IEEE Trans Cybern. 2022 Oct;52(10):10458-10467. doi: 10.1109/TCYB.2021.3062842. Epub 2022 Sep 19.
Given m d -dimensional responsors and n d -dimensional predictors, sparse regression finds at most k predictors for each responsor for linear approximation, 1 ≤ k ≤ d-1 . The key problem in sparse regression is subset selection, which usually suffers from high computational cost. In recent years, many improved approximate methods of subset selection have been published. However, less attention has been paid to the nonapproximate method of subset selection, which is very necessary for many questions in data analysis. Here, we consider sparse regression from the view of correlation and propose the formula of conditional uncorrelation. Then, an efficient nonapproximate method of subset selection is proposed in which we do not need to calculate any coefficients in the regression equation for candidate predictors. By the proposed method, the computational complexity is reduced from O([1/6]k+(m+1)k+mkd) to O([1/6]k+1/2k) for each candidate subset in sparse regression. Because the dimension d is generally the number of observations or experiments and large enough, the proposed method can greatly improve the efficiency of nonapproximate subset selection. We also apply the proposed method in real scenarios of dental age assessment and sparse coding to validate the efficiency of the proposed method.
给定 m 个 d 维响应器和 n 个 d 维预测器，稀疏回归为每个响应器找到最多 k 个预测器进行线性逼近，1 ≤ k ≤ d-1 。稀疏回归的关键问题是子集选择，这通常会带来很高的计算成本。近年来，已经发布了许多改进的子集选择近似方法。然而，对于数据分析中的许多问题，子集选择的非近似方法关注较少。在这里，我们从相关性的角度考虑稀疏回归，并提出了条件不相关性的公式。然后，我们提出了一种有效的非近似子集选择方法，对于候选预测器，我们不需要计算回归方程中的任何系数。通过所提出的方法，稀疏回归中每个候选子集的计算复杂度从 O([1/6]k+(m+1)k+mkd)降低到 O([1/6]k+1/2k)。由于维度 d 通常是观测值或实验的数量，并且足够大，因此所提出的方法可以大大提高非近似子集选择的效率。我们还将所提出的方法应用于牙科年龄评估和稀疏编码的实际场景中，以验证所提出的方法的效率。
