Counterfactual Reasoning in Linear Structural Equation Models
Zhihong Cai, Manabu Kuroki
Consider the case where causal relations among variables can be described as a Gaussian linear structural equation model. This paper deals with the problem of clarifying how the variance of a response variable would have changed if a treatment variable were assigned to some value (counterfactually), given that a set of variables is observed (actually). In order to achieve this aim, we reformulate the formulas of the counterfactual distribution proposed by Balke and Pearl (1995) through both the total effects and a covariance matrix of observed variables. We further extend the framework of Balke and Pearl (1995) from point observations to interval observations, and from an unconditional plan to a conditional plan. The results of this paper enable us to clarify the properties of counterfactual distribution and establish an optimal plan.
PDF Link: /papers/05/p77-cai.pdf
AUTHOR = "Zhihong Cai
and Manabu Kuroki",
TITLE = "Counterfactual Reasoning in Linear Structural Equation Models",
BOOKTITLE = "Proceedings of the Twenty-First Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-05)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2005",
PAGES = "77--84"