A Flexible Framework for Nonparametric Graphical Modeling that Accommodates Machine Learning

Yunhua Xiang, Noah Simon
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:10442-10451, 2020.

Abstract

Graphical modeling has been broadly useful for exploring the dependence structure among features in a dataset. However, the strength of graphical modeling hinges on our ability to encode and estimate conditional dependencies. In particular, commonly used measures such as partial correlation are only meaningful under strongly parametric (in this case, multivariate Gaussian) assumptions. These assumptions are unverifiable, and there is often little reason to believe they hold in practice. In this paper, we instead consider 3 non-parametric measures of conditional dependence. These measures are meaningful without structural assumptions on the multivariate distribution of the data. In addition, we show that for 2 of these measures there are simple, strong plug-in estimators that require only the estimation of a conditional mean. These plug-in estimators (1) are asymptotically linear and non-parametrically efficient, (2) allow incorporation of flexible machine learning techniques for conditional mean estimation, and (3) enable the construction of valid Wald-type confidence intervals. In addition, by leveraging the influence function of these estimators, one can obtain intervals with simultaneous coverage guarantees for all pairs of features.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-xiang20a, title = {A Flexible Framework for Nonparametric Graphical Modeling that Accommodates Machine Learning}, author = {Xiang, Yunhua and Simon, Noah}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {10442--10451}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/xiang20a/xiang20a.pdf}, url = {https://proceedings.mlr.press/v119/xiang20a.html}, abstract = {Graphical modeling has been broadly useful for exploring the dependence structure among features in a dataset. However, the strength of graphical modeling hinges on our ability to encode and estimate conditional dependencies. In particular, commonly used measures such as partial correlation are only meaningful under strongly parametric (in this case, multivariate Gaussian) assumptions. These assumptions are unverifiable, and there is often little reason to believe they hold in practice. In this paper, we instead consider 3 non-parametric measures of conditional dependence. These measures are meaningful without structural assumptions on the multivariate distribution of the data. In addition, we show that for 2 of these measures there are simple, strong plug-in estimators that require only the estimation of a conditional mean. These plug-in estimators (1) are asymptotically linear and non-parametrically efficient, (2) allow incorporation of flexible machine learning techniques for conditional mean estimation, and (3) enable the construction of valid Wald-type confidence intervals. In addition, by leveraging the influence function of these estimators, one can obtain intervals with simultaneous coverage guarantees for all pairs of features.} }
Endnote
%0 Conference Paper %T A Flexible Framework for Nonparametric Graphical Modeling that Accommodates Machine Learning %A Yunhua Xiang %A Noah Simon %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-xiang20a %I PMLR %P 10442--10451 %U https://proceedings.mlr.press/v119/xiang20a.html %V 119 %X Graphical modeling has been broadly useful for exploring the dependence structure among features in a dataset. However, the strength of graphical modeling hinges on our ability to encode and estimate conditional dependencies. In particular, commonly used measures such as partial correlation are only meaningful under strongly parametric (in this case, multivariate Gaussian) assumptions. These assumptions are unverifiable, and there is often little reason to believe they hold in practice. In this paper, we instead consider 3 non-parametric measures of conditional dependence. These measures are meaningful without structural assumptions on the multivariate distribution of the data. In addition, we show that for 2 of these measures there are simple, strong plug-in estimators that require only the estimation of a conditional mean. These plug-in estimators (1) are asymptotically linear and non-parametrically efficient, (2) allow incorporation of flexible machine learning techniques for conditional mean estimation, and (3) enable the construction of valid Wald-type confidence intervals. In addition, by leveraging the influence function of these estimators, one can obtain intervals with simultaneous coverage guarantees for all pairs of features.
APA
Xiang, Y. & Simon, N.. (2020). A Flexible Framework for Nonparametric Graphical Modeling that Accommodates Machine Learning. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:10442-10451 Available from https://proceedings.mlr.press/v119/xiang20a.html.

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