SΩI: Score-based O-INFORMATION Estimation

This repository contains the implementation for the paper SΩI : Score-based O-INFORMATION Estimation presented at ICML 2024.

Description

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SΩI, which allows to compute O-information without restrictive assumptions about the system while leveraging a unique model. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SΩI in the context of a real-world use case.

Installation

This repo was developed and tested under Python 3.9.12.

To install the dependencies :

$ pip install -r requirements.txt

Usage

Demo

Checkout Quickstart.ipynb for a quickstart on how to use SΩI.

First, default config can be loaded :

args=get_default_config()

A synthetic benchmark can be created :

my_settings = [{"rho":0.6,"type":"red","nb":3},{"rho":0.6,"type":"Syn","nb":3} ]
args.dim = 1
task = get_task(args,my_settings)

Groud truth information measures can be obtained:

task.get_summary()

Runing SΩI

Build the dataloaders

train_l, test_l  = get_dataloader(task,args)

Instantiante SOI object

soi = SOI(args, nb_var = task.nb_var)

Fit the model

soi.fit(train_l, test_l)

Compute O_information using the test_loader

soi.compute_o_inf()

Running experiments

Running a particular experiment can be done using the scripts in experiments\. The experiments configurations are described in experiments\config.py

Example:

python -m experiments.run_soi --arch "tx" --bechmark "red" --dim 1 --setting "0" --rho 0.4 --bs 256 --lr 0.001 --max_epochs 200 --use_ema --importance_sampling  --weight_s_functions

To run the experiments and reproduce the results from the paper, the shell scripts are provided in jobs\.

Dataset

The synthetic benchmark are generated and not stored. The VBN dataset used in the neural activity experiments are stored in the data/ directory. The preprocessed VBN dataset can be generated by running src/vbn/download. Please note that this script will require to download the whole VBN dataset (3TB of storage).

Project Structure

soi/
├── experiments/           
│   ├── run_soi.py         # run SOI experiment on synthetic benchmark
│   ├── run_soi_grad.py    # run SOI experiment on synthetic benchmark and estimate gradient of O-information
│   ├── run_soi_vbn.py     # run SOI experiment on the VBN dataset
│   └── run_baseline.py    # run baselines on synthetic benchmark
├── src/                   # Source code for the project
│   ├── models/            # Denoising score models : MLP with skip connection and a transformer implementation
│   ├── benchmark/         # Synthetic benchmark
│   ├── baseline           # baseline constructed using MI neural estimators
│   ├── vis                # visualization notebook
│   └── libs               # SOI models
│       ├──soi.py          # The main SOI model class
│       ├──soi_grad.py     # A subclass of the soi model that takes into account gradint of o-information
│       ├──SDE.py          # The noising process which permits the learn the score functions
│       ├──inf_measures.py # The set of functions to compute all the information measures: O-information, S-information, TC, DTC .. etc
│       ├──importance.py   # Required function to implement importance sampling scheme.
│       └──util.py         # General utility functions
├── jobs                   # bash script to reproduce the paper results
├── quickstart.ipynb       # a jupyter notebook which explain how to use soi                           
├── requirements.txt       # List of dependencies
└── README.md              # This README file

Cite our paper

@inproceedings{
bounoua2024somegai,
title={S\${\textbackslash}Omega\$I: Score-based O-{INFORMATION} Estimation},
author={Mustapha BOUNOUA and Giulio Franzese and Pietro Michiardi},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=LuhWZ2oJ5L}
}

MustaphaBounoua/soi