Sequential Mixture Posterior and Likelihood Estimation (SeMPLE)

SeMPLE is a framework for simulation-based inference that learns surrogate models for the likelihood function and the posterior distribution of model parameters, and outputs draws from the posterior. It provides a faster and lightweight solution compared to samplers using neural networks for density estimation, while retaining accuracy. The methodology is described in H. Häggström, P. Rodrigues, G. Oudoumanessah, F. Forbes and U. Picchini (2024). Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings, Transactions on Machine Learning Research, https://openreview.net/forum?id=Q0nzpRcwWn.

Setup

SeMPLE is written in R. To run SeMPLE you need to install the xLLiM R package that gives access to the GLLiM function. Follow the instructions below, do NOT use the version provided on CRAN.

Run the following command in R to get the correct version of xLLiM (requires the R package "devtools" to be installed):

# install.packages("devtools")
devtools::install_github("epertham/xLLiM", ref = "master")

Set the working directory to be the repository semple folder.

Running SeMPLE

To run SeMPLE with with an implemented model/task run the corresponding model_name.R script in the run_scripts folder, e.g. run_scripts/two_moons.R. The algorithm outputs are saved into the results directory.

Add new model/task

To implement a new model to run SeMPLE with create a new model file according to models/model_name/model_name_model.R. The model file need to define four functions, the model function to simulate data, the prior_pdf function that defines the probability density function of the prior distribution, the sample_prior function that returns a sample from the prior distribution and the jacobian function that defines the optional transformation jacobian. Additionally, at least one observed data set needs to be added to models/model_name/num_observation_X.

SBIBM

To run SNPE-C or SNL to produce results to be compared to SeMPLE results, install the SBIBM fork https://github.com/henhagg/sbibm. It contains modifications to output posterior samples from each SNPE-C and SNL algorithm iteration instead of only from the last algorithm iteration. Additionally, it is modified to output the runtime of SNPE-C and SNL. Furthermore, the fork contains implementations of the hyperboloid model, the Orstein-Uhlenbeck process and the mRNA model.

Reproducing results in the main paper

• The algorithm results can be reproduced by using the scripts in the run_scripts folder. The results presented in the paper are available in the results folder.
• Performance metric computations can be reproduced by running the src/compute_metrics.py script.
• Figures in the main paper can be reproduced by running the scripts plot_scripts folder (make sure to first change the working directory to be the semple folder).
• Calculations reproducing results similar to Table 1 can be produced by running the script energy_test.py that is found in the "energy_test" branch of this repository (results are machine-dependent). Prior to launching the script (⚠️ you need an intel processor):
  • Go to branch "energy_test" of this repository and install pyjoules:

  $pip install pyjoules
  

  • For each of bernoulli_glm.R, two_moons.R, hyperboloid.R, ornstein_uhlenbeck.R, set your working directory as the path of the project
  • Add the path of the GNU library packages at the end of energy_test.py
  • The results are saved in ./energy_results/

Repository structure

• The run_scripts folder contains model_name.R scripts to run SeMPLE with the implemented models. The run_sbibm.py script can be used to run SNPE-C and SNL.

• The src folder contains the semple.R script with the SeMPLE algorithm impelementation. It also contains the bic.R script that computes the Bayesian Information Criterion (BIC) to help determine the number of mixture components K to initialize SeMPLE with. The compute_metrics.py script can be used to compute performance metrics of algorithm posterior samples relative to a reference posterior.

• The plot_scripts folder contains scripts to plot the figures presented in the paper.

• The results folder contains the results presented in the paper. New results from running SeMPLE are saved in this folder.