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The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm which makes local moves by incorporating information about the gradient of the logarithm of the target density. In this paper we study the efficiency of MALA on a…

Probability · Mathematics 2012-11-29 Natesh S. Pillai , Andrew M. Stuart , Alexandre H. Thiéry

In this paper, we examine the computational complexity of sampling from a Bayesian posterior (or pseudo-posterior) using the Metropolis-adjusted Langevin algorithm (MALA). MALA first employs a discrete-time Langevin SDE to propose a new…

Statistics Theory · Mathematics 2024-05-10 Rong Tang , Yun Yang

A classical approach for approximating expectations of functions w.r.t. partially known distributions is to compute the average of function values along a trajectory of a Metropolis-Hastings (MH) Markov chain. A key part in the MH algorithm…

Computation · Statistics 2020-02-20 Daniel Rudolf , Björn Sprungk

A framework for online robust adaptive radiation therapy (ART) is presented. This framework is designed to (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii)…

Medical Physics · Physics 2020-09-09 Michelle Böck

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

Systems and Control · Computer Science 2015-07-22 Reza Abdolee , Benoit Champagne , Ali H. Sayed

Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of…

Machine Learning · Computer Science 2022-09-29 Ali Mousavi , Reza Monsefi , Víctor Elvira

Our article is concerned with adaptive sampling schemes for Bayesian inference that update the proposal densities using previous iterates. We introduce a copula based proposal density which is made more efficient by combining it with…

Methodology · Statistics 2010-02-26 Ralph Silva , Robert Kohn , Paolo Giordani , Xiuyan Mun

A significant part of MCMC methods can be considered as the Metropolis-Hastings (MH) algorithm with different proposal distributions. From this point of view, the problem of constructing a sampler can be reduced to the question - how to…

Machine Learning · Statistics 2019-06-11 Kirill Neklyudov , Evgenii Egorov , Pavel Shvechikov , Dmitry Vetrov

We analyse computational efficiency of Metropolis-Hastings algorithms with AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HMC). By…

Probability · Mathematics 2015-01-15 Richard A. Norton , Colin Fox

The complexity of the Metropolis-Hastings (MH) algorithm arises from the requirement of a likelihood evaluation for the full data set in each iteration. Payne and Mallick (2015) propose to speed up the algorithm by a delayed acceptance…

Computation · Statistics 2017-03-23 Matias Quiroz , Minh-Ngoc Tran , Mattias Villani , Robert Kohn

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter…

Machine Learning · Computer Science 2018-04-13 Noam Shazeer , Mitchell Stern

This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…

Computation · Statistics 2019-09-30 Rui Zhou , Junyan Liu , Sandeep Kumar , Daniel P. Palomar

Pseudo-marginal Metropolis-Hastings (pmMH) is a versatile algorithm for sampling from target distributions which are not easy to evaluate point-wise. However, pmMH requires good proposal distributions to sample efficiently from the target,…

Computation · Statistics 2018-07-30 Johan Dahlin , Adrian Wills , Brett Ninness

This paper presents new dynamic topology adaptation strategies for distributed estimation in smart grids systems. We propose a dynamic exhaustive search--based topology adaptation algorithm and a dynamic sparsity--inspired topology…

Information Theory · Computer Science 2014-01-16 S. Xu , R. C. de Lamare , H. V. Poor

Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is an efficient method for sampling from continuous distributions. It is a faster alternative to HMC: instead of using the whole dataset at each iteration, SGHMC uses only a subsample.…

Machine Learning · Computer Science 2022-02-18 Ruqi Zhang , A. Feder Cooper , Christopher De Sa

We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension $d$. The improved…

Numerical Analysis · Mathematics 2016-11-28 Alain Durmus , Gareth O. Roberts , Gilles Vilmart , Konstantinos C. Zygalakis

Distributed Opportunistic Scheduling (DOS) techniques have been recently proposed to improve the throughput performance of wireless networks. With DOS, each station contends for the channel with a certain access probability. If a contention…

Networking and Internet Architecture · Computer Science 2014-12-16 Andres Garcia-Saavedra , Albert Banchs , Pablo Serrano , Joerg Widmer

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type…

Numerical Analysis · Mathematics 2010-06-21 Evangelia Kalligiannaki , Markos A. Katsoulakis , Petr Plechac

This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online…

Neural and Evolutionary Computing · Computer Science 2012-04-12 Ilya Loshchilov , Marc Schoenauer , Michèle Sebag

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

Data Analysis, Statistics and Probability · Physics 2013-05-29 Fergal P. Casey , Joshua J. Waterfall , Ryan N. Gutenkunst , Christopher R. Myers , James P. Sethna