# Learning Conditional Variational Autoencoders with Missing Covariates

arXiv: https://arxiv.org/abs/2203.01218 · HTML: https://mlsanity.com/paper/2203.01218/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 2 Mar 2022.

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

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Deep Convolutional Inverse Graphics Network](https://mlsanity.com/paper/1503.03167/) (2015)
- [Auxiliary Deep Generative Models](https://mlsanity.com/paper/1602.05473/) (2016)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [SOM-VAE: Interpretable Discrete Representation Learning on Time Series](https://mlsanity.com/paper/1806.02199/) (2018)
- [Generative Models of Visually Grounded Imagination](https://mlsanity.com/paper/1705.10762/) (2017)
- [VAEs in the Presence of Missing Data](https://mlsanity.com/paper/2006.05301/) (2020)
- [Longitudinal Variational Autoencoder](https://mlsanity.com/paper/2006.09763/) (2020)
- [Hybrid VAE: Improving Deep Generative Models using Partial Observations](https://mlsanity.com/paper/1711.11566/) (2017)

## Built on by (most cited first, 10 of 10)

- [VTAE: Variational Transformer Autoencoder with Manifolds Learning](https://mlsanity.com/paper/2304.00948/) (2023)
- [3D Brain and Heart Volume Generative Models: A Survey](https://mlsanity.com/paper/2210.05952/) (2022)
- [Deep Generative Domain Adaptation with Temporal Attention for Cross-User Activity Recognition](https://mlsanity.com/paper/2403.17958/) (2024)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [A Variational Autoencoder for Heterogeneous Temporal and Longitudinal Data](https://mlsanity.com/paper/2204.09369/) (2022)
- [Morphology-Aware Peptide Discovery via Masked Conditional Generative Modeling](https://mlsanity.com/paper/2509.02060/) (2025)
- [Unleashing the Potential of Synthetic Images: A Study on Histopathology Image Classification](https://mlsanity.com/paper/2409.16002/) (2024)
- [High-dimensional reliability-based design optimization using stochastic emulators](https://mlsanity.com/paper/2604.05759/) (2026)
- [Entropy Transformer Networks: A Learning Approach via Tangent Bundle Data Manifold](https://mlsanity.com/paper/2307.12517/) (2023)
- [Characterizing the Predictive Impact of Modalities with Supervised Latent-Variable Modeling](https://mlsanity.com/paper/2602.16979/) (2026)

## Abstract (arXiv)

Conditional variational autoencoders (CVAEs) are versatile deep generative models that extend the standard VAE framework by conditioning the generative model with auxiliary covariates. The original CVAE model assumes that the data samples are independent, whereas more recent conditional VAE models, such as the Gaussian process (GP) prior VAEs, can account for complex correlation structures across all data samples. While several methods have been proposed to learn standard VAEs from partially observed datasets, these methods fall short for conditional VAEs. In this work, we propose a method to learn conditional VAEs from datasets in which auxiliary covariates can contain missing values as well. The proposed method augments the conditional VAEs with a prior distribution for the missing covariates and estimates their posterior using amortised variational inference. At training time, our method marginalises the uncertainty associated with the missing covariates while simultaneously maximising the evidence lower bound. We develop computationally efficient methods to learn CVAEs and GP prior VAEs that are compatible with mini-batching. Our experiments on simulated datasets as well as on a clinical trial study show that the proposed method outperforms previous methods in learning conditional VAEs from non-temporal, temporal, and longitudinal datasets.