Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space

ACO Student Seminar
Friday, February 3, 2023 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 005
Yunbum Kook – Georgia Tech CS – yb.kook@gatech.edu
Abhishek Dhawan

We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimensions, upwards of 100,000, can be sampled efficiently in practice. Our algorithm incorporates constraints into the Riemannian version of Hamiltonian Monte Carlo and maintains sparsity. This allows us to achieve a mixing rate independent of condition numbers. On benchmark data sets from systems biology and linear programming, our algorithm outperforms existing packages by orders of magnitude. In particular, we achieve a 1,000-fold speed-up for sampling from the largest published human metabolic network (RECON3D). Our package has been incorporated into the COBRA toolbox. This is joint work with Yin Tat Lee, Ruoqi Shen, and Santosh Vempala.