Julia code supporting the preprint:

Optimized Annealed Sequential Monte Carlo Samplers. (2024)
S. Syed, A. Bouchard-Côté, K Chern, A. Doucet.

Code is not yet ready for general use as the manuscript is under review. An open source license will be added once the paper is accepted. Please contact us if you would like to use the software in the meantime.

Setup

Test with Julia 1.10.2 and CUDA runtime 12.5.

To setup:

using Pkg
Pkg.instantiate() 

To run a battery of test cases:

include("tests.jl")

Usage

Defining the reference and target (path)

To see an example of how to setup target distributions, see simple_mixture.jl. The main idea is that a custom struct is defined to hold the dataset, and dispatches are defined to specify target and reference.

The functions to dispatch are:

• iid_sample!(...) to sample from the reference,
• log_reference(...) to evaluate the log density of the reference,
• log_density_ratio(...) to evaluate the log of the un-normalized ratio between target and reference (e.g., in Bayesian models this is just the likelihood),
• dimensionality(...) to obtain the dimensionality of the latent space.

After doing so, create a variable say path and assign to it an instance of your custom struct. For example:

include("simple_mixture.jl")
backend = CPU() # or: CUDABackend()
path = SimpleMixture(backend) # since it holds data array, it needs to know if will be in CPU or GPU

Sampling

The interface for sampling is ais(...). The followoing methods are implemented:

• In sais.jl, we implement our SAIS (Sequential Annealed Importance Sampling) algorithm.
• In zha.jl, we implement Zhou et al (2016).

For example:

include("sais.jl")
a = ais(path, SAIS(10);
    N = 100, # number of particles
    backend,
    seed = 1)

Approximating expectation and estimating normalization constant

To approximate expectations:

∫(x -> x.^2, a.particles)

For the normalization constant:

a.particles.log_normalization

For ESS:

ess(a.particles)