# Discovery of Single Independent Latent Variable

arXiv: https://arxiv.org/abs/2110.05887 · HTML: https://mlsanity.com/paper/2110.05887/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 67 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [Fader Networks: Manipulating Images by Sliding Attributes](https://mlsanity.com/paper/1706.00409/) (2017)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [Jasper: An End-to-End Convolutional Neural Acoustic Model](https://mlsanity.com/paper/1904.03288/) (2019)
- [Structured Disentangled Representations](https://mlsanity.com/paper/1804.02086/) (2018)
- [Learning Independent Features with Adversarial Nets for Non-linear ICA](https://mlsanity.com/paper/1710.05050/) (2017)
- [Nonparametric Canonical Correlation Analysis](https://mlsanity.com/paper/1511.04839/) (2015)
- [A Universal Music Translation Network](https://mlsanity.com/paper/1805.07848/) (2018)
- [ESPnet-se: end-to-end speech enhancement and separation toolkit designed for asr integration](https://mlsanity.com/paper/2011.03706/) (2020)
- [Unsupervised Singing Voice Conversion](https://mlsanity.com/paper/1904.06590/) (2019)
- [TTS Skins: Speaker Conversion via ASR](https://mlsanity.com/paper/1904.08983/) (2019)

## Built on by (most cited first, 3 of 3)

- [Contrast Everything: A Hierarchical Contrastive Framework for Medical Time-Series](https://mlsanity.com/paper/2310.14017/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Provable Speech Attributes Conversion via Latent Independence](https://mlsanity.com/paper/2510.05191/) (2025)

## Abstract (arXiv)

Latent variable discovery is a central problem in data analysis with a broad range of applications in applied science. In this work, we consider data given as an invertible mixture of two statistically independent components and assume that one of the components is observed while the other is hidden. Our goal is to recover the hidden component. For this purpose, we propose an autoencoder equipped with a discriminator. Unlike the standard nonlinear ICA problem, which was shown to be non-identifiable, in the special case of ICA we consider here, we show that our approach can recover the component of interest up to entropy-preserving transformation. We demonstrate the performance of the proposed approach in several tasks, including image synthesis, voice cloning, and fetal ECG extraction.