观测值相关的c-最优试验设计的组合优化算法评价
Evaluation of Combinatorial Optimisation Algorithms for c-Optimal Experimental Designs with Correlated Observations
摘要：
我们展示了如何组合优化算法可以应用于识别c-最优试验设计的问题时，可能有相关性和实验单位内，并评估相关算法的性能。我们假设的数据生成过程是一个广义线性混合模型，并表明c-最优设计准则是一个单调的supermodular函数服从一组简单的最小化算法。我们评估了三个相关算法的性能：局部搜索，贪婪搜索和反向贪婪搜索。我们发现，本地和反向贪婪搜索提供了相当的性能与最差的设计输出具有方差$<10\%$大于最佳设计，在一系列的协方差结构。我们表明，这些算法执行以及或更好的乘法方法，产生的权重放在实验单位。我们将这些算法扩展到确定moole-robust c-最优设计。
英文摘要：
We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant algorithms. We assume the data generating process is a generalised linear mixed model and show that the c-optimal design criterion is a monotone supermodular function amenable to a set of simple minimisation algorithms. We evaluate the performance of three relevant algorithms: the local search, the greedy search, and the reverse greedy search. We show that the local and reverse greedy searches provide comparable performance with the worst design outputs having variance $<10\%$ greater than the best design, across a range of covariance structures. We show that these algorithms perform as well or better than multiplicative methods that generate weights to place on experimental units. We extend these algorithms to identifying moole-robust c-optimal designs.
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