  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.
