Monotone response surface of multi-factor condition: estimation and Bayes classifiers
将多因素单调响应面的估计转化为部分有序分类器集成的逆问题，提出高效算法，在维度高于传统等渗回归的场景下，模拟显示基于该方法的置信区间覆盖概率准确且更精确。
We formulate the estimation of monotone response surface of multiple factors as the inverse of an iteration of partially ordered classifier ensembles. Each ensemble (called PIPE-classifiers) is a projection of Bayes classifiers on the constrained space. We prove the inverse of PIPE-classifiers (iPIPE) exists, and propose algorithms to efficiently compute iPIPE by reducing the space over which optimisation is conducted. The methods are applied in analysis and simulation settings where the surface dimension is higher than what the isotonic regression literature typically considers. Simulation shows iPIPE-based credible intervals achieve nominal coverage probability and are more precise compared to unconstrained estimation.