Local hub screening in sparse correlation graphs

Firouzi, Hamed; Hero, Alfred O.

doi:10.1117/12.2024361

Cited by 3 publications

(4 citation statements)

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“…When n ≥ p, P may be the simple plug-in estimator of the matrix inverse of the sample correlation estimator, while if n < p the correlation screening methods developed in [58] uses the Moore-Penrose generalized inverse of the sample correlation estimator. Correlation screening has been studied and applied to hub discovery [58], edge discovery [63] and classification of local node degree [41] in a variety of graphical model applications including: stationary Gaussian spatio-temporal processes models [39], [40]; sparse regression models [37]; and multiple model testing for common sparsity patterns [61].…”

Section: Correlation Mining: Screeningmentioning

confidence: 99%

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

Hero

Rajaratnam

2016

Proc. IEEE

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When can reliable inference be drawn in fue “Big Data” context? This paper presents a framework for answering this fundamental question in the context of correlation mining, wifu implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics fue dataset is often variable-rich but sample-starved: a regime where the number n of acquired samples (statistical replicates) is far fewer than fue number p of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for “Big Data”. Sample complexity however has received relatively less attention, especially in the setting when the sample size n is fixed, and the dimension p grows without bound. To address fuis gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where fue variable dimension is fixed and fue sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa cale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables fua t are of interest. Correlation mining arises in numerous applications and subsumes the regression context as a special case. we demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks.

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Section: Correlation Mining: Screeningmentioning

confidence: 99%

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

Hero

Rajaratnam

2016

Proc. IEEE

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“…Moreover, the authors provided a quantitative criterion to detect hub and non-hub nodes in the network. Other authors proposed methods to screen the hubs in the network in the context of graphical models (Firouzi and Hero (2013); Hero and Rajaratnam (2012)). However, these methods do not aim at estimating the hub network.…”

Section: Introductionmentioning

confidence: 99%

Inferring gene expression networks with hubs using a degree weighted Lasso approach

et al. 2018

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“…where Λ k,ρ is as defined in Theorem 4.1. Using [16,Thm. 3.1] it can easily be shown that the approximation error associated with (14) decays to zero at least as fast as p(1 − ρ 2 ) n/2 ∆ where ∆ is a dependency coefficient associated with the set of U-scores..…”

Section: Theorem 42 ( [16]mentioning

confidence: 99%

“…[16]): Let Σ be row sparse of degree j = o(p). Also let p → ∞ and ρ = ρ p → 1 such that p(1 − ρ 2 ) n/2 → 0.…”

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confidence: 99%

Quickest hub discovery in correlation graphs

Banerjee

Hero

2016

2016 50th Asilomar Conference on Signals, Systems and Computers

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A sequential test is proposed for detection and isolation of hubs in a correlation graph. Hubs in a correlation graph of a random vector are variables (nodes) that have a strong correlation edge. It is assumed that the random vectors are highdimensional and are multivariate Gaussian distributed. The test employs a family of novel local and global summary statistics generated from small samples of the random vectors. Delay and false alarm analysis of the test is obtained and numerical results are provided to show that the test is consistent in identifying hubs, as the false alarm rate goes to zero.

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Local hub screening in sparse correlation graphs

Cited by 3 publications

References 0 publications

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

Inferring gene expression networks with hubs using a degree weighted Lasso approach

Quickest hub discovery in correlation graphs

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