NAME

CInet::Polyhedral - Building blocks for polyhedral geometry

SYNOPSIS

# Imports all related modules
use CInet::Polyhedral;

VERSION

This document describes CInet::Polyhedral v0.1.0.

DESCRIPTION

This module provides access to software for polyhedral geometry, in particular to a linear programming solver. Linear programming is known to apply to conditional independence through concepts such as polymatroids and structural semigraphoids.

The main object of this module is a CInet::Imset. An imset is an integer-valued multiset. It associates to each subset of a given set N an integer number. Studený uses imsets in the theory of conditional independence structures to describe information inequalities, that is linear inequalities with integer coefficients on the cone on multiinformation functions, the faces of which correspond to CI structures. The work of Matúš studies dually integer polymatroids, which are abstractions of entropies or multiinformation functions, which can also be written as imsets. Each imset requires a CInet::Cube domain over which (that is over whose vertices) it is defined.

In the future, syntactic sugar similar to CInet::Propositional will be provided to write down linear programs for CI purposes clearly and quickly. Based on this, objects and methods will be added which expose the link between polyhedral geometry and CI implication but also blend in with the interface of CInet::Base.

AUTHOR

Tobias Boege tobs@taboege.de

COPYRIGHT AND LICENSE

This software is copyright (C) 2020 by Tobias Boege.

This is free software; you can redistribute it and/or modify it under the terms of the Artistic License 2.0.