论文标题
基于部分线性非参数贝叶斯模型的异质治疗效应估计
Heterogeneous Treatment Effect Estimation based on a Partially Linear Nonparametric Bayes Model
论文作者
论文摘要
最近，由于其在统计，社会和生物医学科学等各个领域的重要性，有条件的平均治疗效果（CATE）估计引起了很多关注。这项研究提出了一个部分线性非参数贝叶斯模型，以进行异质治疗效果估计。部分线性模型是一个半参数模型，由以添加剂形式组成的线性和非参数组件。已经研究了使用高斯工艺对非参数组件进行建模的非参数贝叶斯模型。但是，该模型无法处理治疗效果的异质性。在我们提出的模型中，不仅是该模型的非参数成分，而且该处理变量的异质治疗效果都由先验的高斯工艺建模。我们得出CATE后验分布的分析形式，并证明后验具有一致性。也就是说，它集中于真实分布。我们通过基于综合数据来显示提出方法的有效性。
Recently, conditional average treatment effect (CATE) estimation has been attracting much attention due to its importance in various fields such as statistics, social and biomedical sciences. This study proposes a partially linear nonparametric Bayes model for the heterogeneous treatment effect estimation. A partially linear model is a semiparametric model that consists of linear and nonparametric components in an additive form. A nonparametric Bayes model that uses a Gaussian process to model the nonparametric component has already been studied. However, this model cannot handle the heterogeneity of the treatment effect. In our proposed model, not only the nonparametric component of the model but also the heterogeneous treatment effect of the treatment variable is modeled by a Gaussian process prior. We derive the analytic form of the posterior distribution of the CATE and prove that the posterior has the consistency property. That is, it concentrates around the true distribution. We show the effectiveness of the proposed method through numerical experiments based on synthetic data.
