Stochastic Block Model Prior with Ordering Constraints for Gaussian Graphical Models

🏆 This was the highest ranking project in its year batch.

This project was developed for the course of Bayesian Statistics for the MSc. in Mathematical Engineering at Politecnico di Milano, A.Y. 2022/2023.

Table of contents

• Installation
  • How to clone the repository
  • How to build the FGM package
  • How to install the packages
  • How to compile the PDF files
• Running the analysis
• Final results
• Authors

Installation

How to clone the repository

git clone https://github.com/teobucci/bayesian-statistics-project
git submodule update --init
git submodule update --recursive

How to build the FGM package

Open the ./FGM/FGM.Rproj in RStudio and type:

• Ctrl+Shift+B on Windows
• CMD+Shift+B on macOS

On macOS on M1 chip you may get an error involving gfortran, in which case proceed as follows according to this:

1. Install gcc which includes gfortran with

   brew install gcc

2. Create a file ~/.R/Makevars (if it does not exist yet). For example running with a terminal

   mkdir -p ~/.R
   touch ~/.R/Makevars

3. Add the following lines to ~/.R/Makevars

   FC = /opt/homebrew/Cellar/gcc/11.3.0_2/bin/gfortran
   F77 = /opt/homebrew/Cellar/gcc/11.3.0_2/bin/gfortran
   FLIBS = -L/opt/homebrew/Cellar/gcc/11.3.0_2/lib/gcc/11
   

   This can be done by opening it in a normal text editor such as VSCode (code ~/.R/Makevars) or SublimeText (subl ~/.R/Makevars).

   Note that you might have to change gcc version 11.3.0_2 to whatever your gcc version is.

How to install the packages

Install the required packages from CRAN

packages_list <-
    c(
        "tidyverse",
        "mvtnorm",
        "salso",
        "logr",
        "gmp",
        "mcclust",
        "igraph",
        "ggraph",
        "tidygraph",
        "uuid",
        "dittodb",
        "latex2exp",
        "kableExtra",
        "doSNOW",
        "doParallel"
    )
install.packages(packages_list)

and install the custom utilities by Alessandro Colombi and mcclust.ext

devtools::install_github("alessandrocolombi/ACutils")
devtools::install_github("sarawade/mcclust.ext")

How to compile the PDF files

To compile the presentations, run the following in the root of the repo

make prese1
make prese2
make prese3

To compile the report, run

make report

To compile everything, run

make pdf

To remove temporary LaTeX files, run

make clean

To remove both temporary and PDF files, run

make distclean

Running the analysis

The repository contains different files to perform the analysis

• 01_simulations_basic.Rmd is a notebook containing a vanilla implementation for running a single simulation, meant to be used a playground for on-the-go configurations.
• The second block of files implements a grid-search approach to run different simulations varying parameters to see how well the MCMC behaves and how robust it is:
  • 02a_simulation_grid_generation.R generates the grid of required configurations.
  • 02b_simulation_grid_parallel_execution.R runs and saves all the simulations from the grid by the previous file, which is sourced here. The execution is run in parallel and on a MacBook Pro M1 14" takes about 10 minutes.
  • 02c_simulation_grid_visualization_notebook.Rmd reads all the simulations generated from the previous files and, when knitted, produces a PDF where for each section there is a simulation. At the beginning there is a comprehensive table with all the relevant indexes across the grid.
  • 02d_simulation_grid_visualization_export_files.R is a script that, when sourced, reads all the simulations generated by 02b_simulation_grid_parallel_execution.R and saves all the relevant plots and figures to file, useful for embedding in presentations and report.
  • 02e_simulation_grid_kl_comparison.Rmd reads all the simulations generated from the previous files and, when knitted, produces a PDF comparing the evolution of the KL distance across iterations for different configurations. For a better understanding, it is advised to run the simulations without burn-in in this case.
• 03_simulations_real_dataset.Rmd is a notebook where the algorithm is run on a real dataset, which is meant to be stored in dataset, not included in this repository for privacy reasons. It is essentially a copy of 01_simulations_basic.Rmd but without the knowledge of the true graph and partition.
• 04_execution_time_regression.R is a script that implements a polynomial linear regression of the execution time against the number of nodes, taken from the simulation grid results.

Final results

The final presentations can be found here:

• Presentation 2022-11-11
• Presentation 2023-01-09
• Presentation 2023-02-14

The final report can be found here:

• Stochastic_Block_Model_Prior_with_Ordering_Constraints_for_Gaussian_Graphical_Models.pdf

The results from the simulations knitted can be found here:

• 01_simulations_basic.pdf
• 02c_simulation_grid_visualization_notebook.pdf
• 02e_simulation_grid_kl_comparison.pdf
• 03_analysis_real_dataset.pdf

Authors

Supervisor: Alessandro Colombi (@alessandrocolombi)

• Teo Bucci (@teobucci)
• Filippo Cipriani (@SmearyTundra)
• Filippo Pagella (@effefpi2)
• Flavia Petruso (@fl-hi1)
• Andrea Puricelli (@apuri99)
• Giulio Venturini (@Vinavil334)