Bayesian Inference in Nonparanormal Graphical Models

Mulgrave, Jami J.; Ghosal, Subhashis

doi:10.1214/19-ba1159

Cited by 12 publications

(19 citation statements)

References 58 publications

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“…This feature makes a key advantage of GGM that it avoids spurious correlations. The nonparanormal graphical model, one derivative of GGM, is a semiparametric generalization for continuous variables and has emerged as an important tool for modeling dependency structure between items ( Mulgrave and Ghosal, 2020 ; Xue and Zou, 2012 ; Zhang, 2019 , 2020 ). These models can be incorporated to precisely infer the dependency structures of biomolecules ( Liu et al., 2012 ; Yin and Li, 2011 ; Zhang et al., 2016 ).…”

Section: Resultsmentioning

confidence: 99%

Interrogating cell type-specific cooperation of transcriptional regulators in 3D chromatin

Zheng

et al. 2021

iScience

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Summary Context-specific activities of transcription regulators (TRs) in the nucleus modulate spatiotemporal gene expression precisely. Using the largest ChIP-seq data and chromatin loops in the human K562 cell line, we initially interrogated TR cooperation in 3D chromatin via a graphical model and revealed many known and novel TRs manipulating context-specific pathways. To explore TR cooperation across broad tissue/cell types, we systematically leveraged large-scale open chromatin profiles, computational footprinting, and high-resolution chromatin interactions to investigate tissue/cell type-specific TR cooperation. We first delineated a landscape of TR cooperation across 40 human tissue/cell types. Network modularity analyses uncovered the commonality and specificity of TR cooperation in different conditions. We also demonstrated that TR cooperation information can better interpret the disease-causal variants identified by genome-wide association studies and recapitulate cell states during neural development. Our study characterizes shared and unique patterns of TR cooperation associated with the cell type specificity of gene regulation in 3D chromatin.

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Section: Resultsmentioning

confidence: 99%

Interrogating cell type-specific cooperation of transcriptional regulators in 3D chromatin

Zheng

et al. 2021

iScience

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“…Network‐based change‐point detection can then be reduced to a testing problem whether

μ

and/or

normalΣ

are significantly different or not over two nonoverlapping time periods. For more details and recent work on nonparanormal graphical models, we refer the readers to Mulgrave and Ghosal ().…”

Section: Discussion and Future Workmentioning

confidence: 99%

Change‐point analysis in financial networks

Banerjee

Guhathakurta

2020

Stat

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A major impact of globalization has been the information flow across the financial markets rendering them vulnerable to financial contagion. Research has focused on network analysis techniques to understand the extent and nature of such information flow. It is now an established fact that a stock market crash in one country can have a serious impact on other markets across the globe. It follows that such crashes or critical regimes will affect the network dynamics of the global financial markets. In this paper, we use sequential change point detection in dynamic networks to detect changes in the network characteristics of thirteen stock markets across the globe. Our method helps us to detect changes in network behavior across all known stock market crashes during the period of study. In most of the cases, we can detect a change in the network characteristics prior to crash. Our work thus opens the possibility of using this technique to create a warning bell for critical regimes in financial markets.

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“…Liu et al [79] developed a two-step estimation process in which the functions were estimated first using a truncated empirical through the relations f j (x) = Φ −1 (F j (x)), where F j stands for the cumulative distribution function of X j . Two different Bayesian approaches were considered by Mulgrave and Ghosal [90,89,88] -based on imposing a prior on the underlying monotone transforms in the first two papers, and based on a ranklikelihood which eliminates the role of the transformations in the third. In the first approach, a finite random series based on a B-spline basis expansion is used to construct a prior on the transformation.…”

Section: Nonparanormal Graphical Modelmentioning

confidence: 99%

“…Sparsity in these coef-ficients was introduced through continuous shrinkage priors by increasing sparsity with the index as in Subsection 5.3. The resulting procedure is considerably faster than the direct approach of Mulgrave and Ghosal [90]. Mulgrave and Ghosal [89] also considered the mean-field variational approach for even faster computation.…”

Section: Nonparanormal Graphical Modelmentioning

confidence: 99%

Bayesian inference in high-dimensional models

Banerjee,

Castillo,

Ghosal

2021

Preprint

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Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lowerdimensional structure. In regression problems with a large number of predictors, the model is often assumed to be sparse, with only a few predictors active. Interdependence between a large number of variables is succinctly described by a graphical model, where variables are represented by nodes on a graph and an edge between two nodes is used to indicate their conditional dependence given other variables. Many procedures for making inferences in the high-dimensional setting, typically using penalty functions to induce sparsity in the solution obtained by minimizing a loss function, were developed. Bayesian methods have been proposed for such problems more recently, where the prior takes care of the sparsity structure. These methods have the natural ability to also automatically quantify the uncertainty of the inference through the posterior distribution. Theoretical studies of Bayesian procedures in high-dimension have been carried out recently. Questions that arise are, whether the posterior distribution contracts near the true value of the parameter at the minimax optimal rate, whether the correct lower-dimensional structure is discovered with high posterior probability, and whether a credible region has adequate frequentist coverage. In this paper, we review these properties of Bayesian and related methods for several high-dimensional models such as many normal means problem, linear regression, generalized linear models, Gaussian and non-Gaussian graphical models. Effective computational approaches are also discussed.

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Bayesian Inference in Nonparanormal Graphical Models

Cited by 12 publications

References 58 publications

Interrogating cell type-specific cooperation of transcriptional regulators in 3D chromatin

Interrogating cell type-specific cooperation of transcriptional regulators in 3D chromatin

Change‐point analysis in financial networks

Bayesian inference in high-dimensional models

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