Langevin Diffusions and Metropolis-Hastings Algorithms

By Gareth O. Roberts, Osnat Stramer. 2002

377 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

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Citations in the corpus

Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, background): “The idea has been explored in Stramer and Tweedie (1999a, 1999b), Roberts and Stramer (2002) and more recently Girolami and Calderhead (2011) introduced a mathematically-coherent approach of relating σ to a metric tensor on a Riemannian manifold of probability distributions.”
SUBGEOMETRIC ERGODICITY OF STRONG MARKOV PROCESSES (2005, methodology): “In practice, discretizations of the continuous-time process are used to solve the MCMC simulation problem and recent works proved that it is possible to find methods of discretizing which inherit the convergence rates of the continuous-time diffusion (see [ 27 , 28, 30, 32, 33] for methods of discre”
A survey of uncertainty in deep neural networks (2021, methodology): “context, for the first time, Welling and Teh [81] proposed to combine Stochastic Gradient Descent (SGD) with Langevin dynamics (a form of MCMC [162], [163], [159]) in order to obtain a scalable approximation to MCMC algorithm based on mini-batch SGD [164], [165].”
Proximal Markov chain Monte Carlo algorithms (2013, positive): “Alternatively, one could also consider extending our methods to other diffusions that are more robust to anisotropic target densities (Roberts and Stramer 2002; Stramer and Tweedie 1999a,b).”
Riemannian Manifold Hamiltonian Monte Carlo (2009, methodology): “The standard implementation (Roberts and Rosenthal, 1998; Roberts and Stramer, 2003) employs a symmetric proposal distribution, hus when the algorithm adapts its stepsize (according to the acceptance rate) it is limited bythe dimension with the smallest marginal variance.”
Bayesian Learning via Stochastic Gradient Langevin Dynamics (2011, methodology): “We first generalize our method to allow for preconditioning , which can lead to significant speed ups by better adapting the step sizes to the local structure of the posterior (Roberts & Stramer, 2002; Girolami & Calderhead, 2011).”
Measuring Sample Quality with Diffusions (2016, methodology): “We generalize this approach to cover any target with a fast-coupling Itô diffusion by bounding the derivatives of Stein equation solutions in terms of Markov process coupling rates.”
Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms (2014, methodology): “A further simplification would be to select a constant metric tensor G(θ) = M , in which case MMALA coincides with the Metropolis adjusted Langevin algorithm (MALA) with preconditioning matrix M (see Roberts and Stramer (2002), for details).”
Asynchronous Stochastic Quasi-Newton MCMC for Non-Convex Optimization (2018, background): “Under mild regularity conditions on U , the solution process ( θ t ) t ≥ 0 attains a unique stationary distribution with a density that is proportional to exp( − βU ( θ )) (Roberts & Stramer, 2002).”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “The idea has been explored in Stramer and Tweedie (1999a,b); Roberts and Stramer (2002) and more recently Girolami and Calderhead (2010) introduced a mathematically-coherent approach of relating σ to a metric tensor on a Riemannian manifold of probability distributions.”
Dynamical Sampling with Langevin Normalization Flows (2019, methodology): “The main idea of MALA is to give the proposed state through Langevin diffusions, whose equation is given in Equation (8).”
Langevin diffusions and the Metropolis-adjusted Langevin algorithm (2013, methodology): “First, we point out an unfortunate transcription error which has propagated through the literature, whereby a factor of a 1/2 has been missed from one of the terms Roberts and Stramer (2002); Girolami and Calderhead (2011).”