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

Li, Bing; Chun, Hyonho; Zhao, Hongyu

doi:10.1080/01621459.2014.882842

Cited by 27 publications

(46 citation statements)

References 24 publications

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“…Li et al . () used a similar construction based on the

L_{2}

inner product. Similarly, let

{normalΣ}_{X^{i} Y} \in B false(H_{Y}, H_{X^{i}} false)

be defined by

{⟨ f, {normalΣ}_{X^{i} Y} g ⟩}_{H_{X^{i}}} = cov false{f (X^{i}), g (Y) false} .

Let

{normalΣ}_{X Y} \in B false(H_{Y}, H_{X} false)

be defined such that, for each

g \in {scriptH}_{Y}

{normalΣ}_{X Y} g = {normalΣ}_{X^{l} Y} g + \dots + {normalΣ}_{X^{p} Y} g .

We can think of

Σ_{X Y}

as the vector of operators whose i th entry is

Σ_{X^{i} Y}

.…”

Section: Additive Reproducing Kernel Hilbert Space and Related Operatorsmentioning

confidence: 99%

“…Li et al . () showed that relationship (3) captures the spirit of conditional independence (CI) in the sense that it satisfies the axioms of a semigraphoid, as developed by Pearl and Verma () and Pearl et al . ().…”

Section: Introductionmentioning

confidence: 95%

“…To achieve the flexibility that is offered by expression (2) without resorting to multi‐dimensional kernels, we use an alternative criterion, additive conditional independence (ACI), which was introduced by Li et al . (), in the context of statistical graphical models.…”

Section: Introductionmentioning

confidence: 99%

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Variable Selection via Additive Conditional Independence

Lee

Zhao

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

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We propose a non-parametric variable selection method which does not rely on any regression model or predictor distribution. The method is based on a new statistical relationship, called additive conditional independence, that has been introduced recently for graphical models. Unlike most existing variable selection methods, which target the mean of the response, the method proposed targets a set of attributes of the response, such as its mean, variance or entire distribution. In addition, the additive nature of this approach offers non-parametric flexibility without employing multi-dimensional kernels. As a result it retains high accuracy for high dimensional predictors. We establish estimation consistency, convergence rate and variable selection consistency of the method proposed. Through simulation comparisons we demonstrate 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. We apply the new method to a data set concerning how gene expression levels affect the weight of mice.

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“…Li et al . () used a similar construction based on the

L_{2}

inner product. Similarly, let

{normalΣ}_{X^{i} Y} \in B false(H_{Y}, H_{X^{i}} false)

be defined by

{⟨ f, {normalΣ}_{X^{i} Y} g ⟩}_{H_{X^{i}}} = cov false{f (X^{i}), g (Y) false} .

Let

{normalΣ}_{X Y} \in B false(H_{Y}, H_{X} false)

be defined such that, for each

g \in {scriptH}_{Y}

{normalΣ}_{X Y} g = {normalΣ}_{X^{l} Y} g + \dots + {normalΣ}_{X^{p} Y} g .

We can think of

Σ_{X Y}

as the vector of operators whose i th entry is

Σ_{X^{i} Y}

.…”

Section: Additive Reproducing Kernel Hilbert Space and Related Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Variable Selection via Additive Conditional Independence

Lee

Zhao

2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

Self Cite

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show abstract

“…Lee, Li, & Zhao () extended partial correlation to partial correlation operator and used it as a criterion to construct nonparametric graphical models. Due to its better scaling the partial correlation operator performs better than the covariance operator for constructing nonparametric graphical models Li, Chun, & Zhao ().…”

Section: Operators For Nonlinearitymentioning

confidence: 99%

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

2017

Can J Statistics

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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 paradigm can play an important role in analyzing big data due to the nature of linear operators: they process large number of functions in batches. The system accommodates at least four statistical settings: multivariate data analysis, functional data analysis, nonlinear multivariate data analysis via kernel learning, and nonlinear functional data analysis via kernel learning. We develop five linear operators within each statistical setting: the covariance operator, the correlation operator, the conditional covariance operator, the regression operator, and the partial correlation operator, which provide us with a powerful means to study the interconnections between random variables or random functions in a nonparametric and comprehensive way. We present a case study tracing the development of sufficient dimension reduction, and describe in detail how these linear operators play increasingly critical roles in its recent development. We also present a coordinate mapping method which can be systematically applied to implement these operators at the sample level. The Canadian Journal of Statistics 46: 79–103; 2018 © 2017 Statistical Society of Canada

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“…Li et al . () proposed a similar model to study the graphical structure that is induced by additive conditional independence and focused on its theoretical features. Although these methods modelled general associations, they did not allow for adjusting for covariates X .…”

Section: Introductionmentioning

confidence: 99%

False Discovery Rate Control for High Dimensional Networks of Quantile Associations Conditioning on Covariates

Xie

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary. Motivated by gene coexpression pattern analysis, we propose a novel sample quantile contingency (SQUAC) statistic to infer quantile associations conditioning on covariates. It features enhanced flexibility in handling variables with both arbitrary distributions and complex association patterns conditioning on covariates. We first derive its asymptotic null distribution, and then develop a multiple-testing procedure based on the SQUAC statistic to test simultaneously the independence between one pair of variables conditioning on covariates for all p(p–1)/2 pairs. Here, p is the length of the outcomes and could exceed the sample size. The testing procedure does not require resampling or perturbation and thus is computationally efficient. We prove by theory and numerical experiments that this testing method asymptotically controls the false discovery rate. It outperforms all alternative methods when the complex association patterns exist. Applied to a gastric cancer data set, this testing method successfully inferred the gene coexpression networks of early and late stage patients. It identified more changes in the networks which are associated with cancer survivals. We extend our method to the case that both the length of the outcomes and the length of covariates exceed the sample size, and show that the asymptotic theory still holds.

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

Cited by 27 publications

References 24 publications

Variable Selection via Additive Conditional Independence

Variable Selection via Additive Conditional Independence

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

False Discovery Rate Control for High Dimensional Networks of Quantile Associations Conditioning on Covariates

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