub-problems and inducing functional (and thus computational) independence. Such approximations can be speedy, accurate, and sometimes even more flexible than an ordinary GPs. However, a big downside is loss of continuity at partition boundaries. Modern methods like local approximate GPs (LAGPs) imply effectively infinite partitioning and are thus pathologically good and bad in this regard. Model averaging, an alternative to divide-and-conquer, can maintain absolute continuity but often over-smooths, diminishing accuracy. Here we propose putting LAGP-like methods into a local experts-like framework, blending partition-based speed with model-averaging continuity, as a flagship example of what we call precision aggregated local models (PALM). Using $K$ LAGPs, each selecting $n$ from $N$ total data pairs, we illustrate a scheme that is at most cubic in $n$, quadratic in $K$, and linear in $N$, drastically reducing computational and storage demands. Extensive empirical illustration shows how PALM is at least as accurate as LAGP, can be much faster in terms of speed, and furnishes continuous predictive surfaces. Finally, we propose sequential updating scheme which greedily refines a PALM predictor up to a computational budget.
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