论文标题
连续输入和分类输入的高级相关矩阵的高斯过程模型
Gaussian Process Models with Low-Rank Correlation Matrices for Both Continuous and Categorical Inputs
论文作者
论文摘要
我们介绍了一种在混合连续和分类高斯过程模型中使用互相关矩阵的低级别近似值的方法。这种新方法（称为低级相关性（LRC））提供了通过选择适当的近似等级来灵活地适应当前问题的参数数量的能力。此外，我们提出了定义测试功能的系统方法，该方法可用于评估与连续和分类输入有关的模型或优化方法的准确性或优化方法。我们将LRC与对互相关矩阵进行建模的现有方法进行了比较。事实证明，新方法在估计互相关和响应表面预测方面表现良好。因此，LRC是现有方法的灵活且有用的补充，尤其是用于增加分类输入水平的组合数量。
We introduce a method that uses low-rank approximations of cross-correlation matrices in mixed continuous and categorical Gaussian Process models. This new method -- called Low-Rank Correlation (LRC) -- offers the ability to flexibly adapt the number of parameters to the problem at hand by choosing an appropriate rank of the approximation. Furthermore, we present a systematic approach of defining test functions that can be used for assessing the accuracy of models or optimization methods that are concerned with both continuous and categorical inputs. We compare LRC to existing approaches of modeling the cross-correlation matrix. It turns out that the new approach performs well in terms of estimation of cross-correlations and response surface prediction. Therefore, LRC is a flexible and useful addition to existing methods, especially for increasing numbers of combinations of levels of the categorical inputs.
