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Teleological Inference in Structural Causal Models via Intentional Interventions

Dario Compagno, Fabio Massimo Zennaro

Abstract

Structural causal models (SCMs) were conceived to formulate and answer causal questions. This paper shows that SCMs can also be used to formulate and answer teleological questions, concerning the intentions of a state-aware, goal-directed agent intervening in a causal system. We review limitations of previous approaches to modeling such agents, and then introduce intentional interventions, a new time-agnostic operator that induces a twin SCM we call a structural final model (SFM). SFMs treat observed values as the outcome of intentional interventions and relate them to the counterfactual conditions of those interventions (what would have happened had the agent not intervened). We show how SFMs can be used to empirically detect agents and to discover their intentions.

Teleological Inference in Structural Causal Models via Intentional Interventions

Abstract

Structural causal models (SCMs) were conceived to formulate and answer causal questions. This paper shows that SCMs can also be used to formulate and answer teleological questions, concerning the intentions of a state-aware, goal-directed agent intervening in a causal system. We review limitations of previous approaches to modeling such agents, and then introduce intentional interventions, a new time-agnostic operator that induces a twin SCM we call a structural final model (SFM). SFMs treat observed values as the outcome of intentional interventions and relate them to the counterfactual conditions of those interventions (what would have happened had the agent not intervened). We show how SFMs can be used to empirically detect agents and to discover their intentions.
Paper Structure (53 sections, 13 theorems, 4 equations, 7 figures, 1 table)

This paper contains 53 sections, 13 theorems, 4 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Desiderata for intention modeling
  4. Previous approaches to intention modeling
  5. Factoring intention into exogenous variables.
  6. Factoring intention into endogenous variables.
  7. Factoring agents into the time dimension.
  8. A new approach to intention modeling
  9. Assumptions for intention modeling
  10. Intentional interventions and structural final models
  11. Properties of SFMs and intentional interventions
  12. Teleological inference
  13. Detecting agents
  14. Intention discovery
  15. Conclusion
  16. ...and 38 more sections

Key Result

Proposition 1

SFMs imply DAGs.

Figures (7)

  • Figure 1: (a) Causal model for a heating system defined over variables $W,T,H$ (for Weather, room Temperature, Heater status); we collect the data in the adjacent table. (b) Causal model for smoking defined over variables $S,P,D$ (for Smoking, Pleasure, lung Damage).
  • Figure 2: (a) The DAG for a generic SCM $\mathcal{M}_{}$; solid nodes represent endogenous variables, dashed nodes represent exogenous variables. (b) The DAG after intervention $\textrm{do}(X=1)$. (c) The twin graph for the counterfactual $\textrm{ctf}(\cdot_{X=0}\vert X=1)$; black nodes represent actual variables, gray nodes represent counterfactual variables. (d) The twin graph for the intentional intervention $\textrm{do}^\star(X^\star=f(y))$.
  • Figure 3: Existing approaches to account for agents' intentions: (a) factoring into exogenous variables; (b) factoring into endogenous variables; (c) time-based models.
  • Figure 4: (a) SFM for heating. (b) SFM for smoking.
  • Figure 5: SFM for detecting intentional interventions in colliders.
  • ...and 2 more figures

Theorems & Definitions (29)

  • Definition 1: SCM pearl2009causality
  • Definition 2: (Perfect) Intervention pearl2009causality
  • Definition 3: Mechanism Change tian2013causal
  • Definition 4: Counterfactual pearl2009causality
  • Definition 5: Twin model
  • Definition 6: Intentional Intervention and Structural Final Model
  • Proposition 1
  • Lemma 1
  • Lemma 2
  • Proposition 2: Identifiability for detecting agents in simple colliders
  • ...and 19 more