One of the unsolved challenges in the field of Explainable AI (XAI) is determining how to most reliably estimate the quality of an explanation method in the absence of ground truth explanation labels. Resolving this issue is of utmost importance as the evaluation outcomes generated by competing evaluation methods (or ''quality estimators''), which aim at measuring the same property of an explanation method, frequently present conflicting rankings. Such disagreements can be challenging for practitioners to interpret, thereby complicating their ability to select the best-performing explanation method. We address this problem through a meta-evaluation of different quality estimators in XAI, which we define as ''the process of evaluating the evaluation method''. Our novel framework, MetaQuantus, analyses two complementary performance characteristics of a quality estimator: its resilience to noise and reactivity to randomness, thus circumventing the need for ground truth labels. We demonstrate the effectiveness of our framework through a series of experiments, targeting various open questions in XAI such as the selection and hyperparameter optimisation of quality estimators. Our work is released under an open-source license (https://github.com/annahedstroem/MetaQuantus) to serve as a development tool for XAI- and Machine Learning (ML) practitioners to verify and benchmark newly constructed quality estimators in a given explainability context. With this work, we provide the community with clear and theoretically-grounded guidance for identifying reliable evaluation methods, thus facilitating reproducibility in the field.

Explainable artificial intelligence (XAI) methods shed light on the predictions of deep neural networks (DNNs). Several different approaches exist and have partly already been successfully applied in climate science. However, the often missing ground truth explanations complicate their evaluation and validation, subsequently compounding the choice of the XAI method. Therefore, in this work, we introduce XAI evaluation in the context of climate research and assess different desired explanation properties, namely, robustness, faithfulness, randomization, complexity, and localization. To this end we build upon previous work and train a multi-layer perceptron (MLP) and a convolutional neural network (CNN) to predict the decade based on annual-mean temperature maps. Next, multiple local XAI methods are applied and their performance is quantified for each evaluation property and compared against a baseline test. Independent of the network type, we find that the XAI methods Integrated Gradients, Layer-wise relevance propagation, and InputGradients exhibit considerable robustness, faithfulness, and complexity while sacrificing randomization. The opposite is true for Gradient, SmoothGrad, NoiseGrad, and FusionGrad. Notably, explanations using input perturbations, such as SmoothGrad and Integrated Gradients, do not improve robustness and faithfulness, contrary to previous claims. Overall, our experiments offer a comprehensive overview of different properties of explanation methods in the climate science context and supports users in the selection of a suitable XAI method.