Sampling with Riemannian Hamiltonian Monte Carlo in a constrained space

Y Kook, YT Lee, R Shen… - Advances in Neural …, 2022 - proceedings.neurips.cc
We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in
very high dimension, upwards of 100,000, can be sampled efficiently\emph {in practice}. Our …

Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithm

V Srinivasan, A Wibisono… - The Thirty Seventh …, 2024 - proceedings.mlr.press
We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for
approximate sampling from distributions whose support is a compact and convex set. This …

Sampling polytopes with Riemannian HMC: Faster mixing via the Lewis weights barrier

K Gatmiry, J Kelner… - The Thirty Seventh Annual …, 2024 - proceedings.mlr.press
Abstract We analyze Riemannian Hamiltonian Monte Carlo (RHMC) on a manifold endowed
with the metric defined by the Hessian of a convex barrier function and apply it to sample a …

Algorithmic aspects of the log-Laplace transform and a non-Euclidean proximal sampler

S Gopi, YT Lee, D Liu, R Shen… - The Thirty Sixth Annual …, 2023 - proceedings.mlr.press
The development of efficient sampling algorithms catering to non-Euclidean geometries has
been a challenging endeavor, as discretization techniques which succeed in the Euclidean …

Unbiased constrained sampling with self-concordant barrier Hamiltonian Monte Carlo

M Noble, V De Bortoli… - Advances in Neural …, 2023 - proceedings.neurips.cc
In this paper, we propose Barrier Hamiltonian Monte Carlo (BHMC), a version of the HMC
algorithm which aims at sampling from a Gibbs distribution $\pi $ on a manifold $\mathsf {M} …

Sampling with Barriers: Faster Mixing via Lewis Weights

K Gatmiry, J Kelner, SS Vempala - arXiv preprint arXiv:2303.00480, 2023 - arxiv.org
We analyze Riemannian Hamiltonian Monte Carlo (RHMC) for sampling a polytope defined
by $ m $ inequalities in $\R^ n $ endowed with the metric defined by the Hessian of a …

Unbiasing Hamiltonian Monte Carlo algorithms for a general hamiltonian function

T Lelièvre, R Santet, G Stoltz - Foundations of Computational Mathematics, 2024 - Springer
Abstract Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method that allows
to sample high dimensional probability measures. It relies on the integration of the …

Space-time divergence lemmas and optimal non-reversible lifts of diffusions on Riemannian manifolds with boundary

A Eberle, F Lörler - arXiv preprint arXiv:2412.16710, 2024 - arxiv.org
Non-reversible lifts reduce the relaxation time of reversible diffusions at most by a square
root. For reversible diffusions on domains in Euclidean space, or, more generally, on a …

In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies

Y Kook, SS Vempala, MS Zhang - arXiv preprint arXiv:2405.01425, 2024 - arxiv.org
We present a new random walk for uniformly sampling high-dimensional convex bodies. It
achieves state-of-the-art runtime complexity with stronger guarantees on the output than …

Randomized Control in Performance Analysis and Empirical Asset Pricing

C Bachelard, A Chalkis, V Fisikopoulos… - arXiv preprint arXiv …, 2024 - arxiv.org
The present article explores the application of randomized control techniques in empirical
asset pricing and performance evaluation. It introduces geometric random walks, a class of …