Focusing on Difficult Directions for Learning HMC Trajectory Lengths

Understand

Hamiltonian Monte Carlo (HMC) is a premier Markov Chain Monte Carlo (MCMC) algorithm for continuous target distributions.

• Its full potential can only be unleashed when its problem-dependent hyperparameters are tuned well.
• The adaptation of one such hyperparameter, trajectory length ($\tau$), has been closely examined by many research programs with the No-U-Turn Sampler (NUTS) coming out as the preferred method in 2011.
• A decade later, the evolving hardware profile has lead to the proliferation of personal and cloud based SIMD hardware in the form of Graphics and Tensor Processing Units (GPUs, TPUs) which are hostile to certain algorithmic details of NUTS.