Estimating Density Ratio of Marginals to Joint: Applications to Causal Inference
应用最小二乘密度比估计方法，估计处理变量与协变量的边际密度乘积与联合密度之比，用于连续处理效应和剂量反应曲线的因果推断，并通过模拟和总统竞选广告数据验证。
In various fields of data science, researchers often face problems of estimating the ratios of two probability densities. Particularly in the context of causal inference, the product of marginals for a treatment variable and covariates to their joint density ratio typically emerges in the process of constructing causal effect estimators. This article applies the general least square density ratio estimation methodology by Kanamori, Hido and Sugiyama to the product of marginals to joint density ratio, and demonstrates its usefulness particularly for causal inference on continuous treatment effects and dose-response curves. The proposed method is illustrated by a simulation study and an empirical example to investigate the treatment effect of political advertisements in the U.S. presidential campaign data.