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回归中自适应稀疏性与收缩的贝叶斯方法AI 解读

Bayesian and frequentist regularization techniques are commonly employed for estimating regression models from data. However, most existing methods require practitioners to pre-specify whether the target model is dense or sparse. A recent proposal, the GLP prior distribution, addresses this limitation by bridging the gap between sparse and dense model regimes in a data-driven manner. Despite its flexibility, the GLP prior incurs high computational costs due to matrix…

基于伪似然的贝叶斯向量自回归模型强选择一致性AI 解读

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which will provide novel insights into the role of temporal dependence for…

高维贝叶斯向量自回归模型的后验一致性AI 解读

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which provides novel insights into the role of temporal dependence for…

高维贝叶斯有向无环图模型的后验图选择与估计一致性AI 解读

Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying variables. A variety of priors have been…

超越可分解图的高斯图模型贝叶斯推断AI 解读

Summary Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that, when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general non-decomposable setting. Penalized likelihood inference in contrast has made tremendous gains in the past few years in terms of scalability and tractability. Bayesian inference, however, has not had the same level of success, though a…

包络模型的贝叶斯方法AI 解读

The envelope model is a new paradigm to address estimation and prediction in multivariate analysis. Using sufficient dimension reduction techniques, it has the potential to achieve substantial efficiency gains compared to standard models. This model was first introduced by [Statist. Sinica 20 (2010) 927–960] for multivariate linear regression, and has since been adapted to many other contexts. However, a Bayesian approach for analyzing envelope models has not yet been…

具有收敛保证的高维偏相关估计凸伪似然框架AI 解读

Summary Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l 1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear…

可分解协方差图模型的 Wishart 分布AI 解读

Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph G. These models are distinctly different from the traditional concentration graph models (often also referred to as Gaussian graphical models or covariance selection models) since the zeros in the parameter are now reflected in the covariance matrix Σ, as compared to the concentration matrix Ω = Σ−1. The parameter space of interest for…