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We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly…

Machine Learning · Computer Science 2016-03-08 Chao Du , Jun Zhu , Bo Zhang

In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators…

This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially…

Computation · Statistics 2011-11-01 Nimalan Mahendran , Ziyu Wang , Firas Hamze , Nando de Freitas

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…

Methodology · Statistics 2018-12-31 Matias Quiroz , Robert Kohn , Mattias Villani , Minh-Ngoc Tran

In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms.…

Numerical Analysis · Mathematics 2023-01-04 Junpeng Hu , Shi Jin , Jinglai Li , Lei Zhang

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…

Methodology · Statistics 2022-09-05 Mikkel B. Lykkegaard , Tim J. Dodwell , Colin Fox , Grigorios Mingas , Robert Scheichl

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…

Machine Learning · Computer Science 2025-03-03 Hoang Phuc Hau Luu , Hanlin Yu , Bernardo Williams , Marcelo Hartmann , Arto Klami

Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters.…

Computation · Statistics 2026-04-08 Shijie Zhong , Wanggang Shen , Tommie Catanach , Xun Huan

Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the…

Computation · Statistics 2019-12-09 Takashi Goda

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC…

Computation · Statistics 2012-09-19 Antonietta Mira , Reza Solgi , Daniele Imparato

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

Computation · Statistics 2015-05-20 Tim Salimans , Diederik P. Kingma , Max Welling

We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…

Computation · Statistics 2018-06-08 Yang Ni , Peter Müller , Maurice Diesendruck , Sinead Williamson , Yitan Zhu , Yuan Ji

We present a new unbiased algorithm that estimates the expected value of f(U) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. We assume that f does not depend equally on…

Computation · Statistics 2020-06-02 Nabil Kahale

We propose a new procedure named PASOA, for Bayesian experimental design, that performs sequential design optimization by simultaneously providing accurate estimates of successive posterior distributions for parameter inference. The…

Machine Learning · Statistics 2024-10-16 Jacopo Iollo , Christophe Heinkelé , Pierre Alliez , Florence Forbes

In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…

Computation · Statistics 2020-02-18 Johnathan Bardsley , Tiangang Cui

In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…

Machine Learning · Computer Science 2023-10-11 Kei Ishikawa

This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…

Machine Learning · Computer Science 2019-12-06 Brandon Trabucco , Albert Qu , Simon Li , Ganeshkumar Ashokavardhanan

Gaussian random fields play an important role in many areas of science and engineering. In practice, they are often simulated by sampling from a high-dimensional multivariate normal distribution, which arises from the discretisation of a…

Numerical Analysis · Mathematics 2026-02-12 Yoshihito Kazashi , Eike H. Müller , Robert Scheichl

Optimization is becoming increasingly common in scientific and engineering domains. Oftentimes, these problems involve various levels of stochasticity or uncertainty in generating proposed solutions. Therefore, optimization in these…

Machine Learning · Statistics 2020-06-05 Peter D. Tonner , Daniel V. Samarov , A. Gilad Kusne

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…

Numerical Analysis · Mathematics 2025-08-19 Pieter Vanmechelen , Geert Lombaert , Giovanni Samaey