Estimating Density Ratio of Marginals to Joint: Applications to Causal Inference

Yukitoshi Matsushita, Taisuke Otsu, Keisuke Takahata

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
JournalJournal of Business and Economic Statistics
Publication statusAccepted/In press - 2022
Externally publishedYes


  • Causal inference
  • Nonparametric methods
  • Smoothing and nonparametric regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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