Abstract
Classical statistics tells us that Maximum Likelihood Estimation is the asymptotically optimal way to fit a parametric statistical model. However, finding the MLE generally requires the ability to sample or compute normalizing constants, which can be difficult computationally. Hyvarinen proposed a popular alternative method, score matching, which avoids needing to calculate the normalizing constant. We show that the relative statistical efficiency of this estimator is tightly connected to geometric properties of the distribution (e.g. Poincare constant) which have been long studied in probability and geometric and functional analysis.