统计设计和建模中的近似最优子集选择
Approximately Optimal Subset Selection for Statistical Design and Modelling
摘要：
研究了相关随机变量集合的最优子集选择问题。特别是，我们考虑相关的组合优化问题的最大化的对称正定矩阵的特征所选择的子集的行列式。这个问题出现在许多领域，如试验设计，回归建模和环境统计。我们建立了一个有效的多项式时间算法，利用行列式点过程逼近问题的最优解。我们展示了我们的方法的优点，通过提出合成和真实数据集的计算结果。
英文摘要：
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix that characterizes the chosen subset. This problem arises in many domains, such as experimental designs, regression modeling, and environmental statistics. We establish an efficient polynomial-time algorithm using Determinantal Point Process for approximating the optimal solution to the problem. We demonstrate the advantages of our methods by presenting computational results for both synthetic and real data sets.
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