# Variational Selective Autoencoder: Learning from Partially-Observed Heterogeneous Data

arXiv: https://arxiv.org/abs/2102.12679 · HTML: https://mlsanity.com/paper/2102.12679/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 21 of 21)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Multimodal Machine Learning: A Survey and Taxonomy](https://mlsanity.com/paper/1705.09406/) (2017)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Learning to Discover Cross-Domain Relations with Generative Adversarial Networks](https://mlsanity.com/paper/1703.05192/) (2017)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Learning Factorized Multimodal Representations](https://mlsanity.com/paper/1806.06176/) (2018)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Multi-attention Recurrent Network for Human Communication Comprehension](https://mlsanity.com/paper/1802.00923/) (2018)
- [Joint Multimodal Learning with Deep Generative Models](https://mlsanity.com/paper/1611.01891/) (2016)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Improved Variational Autoencoders for Text Modeling using Dilated Convolutions](https://mlsanity.com/paper/1702.08139/) (2017)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Learning Aligned Cross-Modal Representations from Weakly Aligned Data](https://mlsanity.com/paper/1607.07295/) (2016)
- [Statistical Speech Enhancement Based on Probabilistic Integration of Variational Autoencoder and Non-Negative Matrix Factorization](https://mlsanity.com/paper/1710.11439/) (2017)
- [VAEs in the Presence of Missing Data](https://mlsanity.com/paper/2006.05301/) (2020)
- [Data Generation as Sequential Decision Making](https://mlsanity.com/paper/1506.03504/) (2015)
- [Learning to Multitask](https://mlsanity.com/paper/1805.07541/) (2018)

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

- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2202.04599/) (2022)
- [Learning Multimodal VAEs through Mutual Supervision](https://mlsanity.com/paper/2106.12570/) (2021)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [FragmGAN: Generative Adversarial Nets for Fragmentary Data Imputation and Prediction](https://mlsanity.com/paper/2203.04692/) (2022)
- [Deep Generative Imputation Model for Missing Not At Random Data](https://mlsanity.com/paper/2308.08158/) (2023)
- [Characterizing the Predictive Impact of Modalities with Supervised Latent-Variable Modeling](https://mlsanity.com/paper/2602.16979/) (2026)
- [Amortized Variational Inference for Logistic Regression with Missing Covariates](https://mlsanity.com/paper/2603.21244/) (2026)
- [Expert-Guided Class-Conditional Goodness-of-Fit Scores for Interpretable Classification with Informative Missingness: An Application to Seismic Monitoring](https://mlsanity.com/paper/2604.14809/) (2026)

## Abstract (arXiv)

Learning from heterogeneous data poses challenges such as combining data from various sources and of different types. Meanwhile, heterogeneous data are often associated with missingness in real-world applications due to heterogeneity and noise of input sources. In this work, we propose the variational selective autoencoder (VSAE), a general framework to learn representations from partially-observed heterogeneous data. VSAE learns the latent dependencies in heterogeneous data by modeling the joint distribution of observed data, unobserved data, and the imputation mask which represents how the data are missing. It results in a unified model for various downstream tasks including data generation and imputation. Evaluation on both low-dimensional and high-dimensional heterogeneous datasets for these two tasks shows improvement over state-of-the-art models.