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Explainable artificial intelligence is proposed to provide explanations forreasoning performed by an Artificial Intelligence. There is no consensus on howto evaluate the quality of these explanations, since even the definition ofexplanation itself is not clear in the literature. In particular, for thewidely known Local Linear Explanations, there are qualitative proposals for theevaluation of explanations, although they suffer from theoreticalinconsistencies. The case of image is even more problematic, where a visualexplanation seems to explain a decision while detecting edges is what it reallydoes. There are a large number of metrics in the literature specialized inquantitatively measuring different qualitative aspects so we should be able todevelop metrics capable of measuring in a robust and correct way the desirableaspects of the explanations. In this paper, we propose a procedure called REVELto evaluate different aspects concerning the quality of explanations with atheoretically coherent development. This procedure has several advances in thestate of the art: it standardizes the concepts of explanation and develops aseries of metrics not only to be able to compare between them but also toobtain absolute information regarding the explanation itself. The experimentshave been carried out on image four datasets as benchmark where we show REVEL'sdescriptive and analytical power.

REVEL Framework to measure Local Linear Explanations for black-box models: Deep Learning Image Classification case of study