On an additive partial correlation operator and nonparametric estimation of graphical models

  title={On an additive partial correlation operator and nonparametric estimation of graphical models},
  author={Kuang‐Yao Lee and Bing Li and Hongyu Zhao},
  pages={513 - 530}
Abstract We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive… 

Figures and Tables from this paper

An additive graphical model for discrete data

A nonparametric graphical model for discrete node variables based on additive conditional independence that does not suffer from the restriction of a parametric model such as the Ising model is introduced and the new graphical model reduces to a conditional independence graphical model under certain sparsity conditions.

Nonparametric and high-dimensional functional graphical models

A more flexible model is provided which relaxes the linearity assumption by replacing it by an arbitrary additive form and establishes statistical guarantees for the resulting estimators, which can be used to prove consistency if the dimension and the number of functional principal components diverge to infinity with the sample size.

On principal graphical models with application to gene network

Functional structural equation model

  • Kuang‐Yao LeeLexin Li
  • Mathematics, Computer Science
    Journal of the Royal Statistical Society. Series B, Statistical methodology
  • 2022
A functional structural equation model for estimating directional relations from multivariate functional data is introduced, and the consistencies of order determination, sparse functional additive regression, and directed acyclic graph estimation are established.

Multiple matrix Gaussian graphs estimation

  • Yunzhang ZhuLexin Li
  • Computer Science
    Journal of the Royal Statistical Society. Series B, Statistical methodology
  • 2018
This work employs non‐convex penalization to tackle the estimation of multiple graphs from matrix‐valued data under a matrix normal distribution and establishes the asymptotic properties of the estimator, which requires less stringent conditions and has a sharper probability error bound than existing results.

Linear operator‐based statistical analysis: A useful paradigm for big data

In this article we lay out some basic structures, technical machineries, and key applications, of Linear Operator‐Based Statistical Analysis, and organize them toward a unified paradigm. This

Differential network analysis: A statistical perspective

  • A. Shojaie
  • Biology
    WIREs Computational Statistics
  • 2020
This article provides a review of recent statistical machine learning methods for inferring networks and identifying changes in their structures.

A Nonparametric Graphical Model for Functional Data With Application to Brain Networks Based on fMRI

A nonparametric graphical model whose observations on vertices are functions based on additive conditional independence (ACI), a statistical relation that captures the spirit of conditional independence without resorting to multi-dimensional kernels is introduced.

Networks for Compositional Data



Graph Estimation with Joint Additive Models.

This work proposes a semi-parametric method, graph estimation with joint additive models, which allows the conditional means of the features to take on an arbitrary additive form, and shows that it performs better than existing methods when there are non-linear relationships among the features, and is comparable to methods that assume multivariate normality when the conditional Means are linear.

On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis

We introduce a nonparametric method for estimating non-Gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among

Partial Correlation Estimation by Joint Sparse Regression Models

It is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables, and also outperforms two existing methods.

Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models

This work shows that with general nonparametric models, under some mild technical conditions, the proposed independence screening methods have a sure screening property and the extent to which the dimensionality can be reduced by independence screening is also explicitly quantified.

Variable selection via additive conditional independence

It is demonstrated that the method proposed performs better than existing methods when the predictor affects several attributes of the response, and it performs competently in the classical setting where the predictors affect the mean only.

High Dimensional Semiparametric Gaussian Copula Graphical Models

It is proved that the nonparanormal skeptic achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation, and this result suggests that the NonParanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian.

Model selection and estimation in the Gaussian graphical model

The implementation of the penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model is nontrivial, but it is shown that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization.

Sparse Estimation of Conditional Graphical Models With Application to Gene Networks

This work introduces a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects, and introduces two sparse estimators of this matrix using the reproduced kernel Hilbert space combined with lasso and adaptive lasso.

PC algorithm for nonparanormal graphical models

Analyzing the error propagation from marginal to partial correlations, it is proved that high-dimensional consistency carries over to a broader class of Gaussian copula or nonparanormal models when using rank-based measures of correlation.

Kernel dimension reduction in regression

We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate X from