  In this paper we focus on the estimation of mutual information from finite
samples $(\mathcal{X}\times\mathcal{Y})$. The main concern with estimations of
mutual information is their robustness under the class of transformations for
which it remains invariant: i.e. type I (coordinate transformations), III
(marginalizations) and special cases of type IV (embeddings, products).
Estimators which fail to meet these standards are not \textit{robust} in their
general applicability. Since most machine learning tasks employ transformations
which belong to the classes referenced in part I, the mutual information can
tell us which transformations are most optimal\cite{Carrara_Ernst}. There are
several classes of estimation methods in the literature, such as non-parametric
estimators like the one developed by Kraskov et. al\cite{KSG}, and its improved
versions\cite{LNC}. These estimators are extremely useful, since they rely only
on the geometry of the underlying sample, and circumvent estimating the
probability distribution itself. We explore the robustness of this family of
estimators in the context of our design criteria.
