On the Utility of Graphics Cards to Perform Massively Parallel Simulation of Advanced Monte Carlo Methods

Lee, Anthony; Yau, Christopher; Giles, Michael B.; Doucet, Arnaud; Holmes, Connor

doi:10.1198/jcgs.2010.10039

Cited by 257 publications

(239 citation statements)

References 27 publications

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“…More recent work combines the use of multiple chains with adaptive MCMC in an attempt to use these multiple sources of information to learn an appropriate proposal distribution (12,13). Sometimes, specific MCMC algorithms are directly amenable to parallelization, such as independent Metropolis−Hastings (14) or slice sampling (15), as indeed are some statistical models via careful reparameterization (16) or implementation on specialist hardware, such as graphics processing units (GPUs) (17,18); however, these approaches are often problem specific and not generally applicable. For problems involving large amounts of data, parallelization may in some cases also be possible by partitioning the data and analyzing each subset using standard MCMC methods simultaneously on multiple machines (19).…”

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confidence: 99%

A general construction for parallelizing Metropolis−Hastings algorithms

Calderhead

2014

Proc. Natl. Acad. Sci. U.S.A.

119

130

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Markov chain Monte Carlo methods (MCMC) are essential tools for solving many modern-day statistical and computational problems; however, a major limitation is the inherently sequential nature of these algorithms. In this paper, we propose a natural generalization of the Metropolis−Hastings algorithm that allows for parallelizing a single chain using existing MCMC methods. We do so by proposing multiple points in parallel, then constructing and sampling from a finite-state Markov chain on the proposed points such that the overall procedure has the correct target density as its stationary distribution. Our approach is generally applicable and straightforward to implement. We demonstrate how this construction may be used to greatly increase the computational speed and statistical efficiency of a variety of existing MCMC methods, including Metropolis-Adjusted Langevin Algorithms and Adaptive MCMC. Furthermore, we show how it allows for a principled way of using every integration step within Hamiltonian Monte Carlo methods; our approach increases robustness to the choice of algorithmic parameters and results in increased accuracy of Monte Carlo estimates with little extra computational cost. S ince its introduction in the 1970s, the Metropolis−Hastings algorithm has revolutionized computational statistics (1). The ability to draw samples from an arbitrary probability distribution, πðXÞ, known only up to a constant, by constructing a Markov chain that converges to the correct stationary distribution has enabled the practical application of Bayesian inference for modeling a huge variety of scientific phenomena, and has resulted in Metropolis−Hastings being noted as one of the top 10 most important algorithms from the 20th century (2). Despite regular increases in available computing power, Markov chain Monte Carlo (MCMC) algorithms can still be computationally very expensive; many thousands of iterations may be necessary to obtain low-variance estimates of the required quantities with an oftentimes complex statistical model being evaluated for each set of proposed parameters. Furthermore, many Metropolis−Hastings algorithms are severely limited by their inherently sequential nature.Many approaches have been proposed for improving the statistical efficiency of MCMC, and although such algorithms are guaranteed to converge asymptotically to the stationary distribution, their performance over a finite number of iterations can vary hugely. Much research effort has therefore focused on developing transition kernels that enable moves to be proposed far from the current point and subsequently accepted with high probability, taking into account, for example, the correlation structure of the parameter space (3, 4), or by using Hamiltonian dynamics (5) or diffusion processes (6). A recent investigation into proposal kernels suggests that more exotic distributions, such as the Bactrian kernel, might also be used to increase the statistical efficiency of MCMC algorithms (7). The efficient exploration of high-dimensional and multimo...

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mentioning

confidence: 99%

A general construction for parallelizing Metropolis−Hastings algorithms

Calderhead

2014

Proc. Natl. Acad. Sci. U.S.A.

119

130

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“…Some studies such as Lee et al (2010) and Aldrich et al (2011) document massive speed gains, from 35 up to 500, of the GPU code with respect to single-threaded CPU code. Considering these results, it can be concluded that our GPU speed performance could be increased substantially, this observation is right and wrong at the same time.…”

Section: Resultsmentioning

confidence: 99%

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

et al. 2016

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. (2012), provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one. Terms of use: Documents in

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“…The traditionally used MCMC algorithms are sequential and therefore not amendable to simple parallelization, except in a few special cases. In fMRI, this can be circumvented by running many serial MCMC algorithms in parallel (Lee, Yau, Giles, Doucet, & Holmes, 2010), e.g. one for each voxel time series.…”

Section: Bayesian Statisticsmentioning

confidence: 99%

Harnessing graphics processing units for improved neuroimaging statistics

Eklund

Villani

LaConte

2013

Cogn Affect Behav Neurosci

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Harnessing GPUs for improved neuroimaging statistics 2 Abstract Simple models and algorithms based on restrictive assumptions are often used in the field of neuroimaging for studies involving functional magnetic resonance imaging (fMRI), voxel based morphometry (VBM), and diffusion tensor imaging (DTI). Non-parametric statistical methods or flexible Bayesian models can be applied rather easily to yield more trustworthy results. The spatial normalization step required for multi-subject studies can also be improved by taking advantage of more robust algorithms for image registration. A common drawback of algorithms based on weaker assumptions, however, is the increase in computational complexity. In this short overview we will therefore present some examples of how inexpensive PC graphics hardware, normally used for demanding computer games, can be used to enable practical use of more realistic models and accurate algorithms, such that the outcome of neuroimaging studies really can be trusted.

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On the Utility of Graphics Cards to Perform Massively Parallel Simulation of Advanced Monte Carlo Methods

Cited by 257 publications

References 27 publications

A general construction for parallelizing Metropolis−Hastings algorithms

A general construction for parallelizing Metropolis−Hastings algorithms

Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

Harnessing graphics processing units for improved neuroimaging statistics

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