A coincidence detection perspective for the maximum mean discrepancy

An alternative perspective is proposed for the Maximum Mean Discrepancy (MMD), in which coincidence detectors replace Gaussian kernels. It is conjectured that coincidence-based statistics may be a relevant factor behind MMD, for it may explain why MMD works even for small high-dimensional sets of observations. It is further shown how this proposed perspective can be used to simplify interpretations in MMD-based tests, including a straightforward computation of thresholds for hypothesis tests, which is done through the Grassberger–Procaccia method, originally proposed for intrinsic dimensionality estimation. Experimental results corroborate the conjecture that an MMD based on coincidence detection would perform almost equivalently to the MMD based on (frequently used) Gaussian kernels, with advantages in terms of interpretability and computational load.