# Anchored Variational Inference for Personalized Sequential Latent-State Models

arXiv: https://arxiv.org/abs/2604.23454 · HTML: https://mlsanity.com/paper/2604.23454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 25 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Stochastic Variational Inference for Hidden Markov Models](https://mlsanity.com/paper/1411.1670/) (2014)
- [Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation](https://mlsanity.com/paper/2404.09113/) (2024)
- [HMM for Discovering Decision-Making Dynamics Using Reinforcement Learning Experiments](https://mlsanity.com/paper/2401.13929/) (2024)
- [A Hierarchical Random Effects State-space Model for Modeling Brain Activities from Electroencephalogram Data](https://mlsanity.com/paper/2310.03164/) (2023)
- [Joint modeling for learning decision-making dynamics in behavioral experiments](https://mlsanity.com/paper/2506.02394/) (2025)

## Abstract (arXiv)

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.