论文标题
schatten $ p $ - norms中多变量多线性回归的乘法扰动范围
Multiplicative Perturbation Bounds for Multivariate Multiple Linear Regression in Schatten $p$-Norms
论文作者
论文摘要
多变量多线性回归（MMLR）发生在许多实际应用中，将传统最小二乘（多元线性回归）推广到多个右侧。我们将最新的MLR分析扩展到一般的Schatten $ p $ norms中草图的MMLR，通过将草的问题解释为乘法扰动。我们的工作代表了Maher在Schatten $ p $ norms上的结果的扩展。我们从投影仪方面为精确和干扰的解决方案得出表达式，以便于几何解释。我们还提出了对素描矩阵的作用的几何解释，该作用在相关子空间方面。我们表明，评估素描MMLR解决方案的准确性的关键术语可以看作是在某些假设下子空间之间最大的主角度的切线。我们的结果能够对具有相同范围的正交投影仪和倾斜投影仪之间的差异进行更多解释。
Multivariate multiple linear regression (MMLR), which occurs in a number of practical applications, generalizes traditional least squares (multivariate linear regression) to multiple right-hand sides. We extend recent MLR analyses to sketched MMLR in general Schatten $p$-norms by interpreting the sketched problem as a multiplicative perturbation. Our work represents an extension of Maher's results on Schatten $p$-norms. We derive expressions for the exact and perturbed solutions in terms of projectors for easy geometric interpretation. We also present a geometric interpretation of the action of the sketching matrix in terms of relevant subspaces. We show that a key term in assessing the accuracy of the sketched MMLR solution can be viewed as a tangent of a largest principal angle between subspaces under some assumptions. Our results enable additional interpretation of the difference between an orthogonal and oblique projector with the same range.
