no code implementations • 7 Aug 2022 • Sally Dong, Haotian Jiang, Yin Tat Lee, Swati Padmanabhan, Guanghao Ye
In this work, we give an algorithm that minimizes the above convex formulation to $\epsilon$-accuracy in $\widetilde{O}(\sum_{i=1}^n d_i \log (1 /\epsilon))$ gradient computations, with no assumptions on the condition number.
no code implementations • NeurIPS 2020 • Jerry Li, Guanghao Ye
Previous work of Cheng et al demonstrated an algorithm that, given $N = \Omega (d^2 / \varepsilon^2)$ samples, achieved a near-optimal error of $O(\varepsilon \log 1 / \varepsilon)$, and moreover, their algorithm ran in time $\widetilde{O}(T(N, d) \log \kappa / \mathrm{poly} (\varepsilon))$, where $T(N, d)$ is the time it takes to multiply a $d \times N$ matrix by its transpose, and $\kappa$ is the condition number of $\Sigma$.
