Sequential latent-variable models with subject-specific random effects provide a flexible framework for modeling temporally structured data with both local latent dynamics and stable between-subject heterogeneity. In such models, conditional inference for the local latent process is often tractable, but integrating over subject-specific random effects can be computationally demanding. We propose an anchored variational inference framework for efficient approximate inference in this setting. The central idea is to replace the full conditional posterior of the local latent process with its evaluation at a representative value of the subject-specific latent effect, called the anchor point, thereby preserving tractable local inference while substantially reducing computational cost. This approximation is especially appealing in sequential settings, where the posterior distribution of the random effect becomes increasingly concentrated as the sequence length grows. Under suitable conditions, we show that the posterior mean is a nearly optimal anchor point and that the resulting anchored variational EM (AVEM) algorithm approximately preserves the local monotonicity behavior of standard variational inference. We instantiate the framework in two representative classes of sequential latent-variable models, namely mixed hidden Markov models and mixed-effects state-space models, derive the corresponding AVEM algorithms, and use simulation studies to indicate that the resulting methods achieve accurate estimation with substantial computational gains. We also discuss a partially anchored variant of the framework, in which only the components of the subject-specific latent effect whose posteriors are well concentrated are anchored.

翻译：具有受试者特异性随机效应的序列潜变量模型为同时包含局部潜在动态和稳定个体间异质性的时序数据建模提供了灵活框架。在此类模型中，局部潜在过程的条件推断通常易于处理，但对受试者特异性随机效应的积分可能带来高昂的计算代价。我们提出了一种锚定变分推断框架，用于实现该场景下的高效近似推断。核心思想是：用局部潜在过程在受试者特异性潜在效应代表性取值（称为锚定点）处的评估替代其完整条件后验，从而在保留局部推断可处理性的同时大幅降低计算成本。该近似在序列设定中尤其引人关注——随着序列长度增加，随机效应的后验分布会愈加集中。在适当条件下，我们证明后验均值是近乎最优的锚定点，且由此导出的锚定变分期望最大化算法可近似保持标准变分推断的局部单调性特性。我们以两类代表性序列潜变量模型（混合隐马尔可夫模型与混合效应状态空间模型）为例实例化该框架，推导相应AVEM算法，并通过仿真研究表明所提方法能在实现精确估计的同时带来显著计算收益。此外，我们还讨论了框架的部分锚定变体——仅对后验分布高度集中的受试者特异性潜在效应分量进行锚定。