Discussion lead: Bob Carpenter (CCM)
Title: Bob Carpenter, Adrian Seyboldt, Eliot Carlsen. To appear. Warming up Hamiltonian Monte Carlo with smooth Nutpie
Abstract: This week I’ll introduce Nutpie and the blockless variant I have been using to warm up WALNUTS. I should have the technical report written by Friday. Here’s the abstract:
This note introduces a smooth (i.e., blockless) scheme for adapting the step size and mass matrix for Hamiltonian Monte Carlo. Following the no-U-turn sampler (NUTS), the step size is adapted with dual averaging to achieve a user-specified acceptance probability. Following Nutpie, the mass matrix is set to approximately minimize Fisher divergence. It is estimated as the geometric average in the manifold of symmetric, positive-definite matrices of the inverse covariance of the draws and the covariance of the scores. Rather than taking estimates over blocks, as in Stan's implementation of NUTS and Nutpie, this note introduces a smooth variant that exponentially discounts past draws with a rolling schedule motivated by the block sizes of NUTS.
Links: Here’s the original Nutpie: https://pymc-devs.github.io/nutpie/
Smooth version: https://github.com/flatironinstitute/walnuts