Table 1.

Comparisons of sample complexities and Euclidean estimation errors when μ = O(1).

	Sample complexity	Euclidean estimation error
[64]	n log2 n	$\text{max}\left(\sigma ,{\Vert M^{\star }\Vert }_{\infty }\right)\sqrt{(nr\text{log}n)/p}$
[75]	n log n	$\text{max}(\sigma ,1/n){\alpha }^{\star }\sqrt{(nr\text{log}n)/p}$
[62]	n log3 n	$\text{max}\left(\sigma ,{\Vert M^{\star }\Vert }_{\infty }\right)\sqrt{(nr\text{log}n)/p}$
[10]	n	$\sqrt{\text{max}\left(\sigma ,{\Vert M^{\star }\Vert }_{\infty }\right)}{\Vert M^{\star }\Vert }_{\text{max}}{n}^{3/4}/p^{1/4}$
Ours	κ4r2n log3 n	${\kappa }^2\sigma \sqrt{nr/p}$