Bayesian generalized fused lasso modeling via NEG distribution

Shimamura, Kaito; Ueki, Masao; Kawano, Shuichi; Konishi, Satoshi

doi:10.1080/03610926.2018.1489056

Cited by 16 publications

(25 citation statements)

References 20 publications

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“…Hence, it doesn't encourage the posterior of θ i to be grouped with either θ i−1 or θ i+1 . It is worth to mention that the NEG-fusion prior [40] also has a similar plot pattern for its conditional prior density function. But a critical difference between t prior and NEG prior, is that the density for NEG prior is non-differentiable at 0.…”

Section: Bayesian Modelingmentioning

confidence: 67%

“…[29,45]. The penalty term λ n i=2 |θ i − θ i−1 | is can be interpreted as the negative logarithm of prior density used for Bayesian inferences, therefore, a nature Bayesian expansion to (2) is Laplace (double exponential) prior modeling [24,40]. To account for the unknown variance parameter σ 2 and θ 1 , a convenient prior specification could be…”

Section: Bayesian Modelingmentioning

confidence: 99%

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Bayesian Fusion Estimation via t Shrinkage

Song

Cheng

2019

Sankhya A

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Shrinkage prior has gained great successes in many data analysis, however, its applications mostly focus on the Bayesian modeling of sparse parameters. In this work, we will apply Bayesian shrinkage to model high dimensional parameter that possesses an unknown blocking structure. We propose to impose heavy-tail shrinkage prior, e.g., t prior, on the differences of successive parameter entries, and such a fusion prior will shrink successive differences towards zero and hence induce posterior blocking.Comparing to conventional Bayesian fused lasso which implements Laplace fusion prior, t fusion prior induces stronger shrinkage effect and enjoys a nice posterior consistency property. Simulation studies and real data analyses show that t fusion has superior performance to the frequentist fusion estimator and Bayesian Laplace-fusion prior. This t-fusion strategy is further developed to conduct a Bayesian clustering analysis, and simulation shows that the proposed algorithm obtains better posterior distributional convergence than the classical Dirichlet process modeling.

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Section: Bayesian Modelingmentioning

confidence: 67%

Section: Bayesian Modelingmentioning

confidence: 99%

Bayesian Fusion Estimation via t Shrinkage

Song

Cheng

2019

Sankhya A

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“…Specifically, we specify the (i, j)th element of

{bold∑}_{{bold-italicθ}_{bold-italicm}}^{- 1}

as follows:

{([], {bold∑}_{{bold-italicθ}_{bold-italicm}}^{bold- bold1})}_{i j} = ({, \begin{matrix} array \frac{1}{τ_{m i}^{2}} + \frac{k_{i} - 1}{ω_{m}^{2}}, & array i = j, \\ array - \frac{1}{ω_{m}^{2}}, & array i \neq j, gene i and j are positively associated, \\ array \frac{1}{ω_{m}^{2}}, & array i \neq j, gene i and j are negatively associated, \\ array 0, & array i \neq j, gene i and j are not directly associated, \end{matrix})

where k i is the number of nonzero elements in the i th row or column of

{bold∑}_{{bold-italicθ}_{bold-italicm}}^{bold- bold1}

, ie, k i −1 is the number of genes that interact with gene i within the pathway. Note that

{bold∑}_{{bold-italicθ}_{bold-italicm}}^{bold- bold1}

gives the general form of the Bayesian generalized fused lasso formulation by allowing negative and no associations between two off‐diagonal elements in addition to positive associations. Thus, we model the off‐diagonal elements of

{bold∑}_{{bold-italicθ}_{bold-italicm}}^{bold- bold1}

to introduce correlations between interacting genes given prior biological information.…”

Section: Methodsmentioning

confidence: 99%

“…where k i is the number of nonzero elements in the ith row or column of − 1 m , ie, k i − 1 is the number of genes that interact with gene i within the pathway. Note that − 1 m gives the general form of the Bayesian generalized fused lasso formulation 20 by allowing negative and no associations between two off-diagonal elements in addition to positive associations. Thus, we model the off-diagonal elements of − 1 m to introduce correlations between interacting genes given prior biological information.…”

Section: Generalized Fused Hierarchical Structured Variable Selectionmentioning

confidence: 99%

A Bayesian hierarchical variable selection prior for pathway‐based GWAS using summary statistics

Yang

Basu

Zhang

2019

Statistics in Medicine

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While genome‐wide association studies (GWASs) have been widely used to uncover associations between diseases and genetic variants, standard SNP‐level GWASs often lack the power to identify SNPs that individually have a moderate effect size but jointly contribute to the disease. To overcome this problem, pathway‐based GWASs methods have been developed as an alternative strategy that complements SNP‐level approaches. We propose a Bayesian method that uses the generalized fused hierarchical structured variable selection prior to identify pathways associated with the disease using SNP‐level summary statistics. Our prior has the flexibility to take in pathway structural information so that it can model the gene‐level correlation based on prior biological knowledge, an important feature that makes it appealing compared to existing pathway‐based methods. Using simulations, we show that our method outperforms competing methods in various scenarios, particularly when we have pathway structural information that involves complex gene‐gene interactions. We apply our method to the Wellcome Trust Case Control Consortium Crohn's disease GWAS data, demonstrating its practical application to real data.

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“…The most intuitive approaches to solve a sparse linear regression model is lasso [46] and its extensions such as SCAD [47], Elastic net [48], fused lasso [49], adaptive lasso [50], Bayesian-type lasso [51]- [53]. In Bayesian frameworks, lasso estimates can be interpreted as posterior mode estimates with independent and identical Laplace prior for coefficients [46], [51].…”

Section: The Bayesian Lassomentioning

confidence: 99%

A Sparse Bayesian Learning Method for Structural Equation Model-Based Gene Regulatory Network Inference

Liu

Chu

et al. 2020

IEEE Access

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Gene regulatory networks (GRNs) are underlying networks identified by interactive relationships between genes. Reconstructing GRNs from massive genetic data is important for understanding gene functions and biological mechanism, and can provide effective service for medical treatment and genetic research. A series of artificial intelligence based methods have been proposed to infer GRNs from both gene expression data and genetic perturbations. The accuracy of such algorithms can be better than those models that just consider gene expression data. A structural equation model (SEM), which provides a systematic framework integrating both types of gene data conveniently, is a commonly used model for GRN inference. Considering the sparsity of GRNs, in this paper, we develop a novel sparse Bayesian inference algorithm based on Normal-Equation-Gamma (NEG) type hierarchical prior (BaNEG) to infer GRNs modeled with SEMs more accurately. First, we reparameterize an SEM as a linear type model by integrating the endogenous and exogenous variables; Then, a Bayesian adaptive lasso with a three-level NEG prior is applied to deduce the corresponding posterior mode and estimate the parameters. Simulations on synthetic data are run to compare the performance of BaNEG to some state-of-the-art algorithms, the results demonstrate that the proposed algorithm visibly outperforms the others. What's more, BaNEG is applied to infer underlying GRNs from a real data set composed of 47 yeast genes from Saccharomyces cerevisiae to discover potential relationships between genes. INDEX TERMS Sparse Bayesian learning, high-dimensional data, gene regulatory network, gene expression data, structural equation model.

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Bayesian generalized fused lasso modeling via NEG distribution

Cited by 16 publications

References 20 publications

Bayesian Fusion Estimation via t Shrinkage

Bayesian Fusion Estimation via t Shrinkage

A Bayesian hierarchical variable selection prior for pathway‐based GWAS using summary statistics

A Sparse Bayesian Learning Method for Structural Equation Model-Based Gene Regulatory Network Inference

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