Reviews: Gradient-based Adaptive Markov Chain Monte Carlo

Originality: First-order Gradient-based MCMC methods have to deal with determining an appropriate length scale for each variable. NUTS is one approach and this paper gives another approach whereby a parameter theta of a proposal distribution is adaptively improved to account for the covariance structure. At the same time theta is adapted to consider the entropy of the proposal distribution. This trade off for theta is rolled into a new speed measure which is the central point of this paper. The paper includes a lower bound of the speed measure that can be directly differentiated resulting in a practical algorithm. The paper also includes a heuristic that makes this adaptive MCMC algorithm applicable to MALA as well.