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Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Computation · Statistics 2022-03-18 Cosma Rohilla Shalizi

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…

Computation · Statistics 2014-12-23 Jinglai Li , Youssef M. Marzouk

Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the…

Signal Processing · Electrical Eng. & Systems 2025-06-09 Jiří Ajgl , Ondřej Straka

We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays…

Numerical Analysis · Mathematics 2023-05-23 Anastasia Batsheva , Andrei Chertkov , Gleb Ryzhakov , Ivan Oseledets

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…

Instrumentation and Methods for Astrophysics · Physics 2026-04-10 Aditya S. Deshpande , Patrick D. Mullen , Alex A. Gorodetsky , Joshua C. Dolence , Chad D. Meyer , Jonah M. Miller , Luke F. Roberts

Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…

Machine Learning · Statistics 2021-02-03 Adrià Garriga-Alonso , Vincent Fortuin

Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…

Computation · Statistics 2012-07-02 Iain Murray , Zoubin Ghahramani , David MacKay

Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…

Computation · Statistics 2021-01-06 Christophe Andrieu , Sinan Yıldırım , Arnaud Doucet , Nicolas Chopin

Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…

Numerical Analysis · Mathematics 2020-06-16 Peter Georg , Lars Grasedyck , Maren Klever , Rudolf Schill , Rainer Spang , Tilo Wettig

A adapted tensor-structured GMRES method for the TT format is proposed and investigated. The Tensor Train (TT) approximation is a robust approach to high-dimensional problems. One class of problems is solution of a linear system. In this…

Numerical Analysis · Mathematics 2012-06-26 Sergey V. Dolgov

This paper presents a control variate-based Markov chain Monte Carlo algorithm for efficient sampling from the probability simplex, with a focus on applications in large-scale Bayesian models such as latent Dirichlet allocation. Standard…

Methodology · Statistics 2024-10-02 Francesco Barile , Christopher Nemeth

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples…

Numerical Analysis · Mathematics 2022-06-03 Yuming Ba , Jana de Wiljes , Dean S. Oliver , Sebastian Reich

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…

Machine Learning · Statistics 2020-10-09 Zengyi Li , Yubei Chen , Friedrich T. Sommer

We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an…

Machine Learning · Computer Science 2022-12-02 Yinuo Ren , Hongli Zhao , Yuehaw Khoo , Lexing Ying

This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in…

Methodology · Statistics 2015-04-06 Marcelo Pereyra

The mixed effects model for repeated measures (MMRM) has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the MMRM for skewed and heavy-tailed data…

Methodology · Statistics 2019-08-12 Yongqiang Tang

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

Computation · Statistics 2019-10-15 Babak Shahbaba , Luis Martinez Lomeli , Tian Chen , Shiwei Lan

Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…

Machine Learning · Computer Science 2019-10-22 Asif J. Chowdhury , Gabriel Terejanu

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…

Numerical Analysis · Computer Science 2016-06-20 Qibin Zhao , Guoxu Zhou , Shengli Xie , Liqing Zhang , Andrzej Cichocki

Monte Carlo approaches have recently been proposed to quantify connectivity in neuronal networks. The key problem is to sample from the conditional distribution of a single neuronal spike train, given the activity of the other neurons in…

Applications · Statistics 2011-12-01 Yuriy Mishchenko , Liam Paninski