On $L^q$ Convergence of the Hamiltonian Monte Carlo
arXiv:2101.08688v22 citations
AI Analysis
This provides theoretical guarantees for a widely used sampling method in statistics and machine learning, though it appears incremental as it extends existing convergence results.
The paper tackles the problem of proving convergence for Hamiltonian Monte Carlo algorithms, establishing strong and weak $L^q$ convergence to the target distribution under mild conditions on the Hamiltonian motion.
We establish $L_q$ convergence for Hamiltonian Monte Carlo algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for $2\le q<\infty$ and weakly for $1<q<2$) to the desired target distribution.