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$k$找到最佳拟合响应的$k$个特征的子集。 当可用特征总数相对于数据样本数量非常大时，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，可以直接解决线性回归中的最佳子集选择问题。 COMBSS 被证明非常快速，可能使特征数量远远超过数千时的最佳子集选择成为可能。 通过模拟结果展示了 COMBSS 在与现有的流行非穷举方法（如向前逐步选择和 Lasso）以及穷举方法（如混合整数优化）进行比较时的性能。 由于整体性能优异，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 fits 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 directly solves the best subset selection problem in linear regression. COMBSS turns out to be very fast, potentially making best 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 non-exhaustive methods such as Forward Stepwise and the Lasso, as well as for exhaustive methods such as 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.