Minimum Volume Conformal Sets for Multivariate Regression

This package (PyTorch-based) provides tools for constructing and evaluating conformal prediction sets for multivariate regression, implementing our proposed Minimum Volume Conformal Sets (MVCS) method. It accompanies our paper:

Minimum Volume Conformal Sets for Multivariate Regression.

Installation

Clone this repository and install the necessary dependencies using:

pip install -r requirements.txt

Overview

The package is structured as follows:

• code/: Contains the core implementation.
  • torch_functions.py: Defines loss functions used in training.
  • MVCS.py: Implements the MVCSPredictor class.
  • example_usage_MVCS_predictor.ipynb: Demonstrates how to use the implemented methods.
• experiments/: Contains experimental evaluations.
  • one_matrix_MVCS/: Experiments for Section 2 of the paper.
  • adaptive_MVCS/: Experiments for Sections 3 and 5.
    • code/: Code for adaptive MVCS experiments.
    • parameters/: JSON files defining hyperparameters for different strategies.

Using MVCSPredictor

The MVCSPredictor class requires two models as input:

• A center model, which should ideally be pre-trained.
• A matrix model, used to construct conformal sets.

Basic Usage

from code.MVCS import MVCSPredictor

# Initialize with pre-trained models
predictor = MVCSPredictor(center_model, matrix_model)

# Fit the models to data
predictor.fit(trainloader)

# Conformalize the prediction sets
predictor.conformalize(calibrationloader)

# Get volume and coverage
volume = predictor.get_volume(x_test)
coverage = predictor.get_coverage(testloader)

Running Experiments

Section 2: One-Matrix MVCS

Navigate to the experiments/one_matrix_MVCS/ folder and run the Jupyter notebooks to reproduce results from Section 2.

Sections 3 and 5: Adaptive MVCS

Navigate to experiments/adaptive_MVCS/code/ and run:

python generate_experiment.py name_of_the_parameter_file

where name_of_the_parameter_file.json is in experiments/adaptive_MVCS/parameters/ and contains the strategy's hyperparameters. Run the file see_results_normalized.ipynb to generate the tables present in the manuscript.

Plotting Results

Plots can be generated using Jupyter notebooks in experiments/adaptive_MVCS/code/.

Citation

If you use this repository for research purposes, please cite our paper:

Minimum Volume Conformal Sets for Multivariate Regression.

For any questions, feel free to open an issue or contact us.