用于实验设计的自验证增强模型
Self-Validated Ensemble Models for Design of Experiments
摘要：
设计实验时的一个可能目标是建立或制定一个模型来预测未来的观测结果。当主要目标是预测时，规划阶段中的一些典型方法是在设计阶段使用完善的小样本试验设计（例如，连续筛选设计），并使用广泛使用的模型选择算法（如LASSO）构建预测模型。然而，这些设计和分析策略并不能保证高预测性能，部分原因是样本量小，无法将数据划分为训练集和验证集，这是机器学习模型中常用的一种策略，用于改善样本外预测。在这项工作中，我们提出了一个新的框架，用于从实验数据中构建高性能的预测模型，该模型利用了具有训练集和验证集的优势。然而，我们提出了一种基于分数随机权重自举的加权方案，而不是将数据划分为两个相互排斥的子集，该方案通过为每个观察分配反相关的训练和验证权重来模拟数据划分。所提出的方法，称为自验证的包围建模（SVEM），在装袋的精神，使其迭代通过自举反相关权重和拟合模型，最终SVEM模型是自举模型的平均值。我们研究了SVEM算法的性能与几个模型建立方法，如逐步回归，拉索，和Dantzig选择器。最后，通过模拟和案例研究，我们表明，SVEM一般生成的模型具有更好的预测性能相比，一次性的模型选择方法。
英文摘要：
One of the possible objectives when designing experiments is to build or formulate a model for predicting future observations. When the primary objective is prediction, some typical approaches in the planning phase are to use well-established small-sample experimental designs in the design phase (e.g., Definitive Screening Designs) and to construct predictive models using widely used model selection algorithms such as LASSO. These design and analytic strategies, however, do not guarantee high prediction performance, partly due to the small sample sizes that prevent partitioning the data into training and validation sets, a strategy that is commonly used in machine learning models to improve out-of-sample prediction. In this work, we propose a novel framework for building high-performance predictive models from experimental data that capitalizes on the advantage of having both training and validation sets. However, instead of partitioning the data into two mutually exclusive subsets, we propose a weighting scheme based on the fractional random weight bootstrap that emulates data partitioning by assigning anti-correlated training and validation weights to each observation. The proposed methodology, called Self-Validated Ensemble Modeling (SVEM), proceeds in the spirit of bagging so that it iterates through bootstraps of anti-correlated weights and fitted models, with the final SVEM model being the average of the bootstrapped models. We investigate the performance of the SVEM algorithm with several model-building approaches such as stepwise regression, Lasso, and the Dantzig selector. Finally, through simulation and case studies, we show that SVEM generally generates models with better prediction performance in comparison to one-shot model selection approaches.
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