Bayesian Sequential Experimental Design for a Partially Linear Model with a Gaussian Process Prior

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.