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The success of machine learning methods for computer vision tasks has driven a surge in computer assisted prediction for medicine and biology. Based on a data-driven relationship between input image and pathological classification, these predictors deliver unprecedented accuracy. Yet, the numerous approaches trying to explain the causality of this learned relationship have fallen short: time constraints, coarse, diffuse and at times misleading results, caused by the employment of heuristic techniques like Gaussian noise and blurring, have hindered their clinical adoption. In this work, we discuss and overcome these obstacles by introducing a neural-network based attribution method, applicable to any trained predictor. Our solution identifies salient regions of an input image in a single forward-pass by measuring the effect of local image-perturbations on a predictor's score. We replace heuristic techniques with a strong neighborhood conditioned inpainting approach, avoiding anatomically implausible, hence adversarial artifacts. We evaluate on public mammography data and compare against existing state-of-the-art methods. Furthermore, we exemplify the approach's generalizability by demonstrating results on chest X-rays. Our solution shows, both quantitatively and qualitatively, a significant reduction of localization ambiguity and clearer conveying results, without sacrificing time efficiency.