# Overview

Atlassian Sourcetree is a free Git and Mercurial client for Windows.

Atlassian Sourcetree is a free Git and Mercurial client for Mac.

# README

Firstly, this module implements the notion of a "joint probability distribution" among discrete stochastic variables, as well as many common operations for them. Secondly, it implements many information-theoretical quantities such as Shannon entropy, mutual information, information synergy, information-based optimization procedures, and robustness tests.

### QUICK START

- Basic PDF operations.

from jointpdf import JointProbabilityMatrix # randomly generated joint probability mass function p(A,B) # of 2 discrete stochastic variables, each having 3 possible values p_AB = JointProbabilityMatrix(2,3) # all possible value assignments to the stochastic variable # sum to probability 1 assert sum([p_AB(states) for states in p_AB.statespace()]) == 1 # obtain the marginal distribution p(A) by marginalization p_A = p_AB[0] # obtain the conditional probability distribution p(B|A) # [can also directly use .conditional_distributions(...)] p_B_given_A = p_AB - p_A # create the joint pmf again from summing a marginal with a conditional, since p(a,b) = p(a)*p(b|a) assert p_AB == p_A + p_B_given_A

- Basic information-theoretical measures

# Shannon entropy p_AB.entropy() p_A.entropy() # mutual information between I(A:B) p_AB.mutual_information([0], [1]) # append a third variable C which is deterministically computed from A and B, i.e., such that I(A,B:C)=H(C) p_AB.append_redundant_variables(1) p_ABC = p_AB # compute the information synergy that C contains about A and B (takes a while) p_ABC.synergistic_information([2], [0,1])

- Basic information-theoretical measures

from jointpdf import JointProbabilityMatrix # randomly generate a joint probability mass function p(A,B,C) # of 3 discrete stochastic variables, each having 4 possible values p_ABC = JointProbabilityMatrix(3,4) # compute e.g. mutual information between I(A:B) p_ABC.mutual_information([0], [1]) # compute the information synergy that C contains about A and B (takes a while) p_ABC.synergistic_information([2], [0,1])

### LICENSE

Copyright 2016. This software is written and maintained by Rick Quax (University of Amsterdam). See the LICENSE.md file for licensing details.