# Estimating Causal Effects with the Neural Autoregressive Density Estimator

arXiv: https://arxiv.org/abs/2008.07283 · HTML: https://mlsanity.com/paper/2008.07283/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2020.

## Built on by (most cited first, 8 of 8)

- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2110.14690/) (2021)
- [Deep Autoregressive Models as Causal Inference Engines](https://mlsanity.com/paper/2409.18581/) (2024)
- [Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation](https://mlsanity.com/paper/2509.19112/) (2025)
- [One-Shot Multi-Label Causal Discovery in High-Dimensional Event Sequences](https://mlsanity.com/paper/2509.23213/) (2025)
- [Your Autoregressive Model Already Reveals the Causal Graph](https://mlsanity.com/paper/2602.01135/) (2026)
- [Robot Pouring: Identifying Causes of Spillage and Selecting Alternative Action Parameters Using Probabilistic Actual Causation](https://mlsanity.com/paper/2502.09395/) (2025)

## Abstract (arXiv)

Estimation of causal effects is fundamental in situations were the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables given conditional dependencies. In this paper, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within the Pearl's do-calculus framework. Using synthetic data, we show that the approach can retrieve causal effects from non-linear systems without explicitly modeling the interactions between the variables.