Recent works showed how Mutual Information Neural Estimation (MINE) could be applied to side-channel analysis in order to evaluate the amount of leakage of an electronic device. One of the main advantages of MINE over classical estimation techniques is to enable the computation between high dimensional traces and a secret, which is relevant for leakage assessment. However, optimally exploiting this information in an attack context in order to retrieve a secret remains a non-trivial task especially when a profiling phase of the target is not allowed. Within this context, the purpose of this paper is to address this problem based on a simple idea: there are multiple leakage sources in side-channel traces and optimal attacks should necessarily exploit most/all of them. To this aim, a new mathematical framework, designed to bridge classical Mutual Information Analysis (MIA) and the multidimensional aspect of neural-based estimators, is proposed. One of the goals is to provide rigorous proofs consolidating the mathematical basis behind MIA, thus alleviating inconsistencies found in the state of the art. This framework allows to derive a new attack called Neural Estimated Mutual Information Analysis (NEMIA). To the best of our knowledge, it is the first unsupervised attack able to benefit from both the power of deep learning techniques and the valuable theoretical properties of MI. From simulations and experiments conducted in this paper, it seems that NEMIA performs better than classical and more recent deep learning based unsupervised side-channel attacks, especially in low-information contexts.