DHTV is a framework to learn CPWL functions in an interpretable manner.

In this repository, we aim to:

• Solve the regression problem with CPWL functions.

• Reproduce of the results of the following paper:

  • Delaunay-Triangulation-Based Learning with Hessian Total-Variation Regularization.

Table of Contents

• Installation
  • Developper Install
• Usage
  • Learning example
  • Reproducing results
• Developers
• References
• Acknowledgements

Installation

To install the package, we first create an environment with python 3.7 (or greater):

>> conda create -n DHTV python==3.9.7
>> conda activate DHTV

Developper Install

>> git clone https://github.com/mehrsapo/DHTV.git
>> cd <repository_dir>/
>> conda install -n DHTV ipykernel --update-deps --force-reinstall
>> pip install --upgrade -r requirements.txt

Usage

Learning example

First we need to build the DHTV model and compute forward (H) and regularization (L) operators:

tri = MyDelaunay(X, y)  # X: input variables, y: target values
tri.construct_forward_matrix() # constructing H
tri.construct_regularization_matrix() # constructing L

Then we solve the learning task:

dhtv_sol, _ = double_fista(tri.data_values, tri.H, tri.L, tri.lip_H, tri.lip_L, lmbda, n_iter1, n_iter2, device='cuda:0')

We can use this values to predict the model values:

dhtv_predict = tri.evaluate(X, dhtv_sol.cpu().numpy())

In the 2 dimensional case, we can also plot the model using:

tri.update_values(dhtv_sol.cpu().numpy())
plot_with_gradient_map(tri, 0.5, 1, 1, 1)

See for more details <https://github.com/mehrsapo/DHTV/blob/main/intp_metric.ipynb>.

Reproducing results

The paper reults are available in notebooks IV.A, IV.B and IV.C, main_compare.py is resposible for creating the loaded data in IV.C.

Developers

DHTV is developed by the Biomedical Imaging Group, École Polytéchnique Fédérale de Lausanne, Switzerland.

References

[Pourya2022]

<https://arxiv.org/pdf/2208.07787.pdf>

Acknowledgements

This work was supported in part by the European Research Council (ERC Project FunLearn) under Grant 101020573 and in part by the Swiss National Science Foundation, Grant 200020 184646/1.