Efficient Estimation of Mutual Information for Strongly Dependent Variables
Shuyang Gao, Greg Ver Steeg, Aram Galstyan
Abstract
We demonstrate that a popular class of non-parametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI between two strongly dependent variables is possible only for prohibitively large sample size. This important yet overlooked shortcoming of the existing estimators is due to their implicit reliance on local uniformity of the underlying joint distribution. We introduce a new estimator that is robust to local non-uniformity, works well with limited data, and is able to capture relationship strengths over many orders of magnitude. We demonstrate the superior performance of the proposed estimator on both synthetic and real-world data.
BibTeX
@InProceedings{pmlr-v38-gao15,
title = {{Efficient Estimation of Mutual Information for Strongly Dependent Variables}},
author = {Gao, Shuyang and Ver Steeg, Greg and Galstyan, Aram},
booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
pages = {277--286},
year = {2015},
editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
volume = {38},
series = {Proceedings of Machine Learning Research},
address = {San Diego, California, USA},
month = {09--12 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v38/gao15.pdf},
url = {https://proceedings.mlr.press/v38/gao15.html},
abstract = {We demonstrate that a popular class of non-parametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI between two strongly dependent variables is possible only for prohibitively large sample size. This important yet overlooked shortcoming of the existing estimators is due to their implicit reliance on local uniformity of the underlying joint distribution. We introduce a new estimator that is robust to local non-uniformity, works well with limited data, and is able to capture relationship strengths over many orders of magnitude. We demonstrate the superior performance of the proposed estimator on both synthetic and real-world data.}
}