Computational optimal transport: With applications to data science

G Peyré, M Cuturi - Foundations and Trends® in Machine …, 2019 - nowpublishers.com
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Analysis of langevin monte carlo from poincare to log-sobolev

S Chewi, MA Erdogdu, M Li, R Shen… - Foundations of …, 2024 - Springer
Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices

S Vempala, A Wibisono - Advances in neural information …, 2019 - proceedings.neurips.cc
Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

[HTML][HTML] User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient

AS Dalalyan, A Karagulyan - Stochastic Processes and their Applications, 2019 - Elsevier
In this paper, we study the problem of sampling from a given probability density function that
is known to be smooth and strongly log-concave. We analyze several methods of …

High-dimensional Bayesian inference via the unadjusted Langevin algorithm

A Durmus, E Moulines - 2019 - projecteuclid.org
High-dimensional Bayesian inference via the unadjusted Langevin algorithm Page 1
Bernoulli 25(4A), 2019, 2854–2882 https://doi.org/10.3150/18-BEJ1073 High-dimensional …

Software reliability prediction: A survey

S Oveisi, A Moeini, S Mirzaei… - Quality and Reliability …, 2023 - Wiley Online Library
Softwares play an important role in controlling complex systems. Monitoring the proper
functioning of the components of such systems is the principal role of softwares. Often, a …

Convex analysis of the mean field langevin dynamics

A Nitanda, D Wu, T Suzuki - International Conference on …, 2022 - proceedings.mlr.press
As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics
recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide …

Global convergence of Langevin dynamics based algorithms for nonconvex optimization

P Xu, J Chen, D Zou, Q Gu - Advances in Neural …, 2018 - proceedings.neurips.cc
We present a unified framework to analyze the global convergence of Langevin dynamics
based algorithms for nonconvex finite-sum optimization with $ n $ component functions. At …

On sampling from a log-concave density using kinetic Langevin diffusions

AS Dalalyan, L Riou-Durand - 2020 - projecteuclid.org
Langevin diffusion processes and their discretizations are often used for sampling from a
target density. The most convenient framework for assessing the quality of such a sampling …

Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem

A Wibisono - Conference on Learning Theory, 2018 - proceedings.mlr.press
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 …