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： 在线性回归中考虑最佳子集选择的问题，旨在找到一个固定大小的特征子集，该子集能最好地拟合响应变量。 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。 现有的求解此问题的最优方法往往速度较慢，而快速的方法往往准确性较低。 理想情况下，新方法应比现有最优方法更快地进行最佳子集选择，同时保持可比较的准确性，或者在计算速度相当的情况下更加准确。 在这里，我们提出了一种新的连续优化方法，该方法可以识别出一个子集解决方案路径，即一个不同大小的模型的小集合，这些模型包括特征单个最佳子集的候选者，在线性回归中以某种特定方式是最优的。 我们的方法速度快，使得当特征数量远远超过数千时，可以进行最佳子集选择。 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： The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of 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. Existing optimal methods for solving this problem tend to be slow while fast methods tend to have low accuracy. Ideally, new methods perform best subset selection faster than existing optimal methods but with comparable accuracy, or, being more accurate than methods of comparable computational speed. Here, we propose a novel continuous optimization method that identifies a subset solution path, a small set of models of varying size, that consists of candidates for the single best subset of features, that is optimal in a specific sense in linear regression. Our method turns out to be fast, making the best subset selection possible when the number of features is well in excess of thousands. 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.