Strong selection consistency of Bayesian vector autoregressive models based on a pseudo-likelihood approach

Ghosh, Satyajit; Khare, Kshitij; Michailidis, George

doi:10.1214/20-aos1992

Cited by 10 publications

(6 citation statements)

References 30 publications

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“…In particular, greater dependence is estimated between the hand and the wrist on each side. Such findings justify our decision to estimate the full covariance matrix rather than adopt the pseudo likelihood approach of only estimating a diagonal covariance matrix often considered for VAR models (Ghosh et al, 2021). We further illustrate the time-varying behaviour among pairs of measurements (i.e.…”

Section: Resultsmentioning

confidence: 87%

Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity

2023

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We propose a sparse vector autoregressive (VAR) hidden semi-Markov model (HSMM) for modeling temporal and contemporaneous (e.g. spatial) dependencies in multivariate nonstationary time series. The HSMM's generic state distribution is embedded in a special transition matrix structure, facilitating efficient likelihood evaluations and arbitrary approximation accuracy. To promote sparsity of the VAR coefficients, we deploy an l 1 -ball projection prior, which combines differentiability with a positive probability of obtaining exact zeros, achieving variable selection within each switching state. This also facilitates posterior estimation via Hamiltonian Monte Carlo (HMC).We further place non-local priors on the parameters of the HSMM dwell distribution improving the ability of Bayesian model selection to distinguish whether the data is better supported by the simpler hidden Markov model (HMM), or the more flexible HSMM. Our proposed methodology is illustrated via an application to human gesture phase segmentation based on sensor data, where we successfully identify and characterize the periods of rest and active gesturing, as well as the dynamical patterns involved in the gesture movements associated with each of these states.

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Section: Resultsmentioning

confidence: 87%

Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity

2023

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“…Theorem 1 states the joint selection consistency result of

E

and

γ

given

\overset{δ}{true}

, which means that the joint posterior probability assigned to

false(γ_{0}, E_{0} false)

given

\overset{δ}{true}

goes to 1 as

n \to \infty

. As discussed in Ghosh et al (2021), this is the strongest notion of posterior selection consistency, and it implies that the true model will be the mode of the posterior distribution with probability tending to 1 as

n \to \infty

.…”

Section: Joint Selection Consistencymentioning

confidence: 88%

Development of network‐guided transcriptomic risk score for disease prediction

Cao,

Zhang,

Lee

2024

Stat

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SummaryOmics data, routinely collected in various clinical settings, are of a complex and network‐structured nature. Recent progress in RNA sequencing (RNA‐seq) allows us to explore whole‐genome gene expression profiles and to develop predictive model for disease risk. In this study, we propose a novel Bayesian approach to construct RNA‐seq‐based risk score leveraging gene expression network for disease risk prediction. Specifically, we consider a hierarchical model with spike and slab priors over regression coefficients as well as entries in the inverse covariance matrix for covariates to simultaneously perform variable selection and network estimation in high‐dimensional logistic regression. Through theoretical investigation and simulation studies, our method is shown to both enjoy desirable consistency properties and achieve superior empirical performance compared with other state‐of‐the‐art methods. We analyse RNA‐seq gene expression data from 441 asthmatic and 254 non‐asthmatic samples to form a weighted network‐guided risk score and benchmark the proposed method against existing approaches for asthma risk stratification.

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“…The derivation of ( 15) follows from computations similar to those given in Ghosh et al (2021). Let P m k denote the projection matrix into the column space of X m k and…”

Section: Proof Of Theorem 1(a)mentioning

confidence: 99%

“…To bound the third term in the RHS of (48) we recall the distribution of σ 2 k | Y, γ t and use a slight modification of Remark S1.1 of Ghosh et al (2021) with log p replaced by log(pq) wherein we show both the shape and scale of the Inverse gamma distribution are of appropriate order.…”

Section: Let B *mentioning

confidence: 99%

A generalized likelihood based Bayesian approach for scalable joint regression and covariance selection in high dimensions

Samanta¹,

Khare²,

Michailidis³

2022

Preprint

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The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity patterns are crucial to help understand the network of relationships between the predictor and response variables, as well as the conditional relationships among the latter. While Bayesian methods have the advantage of providing natural uncertainty quantification through posterior inclusion probabilities and credible intervals, current Bayesian approaches either restrict to specific sub-classes of sparsity patterns and/or are not scalable to settings with hundreds of responses and predictors. Bayesian approaches which only focus on estimating the posterior mode are scalable, but do not generate samples from the posterior distribution for uncertainty quantification. Using a bi-convex regression based generalized likelihood and spike-and-slab priors, we develop an algorithm called Joint Regression Network Selector (JRNS) for joint regression and covariance selection which (a) can accommodate general sparsity patterns, (b) provides posterior samples for uncertainty quantification, and (c) is scalable and orders of magnitude faster than the state-ofthe-art Bayesian approaches providing uncertainty quantification. We demonstrate the statistical and computational efficacy of the proposed approach on synthetic data and through the analysis of selected cancer data sets. We also establish highdimensional posterior consistency for one of the developed algorithms.

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Strong selection consistency of Bayesian vector autoregressive models based on a pseudo-likelihood approach

Cited by 10 publications

References 30 publications

Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity

Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity

Development of network‐guided transcriptomic risk score for disease prediction

A generalized likelihood based Bayesian approach for scalable joint regression and covariance selection in high dimensions

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