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Machine learning is used more and more often for sensitive applications,sometimes replacing humans in critical decision-making processes. As such,interpretability of these algorithms is a pressing need. One popular algorithmto provide interpretability is LIME (Local Interpretable Model-AgnosticExplanation). In this paper, we provide the first theoretical analysis of LIME.We derive closed-form expressions for the coefficients of the interpretablemodel when the function to explain is linear. The good news is that thesecoefficients are proportional to the gradient of the function to explain: LIMEindeed discovers meaningful features. However, our analysis also reveals thatpoor choices of parameters can lead LIME to miss important features.

Explaining the Explainer: A First Theoretical Analysis of LIME