标题： COMBSS：通过连续优化的最佳子集选择 显示英文标题

标题： COMBSS: Best Subset Selection via Continuous Optimization

摘要： 我们考虑线性回归中的最佳子集选择问题，其中目标是为每个模型大小$k$找到一组$k$特征，这些特征能最好地拟合响应。 当可用特征的总数相对于数据样本的数量非常大时，这尤其具有挑战性。 我们提出了 COMBSS，一种基于连续优化的新方法，该方法识别出一个解路径，即一组不同大小的模型，这些模型包含线性回归中最佳子集的候选。 COMBSS 表现出非常快的速度，使得当特征数量远远超过数千时，可以进行子集选择。 给出了仿真结果，以突出 COMBSS 与现有流行方法（如向前逐步选择、Lasso 和混合整数优化）相比的性能。 由于整体表现优异，将最佳子集选择问题表述为连续优化问题，为各种回归模型的特征提取开辟了新的研究方向。 显示英文摘要

摘要： We consider the problem of best subset selection in linear regression, where the goal is to find for every model size $k$, that subset of $k$ features that best fit the response. This is particularly challenging when the total available number of features is very large compared to the number of data samples. We propose COMBSS, a novel continuous optimization based method that identifies a solution path, a small set of models of varying size, that consists of candidates for the best subset in linear regression. COMBSS turns out to be very fast, making subset selection possible when the number of features is well in excess of thousands. Simulation results are presented to highlight the performance of COMBSS in comparison to existing popular methods such as Forward Stepwise, the Lasso and Mixed-Integer Optimization. Because of the outstanding overall performance, framing the best subset selection challenge as a continuous optimization problem opens new research directions for feature extraction for a large variety of regression models.