# Controlling for discrete unmeasured confounding in nonlinear causal models

arXiv: https://arxiv.org/abs/2408.05647 · HTML: https://mlsanity.com/paper/2408.05647/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 10 Aug 2024.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Resampling Base Distributions of Normalizing Flows](https://mlsanity.com/paper/2110.15828/) (2021)
- [ParceLiNGAM: A causal ordering method robust against latent confounders](https://mlsanity.com/paper/1303.7410/) (2013)
- [On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternatives](https://mlsanity.com/paper/1902.10286/) (2019)
- [Detecting non-causal artifacts in multivariate linear regression models](https://mlsanity.com/paper/1803.00810/) (2018)
- [Detecting confounding in multivariate linear models via spectral analysis](https://mlsanity.com/paper/1704.01430/) (2017)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)

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

- [Causal Inference with Categorical Unobserved Confounder via Mixture Learning](https://mlsanity.com/paper/2605.19006/) (2026)

## Abstract (arXiv)

Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep latent variable models, we show theoretically that confounding can be detected and corrected under the assumption that the observed data is a piecewise affine transformation of a latent Gaussian mixture model and that the identity of the mixture components is confounded. We provide a flow-based algorithm to estimate this model and perform deconfounding. Experimental results on synthetic and real-world data provide support for the effectiveness of our approach.