# Latent mixed-effect models for high-dimensional longitudinal data

arXiv: https://arxiv.org/abs/2409.11008 · HTML: https://mlsanity.com/paper/2409.11008/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 17 Sep 2024.

## Builds on (most cited first, 16 of 16)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Longitudinal Variational Autoencoder](https://mlsanity.com/paper/2006.09763/) (2020)
- [Sparse Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.10177/) (2020)
- [Scalable Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.13472/) (2020)
- [Markovian Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2207.05543/) (2022)
- [Cross-Validation for Correlated Data](https://mlsanity.com/paper/1904.02438/) (2019)

## Built on by (most cited first, 3 of 3)

- [Using latent representations to link disjoint longitudinal data for mixed-effects regression](https://mlsanity.com/paper/2510.25531/) (2025)
- [Deep Generalised Mixed Models: a Novel Neural Network Structure for Analysing Hierarchical Data](https://mlsanity.com/paper/2608.05930/) (2026)
- [Large language models as synthetic clinical experts to inform longitudinal rare-disease modeling](https://mlsanity.com/paper/2608.16507/) (2026)

## Abstract (arXiv)

Modelling longitudinal data is an important yet challenging task. These datasets can be high-dimensional, contain non-linear effects and time-varying covariates. Gaussian process (GP) prior-based variational autoencoders (VAEs) have emerged as a promising approach due to their ability to model time-series data. However, they are costly to train and struggle to fully exploit the rich covariates characteristic of longitudinal data, making them difficult for practitioners to use effectively. In this work, we leverage linear mixed models (LMMs) and amortized variational inference to provide conditional priors for VAEs, and propose LMM-VAE, a scalable, interpretable and identifiable model. We highlight theoretical connections between it and GP-based techniques, providing a unified framework for this class of methods. Our proposal performs competitively compared to existing approaches across simulated and real-world datasets.