Scalable Counterfactual Distribution Estimation in Multivariate Causal Models
This addresses a scalability and accuracy issue in causal inference for researchers and practitioners, though it is incremental as it builds on existing univariate models.
The paper tackles the problem of estimating counterfactual joint distributions in multivariate causal models, where existing methods either ignore correlations or scale poorly, and proposes a method using a latent one-dimensional subspace to capture correlations efficiently, demonstrating advantages on synthetic and real-world data.
We consider the problem of estimating the counterfactual joint distribution of multiple quantities of interests (e.g., outcomes) in a multivariate causal model extended from the classical difference-in-difference design. Existing methods for this task either ignore the correlation structures among dimensions of the multivariate outcome by considering univariate causal models on each dimension separately and hence produce incorrect counterfactual distributions, or poorly scale even for moderate-size datasets when directly dealing with such multivariate causal model. We propose a method that alleviates both issues simultaneously by leveraging a robust latent one-dimensional subspace of the original high-dimension space and exploiting the efficient estimation from the univariate causal model on such space. Since the construction of the one-dimensional subspace uses information from all the dimensions, our method can capture the correlation structures and produce good estimates of the counterfactual distribution. We demonstrate the advantages of our approach over existing methods on both synthetic and real-world data.