`Non-asymptotic Uncertainty Quantification in High-Dimensional Learning`

Code to paper "Non-asymptotic Uncertainty Quantification in High-Dimensional Learning". Image reconstruction from single-coil MRI images with radial line subsampling mask using the It-Net and U-Net. Uncertainty Quantification using debiased estimator for different methods to calculate confidence intervals. Uncertainty Quantification for sparse regression correcting the confidence intervals provided by the debiased LASSO.

How to run the model-based regression experiments (Section 5.1 in paper)

Those experiments are implemented in Matlab.

Install the package Tfocs.
Run the file experiments_model_based_regression.m.

How to run the MRI Reconstruction experiments (Section 5.2 in paper)

Check (and modify if necessary) the configuration file config.py. It specifies the directory paths for the data and results. By default, the data should be stored in the subdirectory raw_data and results and model weights are stored in the subdirectory results.
Download the fastMRI Knee-MRI dataset and place it in the data folder specified in the configuration.
Prepare the data by running data_management.py.
Train networks using the scripts named script_train_*.py.
Test the trained models on the test set and estimation set with the files test_itnet_*.py.
Run the file UQ_Unet_restterm.py to calculate the expectation and variance of the restterm. (Algorithm 1 in the paper)
Run the file finding_gamma.py to calculate the correct gamma value. (Appendix Section A of the paper)
Run the file UQ_Unet.py to calculate hit rates on the test set for different methods to obtain confidence intervals (Algorithm 2 in the paper)
Run the file boxplot.py and confidence_intervals.py for visual representation.

Cite

If you use the method or the code, please cite the arXiv paper:

@article{hoppe2024nonasymp,
  title={{Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning}},
  author={Hoppe, Frederik and Verdun, Claudio Mayrink and Laus, Hannah and Krahmer, Felix and Rauhut, Holger},
  journal={arXiv preprint arXiv:},
  year={2024},
  doi={} 
}

Requirements

The following packages were used for running the Python code, other version might work as well.

matplotlib (v3.7.2)
numpy (v1.24.3)
pandas (v2.0.3)
piq (v0.7.0)
python (v3.8.19)
torch (v1.9.0)
scikit-image (v1.0.2)
scipy (v1.9.1)
torchvision (v0.10.0)
tqdm (v4.65.0)
h5py (v3.7.0)

Acknowledgements

The implementation of the U-Net is based on and adapt from https://github.com/mateuszbuda/brain-segmentation-pytorch/. The implementation of the It-Net and other parts of the code are based on the project https://github.com/jmaces/robust-nets/tree/master/fastmri-radial by M. Genzel, J. Macdonald, and M. März. Processing the fastMRI data is done with the code from https://github.com/facebookresearch/fastMRI. All code in fastmri_utils_new is from this Github. The package Tfocsis available at https://cvxr.com/tfocs/download/.