BROJA_2PID: Bertschinger-Rauh-Olbrich-Jost-Ay (BROJA) bivariate Partial Information Decomposition

This Python module implements the Bertschinger-Rauh-Olbrich-Jost-Ay bivariate Partial Information Decomposition (N. Bertschinger, J. Rauh, E. Olbrich, J. Jost, N. Ay, Quantifying Unique Information. Entropy 2014, 16, 2161-2183; doi:10.3390/e16042161.).

It uses the Exponential Cone Programming approach described in

• A. Makkeh, D.O. Theis, R. Vicente, Bivariate Partial Information Decomposition: The Optimization Perspective (Entropy 19, 530 (2017)), and
• Abdullah Makkeh's PhD thesis Applications of Optimization in Some Complex Systems (2018)

The details of the implementation, user interface, and example code are described in

• A. Makkeh, D.O. Theis, R. Vicente, BROJA-2PID: A cone programming based Partial Information Decomposition estimator, Entropy 2018, 20(4), 271-291; doi:10.3390/e20040271.

If you use this software...

...we ask that you give proper reference. If you use it with only small modifications (note the Apache 2.0 license), use

@Article{makkeh2018broja,
  author =       {Makkeh, Abdullah and Theis, Dirk Oliver and Vicente, Raul},
  title =        {BROJA-2PID: A robust estimator for Bertschinger et al.'s bivariate partial information decomposition},
  journal =      {Entropy},
  volume =    {20},
  number =    {4},
  pages =     {271},
  year =         2018,
  publisher={Multidisciplinary Digital Publishing Institute}
}

If you make significant modifications but stick to the approach based on the Exponential Cone Programming model, use

@Article{makkeh-theis-vicente:pidOpt:2017,
  author =       {Makkeh, Abdullah and Theis, Dirk Oliver and Vicente, Raul},
  title =        {Bivariate Partial Information Decomposition: The Optimization Perspective},
  journal =      {Entropy},
  year =         2017,
  volume =    {19},
  number =    {10},
  pages =     {530},
  note    = {\url{http://dx.doi.org/10.3390/e19100530}}
}

Files

The following files contain tests:

• test_from_file_computeUI_dit.py: testcase for random distributions read from files in randompdfs\ folder to compare the BROJA_2PID algorithms with iterative divergence minimization algorithm from the Github repository computeUI and with the Frank-Wolfe implementation in the dit.

• test_large_random_computeUI_dit.py: testcase for random distributions generated simultaneously to compare the BROJA_2PID algorithms with iterative divergence minimization algorithm from the Github repository computeUI and with the Frank-Wolfe implementation in the dit.

• test_large_copy_computeUI_dit.py: testcase for Copy gate to compare the BROJA_2PID algorithms with iterative divergence minimization algorithm from the Github repository computeUI and with the Frank-Wolfe implementation in the dit.

• test_gates_computeUI_dit.py: testcase for some logical gate to compare the BROJA_2PID algorithms with iterative divergence minimization algorithm from the Github repository computeUI and with the Frank-Wolfe implementation in the dit.

Contributors

• Abdullah Makkeh, Algorithms & theory, Institute of Computer Science, University of Tartu, Tartu, Estonia.

• Dirk Oliver Theis, Algorithms & theory, Institute of Computer Science, University of Tartu, Tartu, Estonia.

• Raul Vicente, Computational Neuroscience Lab, Institute of Computer Science, University of Tartu, Tartu, Estonia.