LangevinFlow

Langevin diffusion Markov chain Monte Carlo samplers for R, with a C++ backend via Rcpp and RcppArmadillo.

Installation

Development version from GitHub:

# install.packages("devtools")
# devtools::install_github("BehroozMoosavi/LangevinFlow")
install.packages("LangevinFlow", repos = c('https://behroozmoosavi.r-universe.dev', 'https://cloud.r-project.org'))

Usage

The package exposes two samplers, both targeting $\pi(x) \propto \exp(-\beta U(x))$ where the user supplies the potential $U(x) = -\log \pi(x)$ (and, for MALA, its gradient).

Unadjusted Langevin Algorithm

library(LangevinFlow)

# Standard 2D Gaussian: U(x) = 0.5 * ||x||^2
grad_u <- function(x) x

set.seed(1)
fit <- ula(init_x = c(3, -3), grad_u = grad_u,
           step_size = 0.05, n_iter = 5000, burn_in = 1000)
summary(fit)
plot(fit)

Metropolis-Adjusted Langevin Algorithm

U      <- function(x) 0.5 * sum(x^2)
grad_u <- function(x) x

set.seed(1)
fit <- mala(init_x = c(3, -3), U = U, grad_u = grad_u,
            step_size = 0.4, n_iter = 5000, burn_in = 1000)
fit$acceptance_rate

When to use which

Sampler	Asymptotically exact?	Tuning sensitivity	Best for
ula()	No — biased by step_size	Less	Quick exploration; stochastic optimization
mala()	Yes	More (target ~0.574 acceptance)	Accurate inference

References

• Roberts, G. O., & Tweedie, R. L. (1996). Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli, 2(4), 341–363.
• Roberts, G. O., & Rosenthal, J. S. (1998). Optimal scaling of discrete approximations to Langevin diffusions. JRSS-B, 60(1), 255–268.