4 results on '"Khue-Dung Dang"'
Search Results
2. Subsampling sequential Monte Carlo for static Bayesian models
- Author
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Khue-Dung Dang, Minh-Ngoc Tran, David Gunawan, Robert Kohn, and Matias Quiroz
- Subjects
Statistics and Probability ,Markov kernel ,Computer science ,Bayesian probability ,Posterior probability ,010103 numerical & computational mathematics ,Bayesian inference ,01 natural sciences ,Statistics::Computation ,Theoretical Computer Science ,Hybrid Monte Carlo ,010104 statistics & probability ,Computational Theory and Mathematics ,Resampling ,Kernel (statistics) ,0101 mathematics ,Statistics, Probability and Uncertainty ,Particle filter ,Algorithm - Abstract
We show how to speed up sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is easy to sample from such as the prior and ending with the posterior distribution. Each update of the particle cloud consists of three steps: reweighting, resampling, and moving. In the move step, each particle is moved using a Markov kernel; this is typically the most computationally expensive part, particularly when the dataset is large. It is crucial to have an efficient move step to ensure particle diversity. Our article makes two important contributions. First, in order to speed up the SMC computation, we use an approximately unbiased and efficient annealed likelihood estimator based on data subsampling. The subsampling approach is more memory efficient than the corresponding full data SMC, which is an advantage for parallel computation. Second, we use a Metropolis within Gibbs kernel with two conditional updates. A Hamiltonian Monte Carlo update makes distant moves for the model parameters, and a block pseudo-marginal proposal is used for the particles corresponding to the auxiliary variables for the data subsampling. We demonstrate both the usefulness and limitations of the methodology for estimating four generalized linear models and a generalized additive model with large datasets.
- Published
- 2020
3. Subsampling MCMC - an Introduction for the Survey Statistician
- Author
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Matias Quiroz, Robert Kohn, Minh-Ngoc Tran, Khue-Dung Dang, and Mattias Villani
- Subjects
Statistics and Probability ,Computer science ,Inference ,Survey sampling ,Astrophysics::Cosmology and Extragalactic Astrophysics ,Machine learning ,computer.software_genre ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,0502 economics and business ,Statistics::Methodology ,0101 mathematics ,050205 econometrics ,business.industry ,05 social sciences ,Estimator ,Sampling (statistics) ,Markov chain Monte Carlo ,Statistics::Computation ,Bayesian statistics ,ComputingMethodologies_PATTERNRECOGNITION ,Scalability ,symbols ,Artificial intelligence ,Statistics, Probability and Uncertainty ,business ,computer ,Statistician - Abstract
The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called Pseudo-Marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.
- Published
- 2018
4. The block-Poisson estimator for optimally tuned exact subsampling MCMC
- Author
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Matias Quiroz, Khue-Dung Dang, Mattias Villani, Minh-Ngoc Tran, and Robert Kohn
- Subjects
Statistics and Probability ,FOS: Computer and information sciences ,Computer science ,Statistics & Probability ,Machine Learning (stat.ML) ,Poisson distribution ,Control variates ,Bayesian inference ,01 natural sciences ,Statistics - Computation ,Methodology (stat.ME) ,010104 statistics & probability ,symbols.namesake ,Statistics - Machine Learning ,Block (telecommunications) ,0502 economics and business ,Discrete Mathematics and Combinatorics ,Statistics::Methodology ,0101 mathematics ,Statistics - Methodology ,Computation (stat.CO) ,050205 econometrics ,05 social sciences ,Estimator ,Markov chain Monte Carlo ,0104 Statistics, 1403 Econometrics ,Statistics::Computation ,symbols ,Statistics, Probability and Uncertainty ,Algorithm - Abstract
Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favourably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature., Comment: The main paper is 28 pages. The supplementary material is 28 pages
- Published
- 2016
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