Title: Marginal Probability Explanation: A Saliency Map with Closed-loop Validation. Abstract: In this work, we propose a saliency map with pixel-level resolution, called Marginal Probability Explanation (MPE), for a black-box classifier. MPE visualizes the contribution of each input dimension to the classifier by calculating marginal probabilities when only one dimension is considered. Marginal probabilities are estimated using Monte Carlo by sampling from the training dataset. Based on MPE, we propose typical samples, i.e. samples that maximize their marginal probability in every input dimension. We verify that our proposed MPE is meaningful through closed-loop validation experiments, where replacing a few pixels with the lowest marginal probability with pixels in the typical sample ``corrects" the classification. Based on experiments, we found deep neural networks are probably still using pixel-level logics for image classification. Moreover, the critical pixels are not necessary related to the subject. 