# Distribution-consistency Structural Causal Models

arXiv: https://arxiv.org/abs/2401.15911 · HTML: https://mlsanity.com/paper/2401.15911/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Uplift Modeling for Multiple Treatments with Cost Optimization](https://mlsanity.com/paper/1908.05372/) (2019)
- [Free Lunch! Retrospective Uplift Modeling for Dynamic Promotions Recommendation within ROI Constraints](https://mlsanity.com/paper/2008.06293/) (2020)
- [Unit Selection with Causal Diagram](https://mlsanity.com/paper/2109.07556/) (2021)
- [Personalised Decision-Making without Counterfactuals](https://mlsanity.com/paper/2301.11976/) (2023)

## Built on by (most cited first, 1 of 1)

- [Toward Machine Learning with the Unit as a Primitive: Learning from Unit-Linked Events](https://mlsanity.com/paper/2608.25118/) (2026)

## Abstract (arXiv)

In the field of causal modeling, potential outcomes (PO) and structural causal models (SCMs) stand as the predominant frameworks. However, these frameworks face notable challenges in practically modeling counterfactuals, formalized as parameters of the joint distribution of potential outcomes. Counterfactual reasoning holds paramount importance in contemporary decision-making processes, especially in scenarios that demand personalized incentives based on the joint values of (Y(0), Y(1)). This paper begins with an investigation of the PO and SCM frameworks for modeling counterfactuals. Through the analysis, we identify an inherent model capacity limitation, termed as the ``degenerative counterfactual problem'', emerging from the consistency rule that is the cornerstone of both frameworks. To address this limitation, we introduce a novel textitdistribution-consistency assumption, and in alignment with it, we propose the Distribution-consistency Structural Causal Models (DiscoSCMs) offering enhanced capabilities to model counterfactuals. To concretely reveal the enhanced model capacity, we introduce a new identifiable causal parameter, textitthe probability of consistency, which holds practical significance within DiscoSCM alone, showcased with a personalized incentive example. Furthermore, we provide a comprehensive set of theoretical results about the ``Ladder of Causation'' within the DiscoSCM framework. We hope it opens new avenues for future research of counterfactual modeling, ultimately enhancing our understanding of causality and its real-world applications.