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.

翻译：提出了一种新的局部与全局解释方法。该方法基于为待解释实例周围有限个点构建凸包，通过凸包将实例表示为生成多面体极点的凸组合，形成对偶表示。不同于在欧氏特征空间中扰动新实例，该方法从单位单纯形中均匀生成凸组合系数向量，构建新的对偶数据集，并在该数据集上训练对偶线性代理模型。通过简单矩阵运算即可计算特征重要性值，可视为对LIME模型的改进。该对偶表示天然支持基于示例的解释，同时采用神经加性模型实现基于示例的解释方法。通过大量真实数据集数值实验验证方法有效性，并公开了所提算法代码。