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Stochastic Gradient Richardson-Romberg Markov Chain Monte Carlo

Alain Durmus, Umut Simsekli, Eric Moulines, Roland Badeau, Gaël Richard
2016 Neural Information Processing Systems  
Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) algorithms have become increasingly popular for Bayesian inference in large-scale applications.  ...  We illustrate our framework on the popular Stochastic Gradient Langevin Dynamics (SGLD) algorithm and propose a novel SG-MCMC algorithm referred to as Stochastic Gradient Richardson-Romberg Langevin Dynamics  ...  We apply the proposed extrapolation scheme described in Section 3 to SGHMC and call the resulting algorithm Stochastic Gradient Richardson-Romberg Hamiltonian Monte Carlo (SGRRHMC).  ... 
dblp:conf/nips/DurmusSMBR16 fatcat:6g7vi7bvzffu3np2tdfznj3s54

Parallelized Stochastic Gradient Markov Chain Monte Carlo algorithms for non-negative matrix factorization

Umut Simsekli, Alain Durmus, Roland Badeau, Gael Richard, Eric Moulines, A. Taylan Cemgil
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have become popular in modern data analysis problems due to their computational efficiency.  ...  Markov Chain Monte Carlo (MCMC) algorithms, which aim to generate samples from the posterior distribution of interest, are one of the most popular approaches for estimating these quantities.  ...  Stochastic Gradient Richardson-Romberg Langevin Dynamics Even though SGLD has proved useful in several applications, its performance is often limited by its bias.  ... 
doi:10.1109/icassp.2017.7952555 dblp:conf/icassp/SimsekliDBRMC17 fatcat:362nxrdr7fghfl572uuej4pkji

SpHMC: Spectral Hamiltonian Monte Carlo

Haoyi Xiong, Kafeng Wang, Jiang Bian, Zhanxing Zhu, Cheng-Zhong Xu, Zhishan Guo, Jun Huan
Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) methods have been widely used to sample from certain probability distributions, incorporating (kernel) density derivatives and/or given datasets.  ...  Instead of exploring new samples from kernel spaces, this piece of work proposed a novel SGHMC sampler, namely Spectral Hamiltonian Monte Carlo (SpHMC), that produces the high dimensional sparse representations  ...  To construct the Markov chain from a distribution, the stochastic gradient Hamiltonian Monte Carlo (SGHMC) (Ma, Chen, and Fox 2015; Chen, Fox, and Guestrin 2014) has been proposed to use the discrete-time  ... 
doi:10.1609/aaai.v33i01.33015516 fatcat:ztmooaau6rbyjjmdaamjypzbxy

The True Cost of Stochastic Gradient Langevin Dynamics [article]

Tigran Nagapetyan, Andrew B. Duncan, Leonard Hasenclever, Sebastian J. Vollmer, Lukasz Szpruch, Konstantinos Zygalakis
2017 arXiv   pre-print
Stochastic Gradient Langevin Dynamics (SGLD) and related stochastic gradient Markov Chain Monte Carlo methods offer scalability by using stochastic gradients in each step of the simulated dynamics.  ...  The problem of posterior inference is central to Bayesian statistics and a wealth of Markov Chain Monte Carlo (MCMC) methods have been proposed to obtain asymptotically correct samples from the posterior  ...  One popular approach is Markov Chain Monte Carlo (MCMC). In recent years there has been growing interest in MCMC methods based on continuous dynamics using stochastic gradients.  ... 
arXiv:1706.02692v1 fatcat:p5uar7tafzh5rc5eiziublwjw4

A higher-order numerical framework for stochastic simulation of chemical reaction systems

Tamás Székely, Kevin Burrage, Radek Erban, Konstantinos C Zygalakis
2012 BMC Systems Biology  
In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics.  ...  Stochastic systems can be modelled using discrete Markov processes.  ...  Monte Carlo error is an unavoidable problem when using stochastic simulations.  ... 
doi:10.1186/1752-0509-6-85 pmid:23256696 pmcid:PMC3529698 fatcat:inatdze5fjheblrmquawiclfcy

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Tamás Székely, Kevin Burrage, Konstantinos C Zygalakis, Manuel Barrio
2014 BMC Systems Biology  
A common stochastic modelling approach is to consider the system as a continuous-time Markov jump process [9] .  ...  The stochastic simulation algorithm (SSA) of Gillespie [10] is a simple and exact method for generating Markov paths.  ...  The SSA is a statistically exact method for generating Monte Carlo paths.  ... 
doi:10.1186/1752-0509-8-71 pmid:24939084 pmcid:PMC4085235 fatcat:jpp7spfciradnkmenx2fbtvj2m

Optimal Delaunay and Voronoi Quantization Schemes for Pricing American Style Options [chapter]

Gilles Pagès, Benedikt Wilbertz
2012 Springer Proceedings in Mathematics  
Quantized Backward Dynamic Programming Principle Let (X k ) 0≤k≤n be an R d -valued homogeneous Feller Markov chain defined on a probability space (Ω , A , P) with transition P(x, dy).  ...  These quantization methods have the common advantage, that they allow a straightforward implementation of the Backward Dynamic Programming Principle for optimal stopping and stochastic control problems  ...  Such a Markov chain is usually not simulatable.  ... 
doi:10.1007/978-3-642-25746-9_6 fatcat:3bfg5ndl4vcj3eeuifcjze27r4

On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo [article]

Niladri S. Chatterji, Nicolas Flammarion, Yi-An Ma, Peter L. Bartlett, Michael I. Jordan
2018 arXiv   pre-print
Stochastic gradient Richardson- Romberg Markov chain Monte Carlo. In Advances in Neural Information Processing Systems 29, pages 2047-2055, 2016. A. Gelman, J. B. Carhn, H. S. Stern, and D. B.  ...  In particular, stochastic-gradient Markov chain Monte Carlo (SG-MCMC) algorithms have been proposed in which approximations to Langevin diffusions make use of stochastic gradients instead of full gradients  ... 
arXiv:1802.05431v1 fatcat:zcikjmzjhrhnfmcmhazey4cb3i

Optimal Quantization for Finance: From Random Vectors to Stochastic Processes [chapter]

Gilles Pagès, Jacques Printems
2009 Handbook of Numerical Analysis  
We make a review of cubature formulas to approximate expectation, an conditional expectation, including the introduction of a quantization-based Richardson-Romberg extrapolation method.  ...  Quantization is a way to approximate a random vector or a stochastic process, viewed as a Hilbert-valued random variable, using a nearest neighbor projection on a finite codebook.  ...  It can be seen as a guided Monte Carlo method or a hybrid quantization/Monte Carlo method.  ... 
doi:10.1016/s1570-8659(08)00015-x fatcat:dgtn7yqrabejzlmebjxuu4nbru

Introduction to vector quantization and its applications for numerics

Gilles Pagès, Nicolas Champagnat, Tony Lelièvre, Anthony Nouy
2015 ESAIM Proceedings and Surveys  
A brief comparison with Quasi-Monte Carlo method is also carried out. * The author thanks B. Jourdain and the referee for their careful reading of the manuscript and S.  ...  and analysis of a Richardson-Romberg extrapolation method which again dramatically improves the convergence rate.  ...  The CLV Q as a stochastic gradient descent.  ... 
doi:10.1051/proc/201448002 fatcat:vwxng3fxtbccji7d3v5ksfibya

Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyond [article]

Xuechen Li, Denny Wu, Lester Mackey, Murat A. Erdogdu
2020 arXiv   pre-print
Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration.  ...  This improves upon the best-known rate for strongly log-concave sampling based on the overdamped Langevin equation using only the gradient oracle without adjustment.  ...  A prominent approach to this problem is the method of Markov chain Monte Carlo (MCMC), where an ergodic Markov chain is simulated so that iterates converge exactly or approximately to the distribution  ... 
arXiv:1906.07868v3 fatcat:txlocvwkdfecxbvz5dvck54qai

HMC and Langevin united in the unadjusted and convex case [article]

Pierre Monmarché
2022 arXiv   pre-print
Then, a stochastic gradient version of the samplers is considered, for which dimension-free convergence rates are established for log-concave smooth targets, gathering in a unified framework previous results  ...  Monmarché thanks Nawaf Bou-Rabee, Andreas Eberle and Katharina Schuh for the organization of a workshop in Bonn on the long-time convergence of Markov processes and related topics which has been the occasion  ...  We are interested in the question of sampling π with Markov Chain Monte Carlo (MCMC) samplers in a class of unadjusted Hamiltonian Monte Carlo (HMC) chains.  ... 
arXiv:2202.00977v2 fatcat:nbwqisoyq5gfvhvky2jo742bwq

Probabilistic Permutation Synchronization using the Riemannian Structure of the Birkhoff Polytope [article]

Tolga Birdal, Umut Şimşekli
2019 arXiv   pre-print
Next, we introduce a new probabilistic synchronization model in the form of a Markov Random Field (MRF).  ...  Carlo for generating samples on the Birkhoff Polytope and estimating the confidence of the found solutions.  ...  Stochastic gradient Richardson-Romberg Markov Chain Monte Carlo. In Advances in Neural Information Processing Systems, pages 2047-2055, 2016.  ... 
arXiv:1904.05814v1 fatcat:ngqtrdaakzfujbqm3scvkptajq

A Survey of Uncertainty in Deep Neural Networks [article]

Jakob Gawlikowski, Cedrique Rovile Njieutcheu Tassi, Mohsin Ali, Jongseok Lee, Matthias Humt, Jianxiang Feng, Anna Kruspe, Rudolph Triebel, Peter Jung, Ribana Roscher, Muhammad Shahzad, Wen Yang (+2 others)
2022 arXiv   pre-print
Richard, laplace approximation for robotic introspection,” arXiv preprint “Stochastic gradient richardson-romberg markov chain monte carlo,” in arXiv:2010.16141, 2020.  ...  Fearnhead, “Stochastic gradient markov chain monte Recognition (ICPR). IEEE, 2021, pp. 1438–1445. carlo,” Journal of the American Statistical Association, pp. 1–18, 2020. [105] Y.  ... 
arXiv:2107.03342v3 fatcat:cex5j3xq5fdijjdtdbt2ixralm

Asymptotic properties of Monte Carlo estimators of diffusion processes

Jérôme Detemple, René Garcia, Marcel Rindisbacher
2006 Journal of Econometrics  
Finally, we derive the limit distributions of Monte Carlo estimators of conditional expectations with unknown initial state.  ...  This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. Two types of estimators are examined.  ...  Chain Monte Carlo (MCMC) Bayesian techniques (Eraker (1999) , Chib, Elerian and Shephard (2000) ).  ... 
doi:10.1016/j.jeconom.2005.06.028 fatcat:cmu5be4pvfasthbd3lo3pk2tve
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