A Flexible Framework for Nonparametric Graphical Modeling that Accommodates Machine Learning.
Year: 2020
Type: article
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 nonparametric 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.
Source: PubMed
Authors: Yunhua Xiang, Noah Simon
Institution: University of Washington
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Institutes of Health
OpenAlex ID: W3035677922