Computational optimal transport: With applications to data science
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 …
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
Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …
Rapid convergence of the unadjusted langevin algorithm: Isoperimetry suffices
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 …
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
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 …
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 …
Bernoulli 25(4A), 2019, 2854–2882 https://doi.org/10.3150/18-BEJ1073 High-dimensional …
Software reliability prediction: A survey
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 …
functioning of the components of such systems is the principal role of softwares. Often, a …
Convex analysis of the mean field langevin dynamics
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 …
recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide …
Global convergence of Langevin dynamics based algorithms for nonconvex optimization
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 …
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 …
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 …
based optimization with the Langevin dynamics as a case study. We investigate the source …