# The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables

arXiv: https://arxiv.org/abs/2102.07921 · HTML: https://mlsanity.com/paper/2102.07921/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2021.

## Built on by (most cited first, 15 of 15)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Learning a Structural Causal Model for Intuition Reasoning in Conversation](https://mlsanity.com/paper/2305.17727/) (2023)
- [Causal Discovery in Mixtures of Populations](https://mlsanity.com/paper/2311.07454/) (2023)
- [Enforcing Conditional Independence for Fair Representation Learning and Causal Image Generation](https://mlsanity.com/paper/2404.13798/) (2024)
- [How to Enhance Causal Discrimination of Utterances: A Case on Affective Reasoning](https://mlsanity.com/paper/2305.02615/) (2023)
- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding](https://mlsanity.com/paper/2510.02117/) (2025)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [Towards Causal Representation Learning and Deconfounding from Indefinite Data](https://mlsanity.com/paper/2305.02640/) (2023)
- [Boosting Causal Additive Models](https://mlsanity.com/paper/2401.06523/) (2024)
- [Towards Causal Relationship in Indefinite Data: Baseline Model and New Datasets](https://mlsanity.com/paper/2401.08221/) (2024)
- [Causal Discovery with Mixed Latent Confounding via Precision Decomposition](https://mlsanity.com/paper/2512.24696/) (2025)
- [LUCID: Learning Under Confounding for Inference and Discovery in Time Series](https://mlsanity.com/paper/2609.31315/) (2026)

## Abstract (arXiv)

Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. Without additional assumptions about the unobserved variables, it is not possible to recover any causal relationships from observational data. Fortunately, in many applied settings, additional structure among the confounders can be expected. In particular, pervasive confounding is commonly encountered and has been utilized for consistent causal estimation in linear causal models. In this paper, we present a provably consistent method to estimate causal relationships in the non-linear, pervasive confounding setting. The core of our procedure relies on the ability to estimate the confounding variation through a simple spectral decomposition of the observed data matrix. We derive a DAG score function based on this insight, prove its consistency in recovering a correct ordering of the DAG, and empirically compare it to previous approaches. We demonstrate improved performance on both simulated and real datasets by explicitly accounting for both confounders and non-linear effects.