Gaussian process (GP) models that combine both categorical and continuous input variables have found use e.g. in longitudinal data analysis and computer experiments. However, standard inference for these models has the typical cubic scaling, and common scalable approximation schemes for GPs cannot be applied since the covariance function is non-continuous. In this work, we derive a basis function approximation scheme for mixed-domain covariance functions, which scales linearly with respect to the number of observations and total number of basis functions. The proposed approach is naturally applicable to Bayesian GP regression with arbitrary observation models. We demonstrate the approach in a longitudinal data modelling context and show that it approximates the exact GP model accurately, requiring only a fraction of the runtime compared to fitting the corresponding exact model.
翻译:将绝对输入变量和连续输入变量相结合的Gausian进程模型(GP)在纵向数据分析和计算机实验中都得到了使用,不过,这些模型的标准推论具有典型的立方比例,而且由于共变功能不连续,因此无法适用通用的GP近似方案。在这项工作中,我们为混合和连续输入变量生成了一个基础函数近似方案,该方案根据观测数量和基准函数的总数进行线性缩放。拟议方法自然适用于带有任意观察模型的Bayesian GP回归。我们用纵向数据模型展示了该方法,并表明它准确接近了精确的GP模型,只需要运行时间的一小部分与相应的精确模型相对应。