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变分贝叶斯稀疏负二项回归AI 解读

Count data with overdispersion and high-dimensional predictors pose significant challenges in modern applications. While negative binomial regression offers a flexible modeling framework, existing Bayesian approaches rely on computationally expensive MCMC methods that become impractical in high-dimensional settings. This paper develops a variational Bayesian framework for sparse negative binomial regression using horseshoe and continuous spike-and-slab priors. Our proposed…

多元回归中高维残差协方差矩阵的受限非线性收缩AI 解读

We study estimation of the p*p residual scatter (shape) matrix in a high-dimensional multivariate linear regression, where p and n grow proportionally. When the coefficient matrix obeys a known linear restriction of rank q < d, as in multivariate analysis of variance, growth-curve models, and reduced-rank regression, the restricted fit leaves additional residual degrees of freedom that sharpen estimation of the shape matrix. To accommodate heavy-tailed errors, we work with…

MENS：金融应用中非正态变换模型的非线性收缩估计AI 解读

We develop a theory of nonlinear shrinkage covariance estimation for nonparanormal (Gaussian-copula) models, in which each observed coordinate is an unknown strictly increasing transformation of a latent Gaussian vector. This model accommodates arbitrary marginal skewness and heavy marginal tails while retaining a Gaussian dependence structure, and it is the natural semiparametric setting for heavy-tailed, asymmetric financial returns. Our estimator, marginal-free nonlinear…

采用局部—全局收缩的非正态变换有向无环图半参数贝叶斯结构学习AI 解读

Bayesian structure learning of directed acyclic graphs (DAGs) is central to high-dimensional causal discovery, yet existing methods mostly assume multivariate Gaussian data, which is routinely violated by measurements displaying heavy tails, skewness, or bounded support. We address this by introducing NPN-DAG-HS, a fully Bayesian semiparametric DAG model coupling the nonparanormal family with horseshoe shrinkage on Cholesky off-diagonals via an extended-rank likelihood. This…

通过拉普拉斯近似实现可扩展的贝叶斯有向无环图结构学习及乳腺癌应用AI 解读

Structure learning of directed acyclic graphs (DAGs) from observational data is a foundational task in causal discovery and is widely used to infer regulatory networks from medical and genomic measurements. The Bayesian formulation quantifies model uncertainty and admits prior biological knowledge, but its practical use has been hampered by the super-exponential growth of the DAG space and by the intractability of the node-marginal likelihood under flexible, non-conjugate…

比例高维下尺度混合误差的贝叶斯DAG结构学习与收缩协方差估计AI 解读

We propose a unified Bayesian framework namely robust DAG-Cholesky horseshoe (R-DACH) for joint directed acyclic graph (DAG) structure learning and precision matrix estimation in the high-dimensional proportional asymptotic regime $p/n \to c \in (0,\infty)$, under the scale mixture of normal errors. The construction places a global-local horseshoe-type prior directly on the strictly lower-triangular entries of the modified Cholesky factor of the DAG-Markov precision matrix,…

非高斯误差下全局-局部收缩先验的稳健高维贝叶斯回归AI 解读

Multivariate regression with many correlated responses and predictors commonly violates Gaussian error assumptions due to heavy tails, outliers, and asymmetry. Gaussian procedures then lose efficiency in coefficient estimation and produce biased estimates of conditional dependence graphs. We develop a robust Bayesian framework using a scale-location mixture error distribution and horseshoe+ global-local priors on both the regression coefficients and off-diagonals of the…

稀疏泊松回归的变分推断AI 解读

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding conjugacy between the approximation component and the Gaussian prior on the regression coefficient. Three sparsity-enforcing priors (Laplace, Continuous Spike and Slab, and Bernoulli) are used for this problem. The proposed models are compared…