# Integrating Random Effects in Variational Autoencoders for Dimensionality Reduction of Correlated Data

arXiv: https://arxiv.org/abs/2412.16899 · HTML: https://mlsanity.com/paper/2412.16899/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 22 Dec 2024.

## Builds on (most cited first, 13 of 13)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [Auxiliary Deep Generative Models](https://mlsanity.com/paper/1602.05473/) (2016)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Variational Recurrent Auto-Encoders](https://mlsanity.com/paper/1412.6581/) (2014)
- [Integrating Random Effects in Deep Neural Networks](https://mlsanity.com/paper/2206.03314/) (2022)
- [Scalable Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.13472/) (2020)
- [Multi-Source Social Feedback of Online News Feeds](https://mlsanity.com/paper/1801.07055/) (2018)
- [Airbnb Price Prediction Using Machine Learning and Sentiment Analysis](https://mlsanity.com/paper/1907.12665/) (2019)

## Built on by (most cited first, 1 of 1)

- [Structure Learning on Clustered Data](https://mlsanity.com/paper/2607.08238/) (2026)

## Abstract (arXiv)

Variational Autoencoders (VAE) are widely used for dimensionality reduction of large-scale tabular and image datasets, under the assumption of independence between data observations. In practice, however, datasets are often correlated, with typical sources of correlation including spatial, temporal and clustering structures. Inspired by the literature on linear mixed models (LMM), we propose LMMVAE -- a novel model which separates the classic VAE latent model into fixed and random parts. While the fixed part assumes the latent variables are independent as usual, the random part consists of latent variables which are correlated between similar clusters in the data such as nearby locations or successive measurements. The classic VAE architecture and loss are modified accordingly. LMMVAE is shown to improve squared reconstruction error and negative likelihood loss significantly on unseen data, with simulated as well as real datasets from various applications and correlation scenarios. It also shows improvement in the performance of downstream tasks such as supervised classification on the learned representations.