# Algorithmic syntactic causal identification

**Authors:** Dhurim Cakiqi, Max A. Little  
**arXiv:** [2403.09580](https://arxiv.org/abs/2403.09580)  
**Date:** 2024-03-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2403.09580v1/

## Key points

- Within plays a crucial role in deriving interventional distributions from observational data in the realm of causal inference.
- Traditional approaches to causal inference, such as d-separation and do-calculus, are rooted in classical probability theory on CBNs but face limitations in various causal settings where probability theory is not applicable.
- A new approach has emerged that replaces classical probability theory with the axiomatic foundation of [unspecified].
- This alternative axiomatization allows for a clear distinction between the syntax of causal models and their semantic implementations.
- Utilizing this framework enables a purely syntactic algorithmic description of general causality through recent formulations of the general ID algorithm.
- The methodology focuses on the non-parametric ADMG structure and algebraic signature of the corresponding monoidal category to derive desired syntactic interventional causal models.
- This approach facilitates the development of purely syntactic analogues to traditional back-door and front-door methods.
- The study by Dhurim Cakiqi and Max A. Little explores this novel approach to algorithmic syntactic causality in depth, leveraging symmetric monoidal categories for modeling complex causal models beyond traditional probabilistic frameworks.

## Summary

In the realm of causal inference,  within  plays a crucial role in deriving interventional distributions from observational data. Traditional approaches to , such as d-separation and do-calculus, are rooted in classical probability theory on CBNs. However, these methods face limitations in various causal settings where probability theory is not applicable, such as relational databases, dataflow programs, distributed systems, and modern machine learning algorithms. To overcome these limitations, a new approach has emerged that replaces classical probability theory with the axiomatic foundation of . This alternative axiomatization allows for a clear distinction between the syntax of causal models and their semantic implementations. By utilizing this framework, a purely syntactic algorithmic description of general  can be achieved through recent formulations of the general ID algorithm. The proposed methodology focuses on the non-parametric ADMG structure that specifies a causal model and the algebraic signature of the corresponding monoidal category. Through a series of manipulations within this framework, a modified monoidal category is obtained, enabling the derivation of desired syntactic interventional causal models. This approach also facilitates the development of purely syntactic analogues to traditional back-door and front-door . The study by Dhurim Cakiqi and Max A. Little explores this novel approach to algorithmic syntactic  in depth. By leveraging symmetric monoidal categories as an alternative foundation for modeling causality, they demonstrate how this methodology can be applied to complex causal models beyond traditional probabilistic frameworks. The paper provides valuable insights into expanding the scope of  by embracing innovative mathematical frameworks like category theory.