Nonparanormal Information Estimation

Shashank Singh, Barnabás Póczos
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3210-3219, 2017.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Nonparanormal Information Estimation %A Shashank Singh %A Barnabás Póczos %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-singh17a %I PMLR %P 3210--3219 %U https://proceedings.mlr.press/v70/singh17a.html %V 70 %X 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.
APA
Singh, S. & Póczos, B.. (2017). Nonparanormal Information Estimation. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3210-3219 Available from https://proceedings.mlr.press/v70/singh17a.html.

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