标题： 关于高斯条件分布的弱收敛性 显示英文标题

标题： On weak convergence of Gaussian conditional distributions

摘要： 联合分布的弱收敛通常不意味着条件分布的收敛。 特别是，当联合高斯分布收敛到一个奇异高斯极限时，条件分布可能不会收敛。 代数上，这是由于在奇异协方差矩阵处，Schur补不是矩阵元素的连续函数。 我们的结果列出了高斯条件分布仍然收敛的特殊条件，并举例说明了这如何使人们能够对一类新的图模型中的条件独立性进行推理。 显示英文摘要

摘要： Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit. Algebraically, this is due to the fact that at singular covariance matrices, Schur complements are not continuous functions of the matrix entries. Our results lay out special conditions under which convergence of Gaussian conditional distributions nevertheless occurs, and we exemplify how this allows one to reason about conditional independence in a new class of graphical models.