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Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…

Machine Learning · Computer Science 2024-03-12 Xunpeng Huang , Hanze Dong , Difan Zou , Tong Zhang

We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…

Dynamical Systems · Mathematics 2021-11-05 J. A. Carrillo , F. Hoffmann , A. M. Stuart , U. Vaes

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…

Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…

Machine Learning · Statistics 2024-06-21 Omar Chehab , Anna Korba

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…

Systems and Control · Electrical Eng. & Systems 2025-06-17 Jichen Zhang , Liqun Zhao , Antonis Papachristodoulou , Jack Umenberger

Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…

Machine Learning · Statistics 2022-11-04 Jacopo Guidolin , Vyacheslav Kungurtsev , Ondřej Kuželka

We present Re-weighted Gradient Descent (RGD), a novel optimization technique that improves the performance of deep neural networks through dynamic sample re-weighting. Leveraging insights from distributionally robust optimization (DRO)…

Machine Learning · Computer Science 2024-10-15 Ramnath Kumar , Kushal Majmundar , Dheeraj Nagaraj , Arun Sai Suggala

We prove fast mixing and characterize the stationary distribution of the Langevin Algorithm for inverting random weighted DNN generators. This result extends the work of Hand and Voroninski from efficient inversion to efficient posterior…

Machine Learning · Computer Science 2022-06-24 Giannis Daras , Yuval Dagan , Alexandros G. Dimakis , Constantinos Daskalakis

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in…

Optimization and Control · Mathematics 2018-06-08 Andre Wibisono

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

Computation · Statistics 2024-04-01 Riddhiman Bhattacharya , Tiefeng Jiang

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two…

Machine Learning · Computer Science 2023-10-13 Kushagra Pandey , Maja Rudolph , Stephan Mandt

Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex…

Machine Learning · Computer Science 2020-12-23 Andrew Lamperski

We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…

Numerical Analysis · Mathematics 2020-12-09 Benedict Leimkuhler , Matthias Sachs

A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…

Computation · Statistics 2023-11-01 Martin Chak , Nikolas Kantas , Tony Lelièvre , Grigorios A. Pavliotis

We propose an interacting contour stochastic gradient Langevin dynamics (ICSGLD) sampler, an embarrassingly parallel multiple-chain contour stochastic gradient Langevin dynamics (CSGLD) sampler with efficient interactions. We show that…

Machine Learning · Statistics 2022-02-22 Wei Deng , Siqi Liang , Botao Hao , Guang Lin , Faming Liang

Stochastic Gradient Langevin Dynamics (SGLD) ensures strong guarantees with regards to convergence in measure for sampling log-concave posterior distributions by adding noise to stochastic gradient iterates. Given the size of many practical…

Machine Learning · Computer Science 2020-06-15 Vyacheslav Kungurtsev , Bapi Chatterjee , Dan Alistarh

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…

Machine Learning · Computer Science 2022-06-22 Ruqi Zhang , Xingchao Liu , Qiang Liu

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…

Machine Learning · Statistics 2020-06-17 Adil Salim , Dmitry Kovalev , Peter Richtárik

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte…

Machine Learning · Statistics 2019-05-27 Yulong Lu , Jianfeng Lu , James Nolen

Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…

Machine Learning · Statistics 2024-05-28 Xunpeng Huang , Difan Zou , Yi-An Ma , Hanze Dong , Tong Zhang