# Longitudinal Variational Autoencoder

arXiv: https://arxiv.org/abs/2006.09763 · HTML: https://mlsanity.com/paper/2006.09763/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2020.

## Built on by (most cited first, 25 of 25)

- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Handling missing values in healthcare data: A systematic review of deep learning-based imputation techniques](https://mlsanity.com/paper/2210.08258/) (2022)
- [Can I trust my fake data -- A comprehensive quality assessment framework for synthetic tabular data in healthcare](https://mlsanity.com/paper/2401.13716/) (2024)
- [Learning Conditional Variational Autoencoders with Missing Covariates](https://mlsanity.com/paper/2203.01218/) (2022)
- [Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes](https://mlsanity.com/paper/2302.04534/) (2023)
- [Multi-modal Gaussian Process Variational Autoencoders for Neural and Behavioral Data](https://mlsanity.com/paper/2310.03111/) (2023)
- [Pedestrian Trajectory Prediction with Missing Data: Datasets, Imputation, and Benchmarking](https://mlsanity.com/paper/2411.00174/) (2024)
- [Learning Patient-Specific Disease Dynamics with Latent Flow Matching for Longitudinal Imaging Generation](https://mlsanity.com/paper/2512.09185/) (2025)
- [Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping](https://mlsanity.com/paper/2409.04140/) (2024)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Learnable Prompt as Pseudo-Imputation: Rethinking the Necessity of Traditional EHR Data Imputation in Downstream Clinical Prediction](https://mlsanity.com/paper/2401.16796/) (2024)
- [Latent mixed-effect models for high-dimensional longitudinal data](https://mlsanity.com/paper/2409.11008/) (2024)
- [A Variational Autoencoder for Heterogeneous Temporal and Longitudinal Data](https://mlsanity.com/paper/2204.09369/) (2022)
- [Modeling Complex Disease Trajectories using Deep Generative Models with Semi-Supervised Latent Processes](https://mlsanity.com/paper/2311.08149/) (2023)
- [Structured Kernel Regression VAE: A Computationally Efficient Surrogate for GP-VAEs in ICA](https://mlsanity.com/paper/2508.09721/) (2025)
- [Dynamic Topic Language Model on Heterogeneous Children's Mental Health Clinical Notes](https://mlsanity.com/paper/2312.14180/) (2023)
- [SeqRisk: Transformer-augmented latent variable model for robust survival prediction with longitudinal data](https://mlsanity.com/paper/2409.12709/) (2024)
- [Towards Foundation Auto-Encoders for Time-Series Anomaly Detection](https://mlsanity.com/paper/2507.01875/) (2025)
- [Time-Aware Latent Space Bayesian Optimization](https://mlsanity.com/paper/2603.00935/) (2026)
- [Pixel-Space Diffusion Transformers](https://mlsanity.com/paper/2607.17585/) (2026)
- [Imputing Knowledge Tracing Data with Subject-Based Training via LSTM Variational Autoencoders Frameworks](https://mlsanity.com/paper/2302.12910/) (2023)
- [Variational Inference for Longitudinal Data Using Normalizing Flows](https://mlsanity.com/paper/2303.14220/) (2023)
- [Semi-Supervised Generative Models for Disease Trajectories: A Case Study on Systemic Sclerosis](https://mlsanity.com/paper/2407.11427/) (2024)
- [Embedding interpretable ℓ1-regression into neural networks for uncovering temporal structure in cell imaging](https://mlsanity.com/paper/2603.02899/) (2026)

## Abstract (arXiv)

Longitudinal datasets measured repeatedly over time from individual subjects, arise in many biomedical, psychological, social, and other studies. A common approach to analyse high-dimensional data that contains missing values is to learn a low-dimensional representation using variational autoencoders (VAEs). However, standard VAEs assume that the learnt representations are i.i.d., and fail to capture the correlations between the data samples. We propose the Longitudinal VAE (L-VAE), that uses a multi-output additive Gaussian process (GP) prior to extend the VAE's capability to learn structured low-dimensional representations imposed by auxiliary covariate information, and derive a new KL divergence upper bound for such GPs. Our approach can simultaneously accommodate both time-varying shared and random effects, produce structured low-dimensional representations, disentangle effects of individual covariates or their interactions, and achieve highly accurate predictive performance. We compare our model against previous methods on synthetic as well as clinical datasets, and demonstrate the state-of-the-art performance in data imputation, reconstruction, and long-term prediction tasks.