  Interpretable explanations for recommender systems and other machine learning
models are crucial to gain user trust. Prior works that have focused on paths
connecting users and items in a heterogeneous network have several limitations,
such as discovering relationships rather than true explanations, or
disregarding other users' privacy. In this work, we take a fresh perspective,
and present PRINCE: a provider-side mechanism to produce tangible explanations
for end-users, where an explanation is defined to be a set of minimal actions
performed by the user that, if removed, changes the recommendation to a
different item. Given a recommendation, PRINCE uses a polynomial-time optimal
algorithm for finding this minimal set of a user's actions from an exponential
search space, based on random walks over dynamic graphs. Experiments on two
real-world datasets show that PRINCE provides more compact explanations than
intuitive baselines, and insights from a crowdsourced user-study demonstrate
the viability of such action-based explanations. We thus posit that PRINCE
produces scrutable, actionable, and concise explanations, owing to its use of
counterfactual evidence, a user's own actions, and minimal sets, respectively.
