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info.json
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{
"abstract": "For sampling from a log-concave density, we study implicit integrators resulting from $\\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for $ \\theta \\in [0,1] $ and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for $\\theta\\ge 1/2$, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We show that obtaining subsequent samples amounts to solving a strongly-convex optimization problem, which is readily achievable using one of numerous existing methods. Numerical examples supporting our theoretical analysis are also presented.",
"authors": [
"Liam Hodgkinson",
"Robert Salomone",
"Fred Roosta"
],
"emails": [
"liam.hodgkinson@berkeley.edu",
"robert.salomone@qut.edu.au",
"fred.roosta@uq.edu.au"
],
"id": "19-292",
"issue": 136,
"pages": [
1,
30
],
"title": "Implicit Langevin Algorithms for Sampling From Log-concave Densities",
"volume": 22,
"year": 2021
}