  As machine learning becomes an important part of many real world applications
affecting human lives, new requirements, besides high predictive accuracy,
become important. One important requirement is transparency, which has been
associated with model interpretability. Many machine learning algorithms induce
models difficult to interpret, named black box. Moreover, people have
difficulty to trust models that cannot be explained. In particular for machine
learning, many groups are investigating new methods able to explain black box
models. These methods usually look inside the black models to explain their
inner work. By doing so, they allow the interpretation of the decision making
process used by black box models. Among the recently proposed model
interpretation methods, there is a group, named local estimators, which are
designed to explain how the label of particular instance is predicted. For
such, they induce interpretable models on the neighborhood of the instance to
be explained. Local estimators have been successfully used to explain specific
predictions. Although they provide some degree of model interpretability, it is
still not clear what is the best way to implement and apply them. Open
questions include: how to best define the neighborhood of an instance? How to
control the trade-off between the accuracy of the interpretation method and its
interpretability? How to make the obtained solution robust to small variations
on the instance to be explained? To answer to these questions, we propose and
investigate two strategies: (i) using data instance properties to provide
improved explanations, and (ii) making sure that the neighborhood of an
instance is properly defined by taking the geometry of the domain of the
feature space into account. We evaluate these strategies in a regression task
and present experimental results that show that they can improve local
explanations.
