论文标题
确认最佳稀疏足够尺寸降低
Certifiably Optimal Sparse Sufficient Dimension Reduction
论文作者
论文摘要
足够的尺寸降低（SDR）是回归分析中的流行工具，它用最小的线性组合将原始预测变量取代。但是，估计的线性组合通常包含所有原始预测指标，这在解释结果时遇到了困难，尤其是当预测变量较大时。在本文中，我们提出了一种自定义的分支和界限，最佳稀疏稀疏广义特征值问题（最佳SGEP），该问题结合了许多SDR方法的SGEP公式以及有效且准确的界限，允许算法快速收敛。最佳SGEP精确解决了基本的非凸优化问题，因此可以确保最佳解决方案。我们通过模拟研究证明了所提出的算法的有效性。
Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original predictors, which brings difficulties in interpreting the results, especially when the number of predictors is large. In this paper, we propose a customized branch and bound algorithm, optimal sparse generalized eigenvalue problem (Optimal SGEP), which combines a SGEP formulation of many SDR methods and efficient and accurate bounds allowing the algorithm to converge quickly. Optimal SGEP exactly solves the underlying non-convex optimization problem and thus produces certifiably optimal solutions. We demonstrate the effectiveness of the proposed algorithm through simulation studies.
