Nonparanormal Information Estimation
Shashank Singh, Barnabás Póczos
Abstract
We study the problem of using i.i.d. samples from an unknown multivariate probability distribution p to estimate the mutual information of p. This problem has recently received attention in two settings: (1) where p is assumed to be Gaussian and (2) where p is assumed only to lie in a large nonparametric smoothness class. Estimators proposed for the Gaussian case converge in high dimensions when the Gaussian assumption holds, but are brittle, failing dramatically when p is not Gaussian, while estimators proposed for the nonparametric case fail to converge with realistic sample sizes except in very low dimension. Hence, there is a lack of robust mutual information estimators for many realistic data. To address this, we propose estimators for mutual information when p is assumed to be a nonparanormal (or Gaussian copula) model, a semiparametric compromise between Gaussian and nonparametric extremes. Using theoretical bounds and experiments, we show these estimators strike a practical balance between robustness and scalability.
BibTeX
@InProceedings{pmlr-v70-singh17a,
title = {Nonparanormal Information Estimation},
author = {Shashank Singh and Barnab{\'a}s P{\'o}czos},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {3210--3219},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/singh17a/singh17a.pdf},
url = {https://proceedings.mlr.press/v70/singh17a.html},
abstract = {We study the problem of using i.i.d. samples from an unknown multivariate probability distribution p to estimate the mutual information of p. This problem has recently received attention in two settings: (1) where p is assumed to be Gaussian and (2) where p is assumed only to lie in a large nonparametric smoothness class. Estimators proposed for the Gaussian case converge in high dimensions when the Gaussian assumption holds, but are brittle, failing dramatically when p is not Gaussian, while estimators proposed for the nonparametric case fail to converge with realistic sample sizes except in very low dimension. Hence, there is a lack of robust mutual information estimators for many realistic data. To address this, we propose estimators for mutual information when p is assumed to be a nonparanormal (or Gaussian copula) model, a semiparametric compromise between Gaussian and nonparametric extremes. Using theoretical bounds and experiments, we show these estimators strike a practical balance between robustness and scalability.}
}