# Moment Matching Deep Contrastive Latent Variable Models

arXiv: https://arxiv.org/abs/2202.10560 · HTML: https://mlsanity.com/paper/2202.10560/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [Information Constraints on Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1805.08672/) (2018)
- [Contrastive Variational Autoencoder Enhances Salient Features](https://mlsanity.com/paper/1902.04601/) (2019)
- [Removal of Batch Effects using Distribution-Matching Residual Networks](https://mlsanity.com/paper/1610.04181/) (2016)
- [Unsupervised learning with contrastive latent variable models](https://mlsanity.com/paper/1811.06094/) (2018)
- [Probabilistic Contrastive Principal Component Analysis](https://mlsanity.com/paper/2012.07977/) (2020)
- [Contrastive latent variable modeling with application to case-control sequencing experiments](https://mlsanity.com/paper/2102.06731/) (2021)
- [Learning Disentangled Representations with Reference-Based Variational Autoencoders](https://mlsanity.com/paper/1901.08534/) (2019)

## Built on by (most cited first, 13 of 13)

- [Learning Fair Representation via Distributional Contrastive Disentanglement](https://mlsanity.com/paper/2206.08743/) (2022)
- [SepVAE: a contrastive VAE to separate pathological patterns from healthy ones](https://mlsanity.com/paper/2307.06206/) (2023)
- [Double InfoGAN for Contrastive Analysis](https://mlsanity.com/paper/2401.17776/) (2024)
- [Separating common from salient patterns with Contrastive Representation Learning](https://mlsanity.com/paper/2402.11928/) (2024)
- [Toward the Identifiability of Comparative Deep Generative Models](https://mlsanity.com/paper/2401.15903/) (2024)
- [Feature Selection in the Contrastive Analysis Setting](https://mlsanity.com/paper/2310.18531/) (2023)
- [Learning Common and Salient Generative Factors Between Two Image Datasets](https://mlsanity.com/paper/2512.12800/) (2025)
- [Contrastive independent component analysis](https://mlsanity.com/paper/2407.02357/) (2024)
- [H-SPLID: HSIC-based Saliency Preserving Latent Information Decomposition](https://mlsanity.com/paper/2510.20627/) (2025)
- [Unsupervised contrastive analysis for anomaly detection in brain MRIs via conditional diffusion models](https://mlsanity.com/paper/2406.00772/) (2024)
- [Diff-CA: Separating Common and Salient Factors with Diffusion Models](https://mlsanity.com/paper/2606.06120/) (2026)
- [CASL-VAE: Learning Structured Latent Variables from Unpaired Data for Semi-supervised Clustering and Paired Sample Generation](https://mlsanity.com/paper/2607.08254/) (2026)
- [Counterfactual Contrastive Analysis](https://mlsanity.com/paper/2608.19032/) (2026)

## Abstract (arXiv)

In the contrastive analysis (CA) setting, machine learning practitioners are specifically interested in discovering patterns that are enriched in a target dataset as compared to a background dataset generated from sources of variation irrelevant to the task at hand. For example, a biomedical data analyst may seek to understand variations in genomic data only present among patients with a given disease as opposed to those also present in healthy control subjects. Such scenarios have motivated the development of contrastive latent variable models to isolate variations unique to these target datasets from those shared across the target and background datasets, with current state of the art models based on the variational autoencoder (VAE) framework. However, previously proposed models do not explicitly enforce the constraints on latent variables underlying CA, potentially leading to the undesirable leakage of information between the two sets of latent variables. Here we propose the moment matching contrastive VAE (MM-cVAE), a reformulation of the VAE for CA that uses the maximum mean discrepancy to explicitly enforce two crucial latent variable constraints underlying CA. On three challenging CA tasks we find that our method outperforms the previous state-of-the-art both qualitatively and on a set of quantitative metrics.