malt: malt

In lrioudurand/malt: Metropolis Adjusted Langevin Trajectories

malt

Description

Implements the sampling algorithm: Metropolis Adjusted Langevin Trajectories (MALT) as described in Riou-Durand and Vogrinc (2022).

Usage

malt(init, U, grad, n, g, h, L, warm = FALSE)

Arguments

init	Real vector. Initial values for the sampling algorithm.
U	A potential function to return the log-density of the distribution to be sampled from, up to an additive constant. It should input a real vector of the same length as init and output a scalar.
grad	A function to return the gradient of the potential. It should input and output a real vector of the same length as init.
n	The number of samples to be generated. Positive integer.
g	The friction, a.k.a damping parameter. Non-negative real number. The choice g=0 boils down to Hamiltonian Monte Carlo.
h	The time step. Positive real number.
L	The number of steps per trajectory. Positive integer. The choice L=1 boils down to the Metropolis Adjusted Langevin Algorithm.
warm	Should the chain be warmed up? Logical. If TRUE, the samples are generated after a warm-up phase of n successive trajectories. The first half of the warm-up phase is composed by unadjusted trajectories.

Details

Generates approximate samples from a distribution with density

Pi(x)=exp(-U(x))/C

A Markov chain is generated by drawing successive Langevin trajectories. Each trajectory starts from a fresh Gaussian velocity and is faced with an accept-reject test known as Metropolis adjustment. The Hamiltonian Monte Carlo (HMC) algorithm is recovered as a particular case when the damping parameter is set to zero. A positive choice of damping can ensure robustness of tuning, see Riou-Durand and Vogrinc (2022) for further details.

Value

Returns a list with the following objects:

samples	a matrix whose rows are the samples generated.
draw	a vector corresponding to the last draw of the chain.
accept	the acceptance rate of the chain. An acceptance rate close to zero/one indicates that the time step chosen is respectively too large/small. Optimally, the time step should be tuned to obtain an acceptance rate slightly above 65%.
param	the input parameters of the malt algorithm.

References

Riou-Durand and Vogrinc (2022). Available at: https://arxiv.org/abs/2202.13230.

See Also

trajectory, which draws a Langevin trajectory and computes the numerical error along the path.

Examples

d=50
sigma=((d:1)/d)^(1/2)
init=rnorm(d)*sigma
U=function(x){sum(0.5*x^2/sigma^2)}
grad=function(x){x/sigma^2}
n=10^4
g=1.5
h=0.20
L=8
malt(init,U,grad,n,g,h,L)

lrioudurand/malt documentation built on July 28, 2022, 11:06 p.m.