AISTATS 2020poster331 citations

Formal Limitations on the Measurement of Mutual Information

David McAllester, Karl Stratos

Abstract

Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confidence lower bound on mutual information estimated from N samples cannot be larger than O(ln N).

BibTeX
@InProceedings{pmlr-v108-mcallester20a,
  title = 	 {Formal Limitations on the Measurement of Mutual Information},
  author =       {McAllester, David and Stratos, Karl},
  booktitle = 	 {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
  pages = 	 {875--884},
  year = 	 {2020},
  editor = 	 {Chiappa, Silvia and Calandra, Roberto},
  volume = 	 {108},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {26--28 Aug},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v108/mcallester20a/mcallester20a.pdf},
  url = 	 {https://proceedings.mlr.press/v108/mcallester20a.html},
  abstract = 	 {Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confidence lower bound on mutual information estimated from N samples cannot be larger than O(ln N).}
}
Formal Limitations on the Measurement of Mutual Information · AISTATS 2020