Maximum Weight Entropy

This repository provides the source code of the experiments for the paper: Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy Maximization (JMLR)

📦 Install & Use the PyPI Package

Our method is now available as a Python package on PyPI! 🚀 Easily install it with:

pip install maxwent

For detailed usage and examples, visit this GitHub repository.

🔹 Compatible with TensorFlow & PyTorch

🔹 Comprehensive tutorials included in the documentation

🔹 Easily adaptable to new data

Overview

MaxWEnt is an uncertainty quantification method, particularly suited for Out-Of-Distribution detection. The method is designed as an application of the Maximum Entropy principle to stochastic neural networks. Given a set of observations $\mathcal{S} = \{ (x_1, y_1), ..., (x_n, y_n) \} \subset \mathcal{X} \times \mathcal{Y}$ and a neural network $h_w: \mathcal{X} \to \mathcal{Y}$, parameterized by the weight vector $w \in \mathcal{W}$, the method learns the parameters $\phi \in \mathbb{R}^D$ of a distribution $q_{\phi}$ defined over $\mathcal{W}$. MaxWEnt fosters the weight diversity of $q_{\phi}$ by penalizing the average empirical risk of the distribution by the weight entropy. Formally, the MaxWEnt optimization is expressed as follows:

$$\min_{\phi \in \mathbb{R}^D} \; \mathbb{E}_{q_{\phi}}[\mathcal{L}_{\mathcal{S}}(w)] - \lambda \mathbb{E}_{q_{\phi}}[-\log(q_{\phi}(w))].$$

Where:

• $\mathbb{E}_{q_{\phi}}[\mathcal{L}_{\mathcal{S}}(w)]$ is the average empirical risk over $q_{\phi}$
• $\mathbb{E}_{q_{\phi}}[-\log(q_{\phi}(w))]$ is the entropy of $q_{\phi}$
• $\lambda$ is a trade-off parameter

MaxWEnt significantly improves the out-of-distribution uncertainty estimation in comparison to the main baselines: DeepEnsemble and the standard Bayesian Neural Network (BNN) with centered gaussian prior. The figure below presents the results obtained on two synthetic datasets:

Deep Ensemble	MCDropout	BNN	MaxWEnt	MaxWEnt-SVD
Uncertainty Estimation Comparison. Above: "two-moons" 2D classification dataset. Below: 1D-regression. For classification, uncertainty estimates, in shades of blue, are computed with the average of prediction entropy over multiple predictions (darker areas correspond to higher uncertainty). For regression, the ground-truth is represented in black and the predicted confidence intervals of length $4 \sigma_w(x)$ in light blue, with $\sigma_w(x)$ computed as the standard deviation over multiple predictions. The two eperiments can be run in the respective notebooks `Synthetic_Classification.ipynb` and `Synthetic_Regression.ipynb`.

Experiments

To run the experiments, first clone the repository with:

git clone https://github.com/antoinedemathelin/maxwent-expe.git

or

git clone [email protected]:antoinedemathelin/maxwent-expe.git

On your labtop, create a conda environment (with python 3.11 preferably). Run, for instance,

conda create -n maxwent python=3.11
conda activate maxwent

Then, install the requirements from the requirements.txt file:

pip install -r requirements.txt

The experiments can then be conducted using one of the following config files: 1d_reg_all, 2d_classif_all, uci_all, citycam_all in the configs/ folder. For instance:

python run.py --config configs/1d_reg_all.yml

A single experiment can also be conducted for a particular dataset and method:

python run.py -c configs/uci.yml -d yacht_interpol -m MCDropout -p {'rate':0.1}

The models are stored in the results/ folder and the scores in the logs/ folder.

Note : the CityCam dataset should first be downloaded from this website, then preprocessed with the following command line:

python preprocessing_citycam.py <path_to_the_citycam_dataset_on_your_labtop>

Reference

If you use this repository in your research, please cite our work using the following reference:

@article{JMLR:v26:23-1359,
  author  = {Antoine de Mathelin and Fran{\c{c}}ois Deheeger and Mathilde Mougeot and Nicolas Vayatis},
  title   = {Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy Maximization},
  journal = {Journal of Machine Learning Research},
  year    = {2025},
  volume  = {26},
  number  = {4},
  pages   = {1--68},
  url     = {http://jmlr.org/papers/v26/23-1359.html}
}