# Multivariate Counterfactual Systems And Causal Graphical Models

@article{Shpitser2020MultivariateCS, title={Multivariate Counterfactual Systems And Causal Graphical Models}, author={I. Shpitser and T. Richardson and J. Robins}, journal={arXiv: Methodology}, year={2020} }

Among Judea Pearl's many contributions to Causality and Statistics, the graphical d-separation} criterion, the do-calculus and the mediation formula stand out. In this chapter we show that d-separation} provides direct insight into an earlier causal model originally described in terms of potential outcomes and event trees. In turn, the resulting synthesis leads to a simplification of the do-calculus that clarifies and separates the underlying concepts, and a simple counterfactual formulation of… Expand

#### 5 Citations

An Interventionist Approach to Mediation Analysis.

- Mathematics, Computer Science
- 2020

A novel theory is developed here, showing that it provides a self-contained framework for discussing mediation without reference to cross-world (nested) counterfactuals or interventions on the mediator and preserves the dictum `no causation without manipulation'. Expand

Path-specific Effects Based on Information Accounts of Causality

- Computer Science, Mathematics
- ArXiv
- 2021

This paper proposes a new path intervention inspired by information accounts of causality, and develops the corresponding intervention diagrams and π-formula that could serve useful communications and theoretical focuses for mediation analysis. Expand

Entropic Inequality Constraints from e-separation Relations

- 2021

Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously… Expand

Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables

- Computer Science, Mathematics
- ArXiv
- 2021

This work presents entropic inequality constraints that are implied by eseparation relations in hidden variable DAGs with discrete observed variables, and proposes a measure of causal influence called the minimal mediary entropy, and demonstrates that it can augment traditional measures such as the average causal effect. Expand

A Formal Causal Interpretation of the Case-Crossover Design

- Mathematics
- 2020

The case-crossover design (Maclure, 1991) is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal… Expand

#### References

SHOWING 1-10 OF 51 REFERENCES

Alternative Graphical Causal Models and the Identification of Direct E!ects

- Mathematics
- 2010

We consider four classes of graphical causal models: the Finest Fully Randomized Causally Interpretable Structured Tree Graph (FFRCISTG) of Robins (1986), the agnostic causal model of Spirtes et al.… Expand

On the Testable Implications of Causal Models with Hidden Variables

- Computer Science, Mathematics
- UAI
- 2002

This paper offers a systematic way of identifying functional constraints and facilitates the task of testing causal models as well as inferring such models from data. Expand

Pearl's Calculus of Intervention Is Complete

- Mathematics, Computer Science
- UAI
- 2006

It is proved that the three basic do-calculus rules that Pearl presents are complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-Calculus that transforms the causal effect formula into a formula that only includes observational quantities. Expand

A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects

- Computer Science, Medicine
- AISTATS
- 2019

This paper uses po-calculus to give a complete identification algorithm for conditional path-specific effects with applications to problems in mediation analysis and algorithmic fairness. Expand

Causality: Models, Reasoning and Inference

- Philosophy
- 2000

1. Introduction to probabilities, graphs, and causal models 2. A theory of inferred causation 3. Causal diagrams and the identification of causal effects 4. Actions, plans, and direct effects 5.… Expand

Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality

- Mathematics
- 2013

We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a node-splitting transformation. We introduce a new graph, the… Expand

An Axiomatic Characterization of Causal Counterfactuals

- Mathematics
- 1998

This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and… Expand

Identification of Joint Interventional Distributions in Recursive Semi-Markovian Causal Models

- Computer Science
- AAAI
- 2006

A necessary and sufficient graphical condition is provided for the cases when the causal effect of an arbitrary set of variables on another arbitrary set can be determined uniquely from the available information, as well as an algorithm which computes the effect whenever this condition holds. Expand

Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias

- Mathematics, Computer Science
- UAI
- 2019

We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal… Expand

An Interventionist Approach to Mediation Analysis.

- Mathematics, Computer Science
- 2020

A novel theory is developed here, showing that it provides a self-contained framework for discussing mediation without reference to cross-world (nested) counterfactuals or interventions on the mediator and preserves the dictum `no causation without manipulation'. Expand