goent - GO Implementation of Entropy Measures

Measures for discrete state spaces

Averaged measures

• Entropy

  • Shannon
  • Maximum Likelihood with Bias Correction
  • Horvitz-Thompson
  • Chao-Shen

• Conditional Entropy

• Mutual Information

• Conditional Mutual Information

• Max Entropy Estimations:

  • Iterative Scaling

• Information Decomposition (Bertschinger et al., 2014) for binary variables

• Morphological Computation measures have been moved to gomi https://github.com/kzahedi/gomi

State-dependent measures

• Mutual Information

• Conditional Mutual Information

• Entropy (Shannon)

• Morphological Computation measures have been moved to gomi https://github.com/kzahedi/gomi

Measures for continuous state spaces

Averaged measures

• Kraskov-Stoegbauer-Grassberger, Algorithm 1

• Kraskov-Stoegbauer-Grassberger, Algorithm 2

• Frenzel-Pompe

• Morphological Computation measures have been moved to gomi https://github.com/kzahedi/gomi

State-dependent measures

• Kraskov-Stoegbauer-Grassberger, Algorithm 1

• Kraskov-Stoegbauer-Grassberger, Algorithm 2

• Frenzel-Pompe

• Morphological Computation measures have been moved to gomi https://github.com/kzahedi/gomi

References:

• T. M. Cover and J. A. Thomas. Elements of Information Theory, Volume 2nd. Wiley, Hoboken, New Jersey, USA, 2006.
• I. Csiszar. i-divergence geometry of probability distributions and minimization problems. Ann. Probab., 3(1):146–158, 02 1975.
• A. Chao and T.-J. Shen. Nonparametric estimation of shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003.
• S. Frenzel and B. Pompe. Partial mutual information for coupling analysis of multivariate time series. Phys. Rev. Lett., 99:204101, Nov 2007.
• A. Kraskov, H. Stoegbauer, and P. Grassberger. Estimating mutual information. Phys. Rev. E, 69:066138, Jun 2004. Bertschinger2013aQuantifying
• N. Bertschinger, J. Rauh, E. Olbrich, J. Jost, and N. Ay, Quantifying unique information, CoRR, 2013