Bayesian Sequential Experimental Design for a Partially Linear Model with a Gaussian Process Prior
Bayesian Sequential Experimental Design for a Partially Linear Model with a Gaussian Process Prior
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发表时间：
2022-11
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通讯作者：
Shunsuke Horii
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作者：
Shunsuke Horii
研究了在高斯过程先验下估计部分线性模型参数分量的序贯试验设计问题。我们考虑一个主动学习设置，实验者自适应地决定收集哪些数据，以有效地实现他们的目标。实验者的目标可能会有所不同，例如降低分类错误概率或提高估计数据生成过程的参数的准确性。本研究旨在改善部分线性模型参数分量的估计精度。在某些假设下，部分线性模型的参数分量可被视为因果参数，即平均治疗效应（ATE）或平均因果效应（ACE）。我们提出了一个贝叶斯序贯实验设计算法的部分线性模型与高斯过程先验，这也被认为是一个序贯实验设计适合于估计ATE或ACE。我们通过数值实验的基础上合成和半合成数据所提出的方法的有效性。
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.