Python Symbolic Information Theoretic Inequality Prover
Project description
Python Symbolic Information Theoretic Inequality Prover
PSITIP is a computer algebra system for information theory written in Python. Random variables, expressions and regions are objects in Python that can be manipulated easily. Moreover, it implements a versatile deduction system for automated theorem proving. PSITIP supports features such as:
Proving linear information inequalities via the linear programming method by Yeung and Zhang. The linear programming method was first implemented in the ITIP software developed by Yeung and Yan ( http://user-www.ie.cuhk.edu.hk/~ITIP/ ).
Automated inner and outer bounds for multiuser settings in network information theory (see the Jupyter Notebook examples ).
Numerical optimization over distributions, and evaluation of rate regions involving auxiliary random variables.
Interactive mode and Parsing LaTeX code.
Finding examples of distributions where a set of constraints is satisfied.
Fourier-Motzkin elimination.
Discover inequalities via the convex hull method for polyhedron projection [Lassez-Lassez 1991].
Non-Shannon-type inequalities.
Integration with Jupyter Notebook and LaTeX output.
Generation of human-readable proofs.
Drawing information diagrams.
User-defined information quantities.
Documentation: https://github.com/cheuktingli/psitip
Jupyter Notebook examples: https://nbviewer.jupyter.org/github/cheuktingli/psitip/tree/master/examples/
About
Author: Cheuk Ting Li ( https://www.ie.cuhk.edu.hk/people/ctli.shtml ). The source code of PSITIP is released under the GNU General Public License v3.0 ( https://www.gnu.org/licenses/gpl-3.0.html ). The author would like to thank Raymond W. Yeung, Chandra Nair and Pascal O. Vontobel for their invaluable comments.
The working principle of PSITIP (existential information inequalities) is described in the following article:
C. T. Li, “An Automated Theorem Proving Framework for Information-Theoretic Results,” arXiv preprint, available: https://arxiv.org/pdf/2101.12370.pdf , 2021.
If you find PSITIP useful in your research, please consider citing the above article.
WARNING
This program comes with ABSOLUTELY NO WARRANTY. This program is a work in progress, and bugs are likely to exist. The deduction system is incomplete, meaning that it may fail to prove true statements (as expected in most automated deduction programs). On the other hand, declaring false statements to be true should be less common. If you encounter a false accept in PSITIP, please let the author know.
Installation
Running pip install psitip will install PSITIP without the necessary solvers (which may not work correctly). To install PSITIP with its dependencies, use one of the following two options:
A. Installation with conda (recommended)
Install Python via Anaconda (https://www.anaconda.com/).
Open Anaconda prompt and run:
conda install -c conda-forge glpk conda install -c conda-forge pulp conda install -c conda-forge pyomo conda install -c conda-forge lark-parser pip install pycddlib pip install --no-deps psitip(Optional) Graphviz (https://graphviz.org/) is required for drawing Bayesian networks and communication network model. It can be installed via
conda install -c conda-forge python-graphviz(Optional) If numerical optimization is needed, also install PyTorch (https://pytorch.org/).
B. Installation with pip
Install Python (https://www.python.org/downloads/).
Run (you might need to use
python3 -m piporpy -m pipinstead ofpip):pip install numpy pip install scipy pip install matplotlib pip install pulp pip install pyomo pip install lark-parser pip install pycddlib pip install psitipA linear programming solver supported by Pyomo or PuLP is required. We recommend GLPK, which can be installed on https://www.gnu.org/software/glpk/ or via conda.
(Optional) Graphviz (https://graphviz.org/) is required for drawing Bayesian networks and communication network model. A Python binding can be installed via
pip install graphviz(Optional) If numerical optimization is needed, also install PyTorch (https://pytorch.org/).
References
The general method of using linear programming for solving information theoretic inequality is based on the following work:
R. W. Yeung, “A new outlook on Shannon’s information measures,” IEEE Trans. Inform. Theory, vol. 37, pp. 466-474, May 1991.
R. W. Yeung, “A framework for linear information inequalities,” IEEE Trans. Inform. Theory, vol. 43, pp. 1924-1934, Nov 1997.
Z. Zhang and R. W. Yeung, “On characterization of entropy function via information inequalities,” IEEE Trans. Inform. Theory, vol. 44, pp. 1440-1452, Jul 1998.
Convex hull method for polyhedron projection:
C. Lassez and J.-L. Lassez, Quantifier elimination for conjunctions of linear constraints via a convex hull algorithm, IBM Research Report, T.J. Watson Research Center, RC 16779 (1991)
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