# Interpretable Neural Causal Models with TRAM-DAGs

arXiv: https://arxiv.org/abs/2503.16206 · HTML: https://mlsanity.com/paper/2503.16206/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Deep Conditional Transformation Models](https://mlsanity.com/paper/2010.07860/) (2020)
- [Deep transformation models: Tackling complex regression problems with neural network based transformation models](https://mlsanity.com/paper/2004.00464/) (2020)
- [Compositional Probabilistic and Causal Inference using Tractable Circuit Models](https://mlsanity.com/paper/2304.08278/) (2023)
- [Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challenges](https://mlsanity.com/paper/2405.05025/) (2024)
- [Deep Learning With DAGs](https://mlsanity.com/paper/2401.06864/) (2024)
- [chiSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains](https://mlsanity.com/paper/2408.07545/) (2024)
- [Top-down Transformation Choice](https://mlsanity.com/paper/1706.08269/) (2017)

## Built on by (most cited first, 4 of 4)

- [Rethinking Spatio-Temporal Anomaly Detection: A Vision for Causality-Driven Cybersecurity](https://mlsanity.com/paper/2507.08177/) (2025)
- [Mechanistic Interpretability of Fine-Tuned Vision Transformers on Distorted Images: Decoding Attention Head Behavior for Transparent and Trustworthy AI](https://mlsanity.com/paper/2503.18762/) (2025)
- [Kolmogorov-Arnold causal generative models](https://mlsanity.com/paper/2603.20184/) (2026)
- [Estimating Individualized Treatment Effects in Acute Ischemic Stroke with Causal Transformation Models (TRAM-DAG): A Multi-Centre Observational Study with External RCT Validation](https://mlsanity.com/paper/2606.12623/) (2026)

## Abstract (arXiv)

The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries on all three levels of Pearl's causal hierarchy can be answered: L1 observational, L2 interventional, and L3 counterfactual. An essential aspect of modeling the SCM is to model the dependency of each variable on its causal parents. Traditionally this is done by parametric statistical models, such as linear or logistic regression models. This allows to handle all kinds of data types and fit interpretable models but bears the risk of introducing a bias. More recently neural causal models came up using neural networks (NNs) to model the causal relationships, allowing the estimation of nearly any underlying functional form without bias. However, current neural causal models are generally restricted to continuous variables and do not yield an interpretable form of the causal relationships. Transformation models range from simple statistical regressions to complex networks and can handle continuous, ordinal, and binary data. Here, we propose to use TRAMs to model the functional relationships in SCMs allowing us to bridge the gap between interpretability and flexibility in causal modeling. We call this method TRAM-DAG and assume currently that the underlying directed acyclic graph is known. For the fully observed case, we benchmark TRAM-DAGs against state-of-the-art statistical and NN-based causal models. We show that TRAM-DAGs are interpretable but also achieve equal or superior performance in queries ranging from L1 to L3 in the causal hierarchy. For the continuous case, TRAM-DAGs allow for counterfactual queries for three common causal structures, including unobserved confounding.