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This paper addresses the task of explaining anomalous predictions of a black-box regression model. When using a black-box model, such as one to predict building energy consumption from many sensor measurements, we often have a situation where some observed samples may significantly deviate from their prediction. It may be due to a sub-optimal black-box model, or simply because those samples are outliers. In either case, one would ideally want to compute a responsibility score indicative of the extent to which an input variable is responsible for the anomalous output. In this work, we formalize this task as a statistical inverse problem: Given model deviation from the expected value, infer the responsibility score of each of the input variables. We propose a new method called likelihood compensation (LC), which is founded on the likelihood principle and computes a correction to each input variable. To the best of our knowledge, this is the first principled framework that computes a responsibility score for real valued anomalous model deviations. We apply our approach to a real-world building energy prediction task and confirm its utility based on expert feedback.