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Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large…

Computation · Statistics 2015-12-07 Roberto Casarin , Radu V. Craiu , Fabrizio Leisen

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge…

Computation · Statistics 2022-12-01 Joris Bierkens , Sebastiano Grazzi , Frank van der Meulen , Moritz Schauer

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Numerical Analysis · Mathematics 2017-11-15 Matthias Morzfeld , Marcus S. Day , Ray W. Grout , George Shu Heng Pau , Stefan A. Finsterle , John B. Bell

Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with…

Machine Learning · Computer Science 2019-10-17 Yichuan Zhang , José Miguel Hernández-Lobato

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…

Methodology · Statistics 2019-01-21 Zheng Wei , Erin M. Conlon

Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…

Methodology · Statistics 2023-02-27 Daniel R. Kowal , Bohan Wu

Performing reliable Bayesian inference on a big data scale is becoming a keystone in the modern era of machine learning. A workhorse class of methods to achieve this task are Markov chain Monte Carlo (MCMC) algorithms and their design to…

Methodology · Statistics 2021-06-21 Vincent Plassier , Maxime Vono , Alain Durmus , Eric Moulines

We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic…

Statistics Theory · Mathematics 2024-09-04 Joris Bierkens , Sebastiano Grazzi , Frank van der Meulen , Moritz Schauer

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…

Methodology · Statistics 2023-06-14 Thomas Y. Sun , Daniel R. Kowal

Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at…

Machine Learning · Statistics 2014-03-25 Dougal Maclaurin , Ryan P. Adams

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

Machine Learning · Computer Science 2024-01-08 Zeji Yi , Yunyue Wei , Chu Xin Cheng , Kaibo He , Yanan Sui

Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of…

Methodology · Statistics 2020-02-18 Robert Salomone , Matias Quiroz , Robert Kohn , Mattias Villani , Minh-Ngoc Tran

Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…

Numerical Analysis · Mathematics 2014-11-18 Felix Lucka

The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…

Instrumentation and Methods for Astrophysics · Physics 2014-08-19 Yi-Ming Hu , Martin Hendry , Ik Siong Heng

We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…

Statistics Theory · Mathematics 2019-08-21 Yves Atchade , Anwesha Bhattacharyya

Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…

Methodology · Statistics 2015-05-13 Rémi Bardenet , Arnaud Doucet , Chris Holmes

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

Computation · Statistics 2026-03-30 Yujie Chen , Antik Chakraborty , Anindya Bhadra

The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly…

Machine Learning · Statistics 2015-10-27 Xiangyu Wang , Fangjian Guo , Katherine A. Heller , David B. Dunson

The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires…

Computation · Statistics 2020-03-11 Haoyun Ying , Keheng Mao , Klaus Mosegaard