  Automated decision making is used routinely throughout our everyday life.
Recommender systems decide which jobs, movies, or other user profiles might be
interesting to us. Spell checkers help us to make good use of language. Fraud
detection systems decide if a credit card transactions should be verified more
closely. Many of these decision making systems use machine learning methods
that fit complex models to massive datasets. The successful deployment of
machine learning (ML) methods to many (critical) application domains crucially
depends on its explainability. Indeed, humans have a strong desire to get
explanations that resolve the uncertainty about experienced phenomena like the
predictions and decisions obtained from ML methods. Explainable ML is
challenging since explanations must be tailored (personalized) to individual
users with varying backgrounds. Some users might have received university-level
education in ML, while other users might have no formal training in linear
algebra. Linear regression with few features might be perfectly interpretable
for the first group but might be considered a black-box by the latter. We
propose a simple probabilistic model for the predictions and user knowledge.
This model allows to study explainable ML using information theory. Explaining
is here considered as the task of reducing the "surprise" incurred by a
prediction. We quantify the effect of an explanation by the conditional mutual
information between the explanation and prediction, given the user background.
