# Learning Structural Causal Models from Ordering: Identifiable Flow Models

**Authors:** Minh Khoa Le, Kien Do, Truyen Tran  
**arXiv:** [2412.09843](https://arxiv.org/abs/2412.09843)  
**Date:** 2024-12-13  
**Summary page:** https://www.summarizepaper.com/en/paper/2412.09843v1/

## Key points

- Study focuses on causal inference with limited observational data and valid causal ordering from causal graph
- Introduces novel flow models for recovering component-wise, invertible transformations of exogenous variables
- Flow-based approach offers flexibility while maintaining causal consistency across discretization steps
- Design improvements enable simultaneous learning of all causal mechanisms, reducing abduction and prediction complexity to linear O(n)
- Outperforms existing state-of-the-art approaches in answering observational, interventional, and counterfactual questions
- Demonstrated superior performance across various synthetic and real datasets in estimating interventional and counterfactual distributions
- Proves identifiability of flow models for learning Structural Causal Models (SCMs) from observational data and causal ordering
- Novel model designs enable parallel abduction and approximated prediction, reducing computational requirements while maintaining high performance levels
- Validation on diverse datasets confirms effectiveness and efficiency of proposed methods
- Innovative approach to learning SCMs from limited data sources without compromising on model flexibility or computational efficiency

## Summary

This study focuses on addressing causal inference with limited observational data and a valid causal ordering from the causal graph. The researchers introduce a novel set of flow models that can recover component-wise, invertible transformations of exogenous variables. Unlike previous methods, their flow-based approach offers flexibility while maintaining causal consistency across different discretization steps. The proposed method includes design improvements that enable simultaneous learning of all causal mechanisms, reducing abduction and prediction complexity to linear O(n) relative to the number of layers. This advancement allows for efficient handling of large structural causal models and outperforms existing state-of-the-art approaches in answering observational, interventional, and counterfactual questions. Empirical demonstrations showcase the superior performance of the method across various synthetic and real datasets. It excels in estimating both the mean and overall shape of interventional and counterfactual distributions, proving its scalability and effectiveness as dataset complexity increases. Key contributions include proving the identifiability of flow models for learning Structural Causal Models (SCMs) from observational data and causal ordering. The introduction of novel model designs enables parallel abduction and approximated prediction, significantly reducing computational requirements while maintaining high performance levels. Validation on diverse datasets further confirms the effectiveness and efficiency of the proposed methods. In comparison to recent advances in deep generative models applied to SCMs, this study stands out for its innovative approach to learning SCMs from limited data sources without compromising on model flexibility or computational efficiency. The research opens up new possibilities for practical applications requiring accurate causal inference in complex systems.