Causal Effect Estimation.pdf

Estimating the effect of multiple simultaneous interventions in the presence of hidden confounders.

Approach: Utilize single-variable interventions, where each treatment variable is intervened on separately, in addition to observational data.

Key Assumptions:

1. Data generated from a nonlinear continuous structural causal model with additive Gaussian noise.
2. Access to sets of single-variable interventional data.

Methodology:

1. Identifiability: Prove that the effect of joint interventions is identifiable under the assumed model.
2. Parameter Estimation: Propose a simple method by pooling all data from different regimes and jointly maximizing the combined likelihood.

Experiments:

1. Conduct comprehensive experiments to verify the identifiability result.
2. Compare the performance of the proposed approach against a baseline on both synthetic and real-world data.

Contribution:

1. Introduce a setting where single-variable interventions are used to estimate joint interventional effects.
2. Provide a means to dramatically reduce the number of interventional experiments needed to estimate the effect of joint interventions.

Background and Related Work:

1. Structural Causal Models (SCMs): Utilize the SCM framework to encode causal assumptions.
2. Perfect Intervention: Leverage the invariance of structural equations to define a mathematical operator for performing perfect intervention.