提出新算法高效求解高维线性回归的最优子集选择问题
Solving the Best Subset Selection Problem via Suboptimal Algorithms
- 设计新近似算法，以显著降低计算开销
- 在真实与合成数据上表现优于现有主流方法
- 适合处理维度达数千的高维数据场景
线性回归中的最优子集选择问题因其非凸性和随维度增长而急剧膨胀的可能子集数量，导致精确求解在高维情况下计算成本极高，如千维问题可能需不切实际的大量CPU时间。因此，发展能以远低于精确方法的计算量获得良好近似解的次优算法至关重要。本文提出一种新算法，并与多种流行次优方法进行对比实验，涵盖合成数据和真实数据。结果揭示了不同方法在各类数据设置下的性能差异。新算法在高维数据中表现出较强的竞争力，是求解此类问题的有效近似方案。
原文摘要 · Abstract (English)
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the global optimal solution via an exact optimization method for a problem with dimensions of 1000s may take an impractical amount of CPU time. This suggests the importance of finding suboptimal procedures that can provide good approximate solutions using much less computational effort than exact methods. In this work, we introduce a new procedure and compare it with other popular suboptimal algorithms to solve the best subset selection problem. Extensive computational experiments using synthetic and real data have been performed. The results provide insights into the performance of these methods in different data settings. The new procedure is observed to be a competitive suboptimal algorithm for solving the best subset selection problem for high-dimensional data.
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