Bijective Causal Models: Identifiability & Theorems
Explore the counterfactual identifiability of bijective causal models, including the Backdoor Criterion, practical algorithms, and other theorems in causal modeling. Discover the implications and applications of bijective generation mechanisms in establishing causal relationships.
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Presentation Transcript
Counterfactual Identifiability of Bijective Causal Models Arash Nasr-Esfahany, Mohammad Alizadeh, Devavrat Shah
Ladder of Causation Counterfactuals ?3: Imagining ?2: Doing Interventions ?1: Seeing Associations 1/10
Background: Causal Models Causal DAG Structural Causal Model Exogenous Noise ? = ? ?,? Causal Parents 2/10
Bijective Causal Models Consist of Bijective Generation Mechanism (BGM) BGM Definition ?: ? ?, is a bijection. ?: ? = ? 1?,? . Subsumes several causal models studied in the literature: Nonlinear Additive Noise models (ANM) [Hoyer et. al., NeurIPS 2008] Location Scale Noise models (LSNM) [Immer et. al., ICML 2023] Post Nonlinear Causal Model (PNL) [Zhang et. al., UAI 2009] 3/10
Counterfactual Identifiability of BGMs ? ?( , ) ??,??~??,? Observational Data 4/10
Identifiability Theorem: The Backdoor Criterion (BC) ? X ? = ? ?,? 5/10
Identifiability Theorem: The Backdoor Criterion (BC) ? ?|? ?,? ?. X and Z can be discrete or continuous. Identifiable from ??,?,? if: ?: ?det?? ?, and ?det?? 1?, exist. (Variability) ?1, ,??+1:??|? ( |??) are distinct. Please see the paper for precise definition of this condition. 6/10
Other Identifiability Theorems The Markovian Case Instrumental Variable (IV) 7/10
Practical Algorithm ? ?|? BC Conditional Generative Model 8/10
Video Streaming Simulation CausalSim: A Causal Framework for Unbiased Trace-Driven Simulation [Alomar et. al., NSDI 2023] 9/10
Contributions Introduced Bijective Causal Models. Established their counterfactual identifiability in three well-known causal structures. Proposed a practical method for learning them. bgm.csail.mit.edu 10/10
