We study the problem of sequential experimental design to estimate the parametric component of a partially linear model with a Gaussian process prior. We consider an active learning setting where an experimenter adaptively decides which data to collect to achieve their goal efficiently. The experimenter's goals may vary, such as reducing the classification error probability or improving the accuracy of estimating the parameters of the data generating process. This study aims to improve the accuracy of estimating the parametric component of a partially linear model. Under some assumptions, the parametric component of a partially linear model can be regarded as a causal parameter, the average treatment effect (ATE) or the average causal effect (ACE). We propose a Bayesian sequential experimental design algorithm for a partially linear model with a Gaussian process prior, which is also considered as a sequential experimental design tailored to the estimation of ATE or ACE. We show the effectiveness of the proposed method through numerical experiments based on synthetic and semi-synthetic data.

翻译：我们研究连续实验设计的问题,以估计部分线性模型的参数组成部分,并在此之前采用高斯进程。我们考虑一个积极的学习环境,让实验者适应性地决定要收集哪些数据以有效实现其目标。实验者的目标可能各不相同,例如降低分类误差概率或提高估计数据生成过程参数的准确性。这项研究旨在提高估计部分线性模型的参数组成部分的准确性。根据一些假设,部分线性模型的参数组成部分可被视为因果参数、平均处理效果(ATE)或平均因果效应(ACE)。我们建议采用巴伊西亚连续实验算法,以部分线性模型为部分线性模型,而先采用高斯进程,这也被视为一种与估计ATE或ACE相适应的顺序实验设计。我们通过基于合成和半合成数据的数字实验来显示拟议方法的有效性。