A new approach to the local and global explanation is proposed. It is based
on selecting a convex hull constructed for the finite number of points around
an explained instance. The convex hull allows us to consider a dual
representation of instances in the form of convex combinations of extreme
points of a produced polytope. Instead of perturbing new instances in the
Euclidean feature space, vectors of convex combination coefficients are
uniformly generated from the unit simplex, and they form a new dual dataset. A
dual linear surrogate model is trained on the dual dataset. The explanation
feature importance values are computed by means of simple matrix calculations.
The approach can be regarded as a modification of the well-known model LIME.
The dual representation inherently allows us to get the example-based
explanation. The neural additive model is also considered as a tool for
implementing the example-based explanation approach. Many numerical experiments
with real datasets are performed for studying the approach. The code of
proposed algorithms is available.

提出了一种基于选择围绕受解释实例的有限数据点构建的凸包的本地和全局解释新方法。该方法通过考虑由产生的多面体的极端点的凸组合形式的实例的双重表示来获得解释的特征重要性值。该方法被视为著名模型 LIME 的修改版本，具有例子为基础的解释方法实现的工具也被考虑。通过对真实数据集进行的许多数值实验来研究该方法，其中也提供了所提算法的代码。