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超越局部独立：具有共享块结构的高维潜类别图模型AI 解读

Latent class models are central tools for multivariate categorical data from heterogeneous populations, but their standard local-independence assumption is often unrealistic in modern high-dimensional applications. We propose a high-dimensional latent class graphical model for ordinal responses with block-structured local dependence. The model retains the interpretability and parsimony of classical latent class analysis by imposing a shared block partition of variables,…

高维线性回归中的参数化平均场经验贝叶斯AI 解读

In this paper, we consider the problem of parametric empirical Bayes estimation of an i.i.d. prior in high-dimensional Bayesian linear regression, with random design. We obtain the asymptotic distribution of the variational Empirical Bayes (vEB) estimator, which approximately maximizes a variational lower bound of the intractable marginal likelihood. We characterize a sharp phase transition behavior for the vEB estimator -- namely that it is information theoretically optimal…