Yukitoshi Matsushita, Taisuke Otsu and Keisuke Takahata

Published 7 January 2022

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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 paper applies the general least square density ratio estimation methodology by Kanamori, Hido and Sugiyama (2009) 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.