In this paper, we present a thorough theoretical analysis of the default implementation of LIME in the case of tabular data. We prove that in the large sample limit, the interpretable coefficients provided by Tabular LIME can be computed in an explicit way as a function of the algorithm parameters and some expectation computations related to the black-box model. When the function to explain has some nice algebraic structure (linear, multiplicative, or sparsely depending on a subset of the coordinates), our analysis provides interesting insights into the explanations provided by LIME. These can be applied to a range of machine learning models including Gaussian kernels or CART random forests. As an example, for linear functions we show that LIME has the desirable property to provide explanations that are proportional to the coefficients of the function to explain and to ignore coordinates that are not used by the function to explain. For partition-based regressors, on the other side, we show that LIME produces undesired artifacts that may provide misleading explanations.
翻译:在本文中,我们对LIME在表格数据方面的默认实施进行了透彻的理论分析。我们证明,在大型样本限值中,Tabul LIME提供的可解释系数可以作为算法参数的函数以及与黑箱模型有关的某些预期计算,以明确的方式计算出。当解释的函数具有一些不错的代数结构(线性、倍增性或根据坐标的子集而分散)时,我们的分析为LIME提供的解释提供了有趣的洞察力。这些可以应用于一系列机器学习模型,包括高斯内核或CART随机森林。举例来说,对于线性功能,我们表明LIME具有理想的属性,可以提供与函数的系数成比例的解释,解释和忽略函数没有用来解释的坐标。对于基于分区的回归者,我们则表明,LIME产生一些不理想的工艺品,可能提供误导性的解释。