Partial dependence plots. Visualization is one ofthe most powerful interpretational tools. Graphical renderings ofthe value of F(x) as a function of its arguments provides a comprehensive summary ofits dependence on the joint values ofthe input variables. Unfortunately, such visualization is limited to low-dimensional arguments. Functions ofa single real-valued variable x, F(x) can be plotted as a graph ofthe values of F(x) against each corresponding value of x. Functions ofa single categorical variable can be represented by a bar plot, each bar representing one ofits values, and the bar height the value ofthe function. Functions oftwo real-valued variables can be pictured using contour or perspective mesh plots. Functions ofa categorical variable and another variable (real or categorical) are best summarized by a sequence of(“trellis”) plots, each one showing the dependence of F(x) on the second variable, conditioned on the respective values ofthe first variable [Becker and Cleveland (1996)]. Viewing functions of higher-dimensional arguments is more difficult. It is therefore useful to be able to view the partial dependence of the approximation F(x) on selected small subsets ofthe input variables. Although a collection of such plots can seldom provide a comprehensive depiction ofthe approximation, it can often produce helpful clues, especially when F(x) is dominated by loworder interactions (Section 7). | 局部依赖图。可视化是最强大的解释工具之一。 F(x) 的值作为其参数的函数的图形渲染提供了它对输入变量联合值的依赖性的综合总结。不幸的是,这种可视化仅限于低维参数。单个实值变量 x,F(x) 的函数可以绘制为 F(x) 的值与 x 的每个对应值的关系图。单个分类变量的函数可以用条形图表示,每个条形代表它的一个值,条形高度代表函数的值。可以使用等高线或透视网格图来描绘两个实值变量的函数。一个分类变量和另一个变量(实数或分类)的函数最好用一系列(“格子”)图来概括,每个图都显示了 F(x) 对第二个变量的依赖性,条件是第一个变量的各自值 [Becker and Cleveland(1996)]。 观察高维参数的函数比较困难。因此,能够查看近似 F(x) 对输入变量的选定小子集的局部依赖性是很有用的。尽管此类图的集合很少能提供对近似值的全面描述,但它通常可以产生有用的线索,尤其是当 F(x) 由低阶交互作用支配时(第 7 节)。 |