# Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learning

arXiv: https://arxiv.org/abs/2502.10883 · HTML: https://mlsanity.com/paper/2502.10883/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 57 references that are in the map.
- First posted on arXiv 15 Feb 2025.

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

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Discovering Causal Signals in Images](https://mlsanity.com/paper/1605.08179/) (2016)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [The Randomized Causation Coefficient](https://mlsanity.com/paper/1409.4366/) (2014)
- [Causal discovery for observational sciences using supervised machine learning](https://mlsanity.com/paper/2202.12813/) (2022)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [A Review on Algorithms for Constraint-based Causal Discovery](https://mlsanity.com/paper/1611.03977/) (2016)

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

- [DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms](https://mlsanity.com/paper/2607.11510/) (2026)
- [Test Time Training for Supervised Causal Learning](https://mlsanity.com/paper/2605.30015/) (2026)
- [Demistifying Data and Simulator Assumptions in Supervised Causal Discovery](https://mlsanity.com/paper/2609.37446/) (2026)

## Abstract (arXiv)

Causal discovery is a structured prediction task that aims to predict causal relations among variables based on their data samples. Supervised Causal Learning (SCL) is an emerging paradigm in this field. Existing Deep Neural Network (DNN)-based methods commonly adopt the "Node-Edge approach", in which the model first computes an embedding vector for each variable-node, then uses these variable-wise representations to concurrently and independently predict for each directed causal-edge. In this paper, we first show that this architecture has some systematic bias that cannot be mitigated regardless of model size and data size. We then propose SiCL, a DNN-based SCL method that predicts a skeleton matrix together with a v-tensor (a third-order tensor representing the v-structures). According to the Markov Equivalence Class (MEC) theory, both the skeleton and the v-structures are identifiable causal structures under the canonical MEC setting, so predictions about skeleton and v-structures do not suffer from the identifiability limit in causal discovery, thus SiCL can avoid the systematic bias in Node-Edge architecture, and enable consistent estimators for causal discovery. Moreover, SiCL is also equipped with a specially designed pairwise encoder module with a unidirectional attention layer to model both internal and external relationships of pairs of nodes. Experimental results on both synthetic and real-world benchmarks show that SiCL significantly outperforms other DNN-based SCL approaches.