We establish non-asymptotic lower bounds for the estimation of principal subspaces. As applications, we obtain new results for the excess risk of principal component analysis and the matrix denoising problem.

翻译：我们为估算主要次空间建立了非无药可治的下限界限。 作为应用程序,我们获得了主要部件分析的超重风险和矩阵分泌问题的新结果。