In this paper, we present a sharp analysis for an alternating gradient descent algorithm which is used to solve the covariate adjusted precision matrix estimation problem in the high dimensional setting. Without the resampling assumption, we demonstrate that this algorithm not only enjoys a linear rate of convergence, but also attains the optimal statistical rate (i.e., minimax rate). Moreover, our analysis also characterizes the time-data tradeoffs in the covariate adjusted precision matrix estimation problem. Numerical experiments are provided to verify our theoretical results.

翻译：在本文中,我们对一种交替的梯度下降算法进行了尖锐的分析,该算法用于解决高维环境中的共变调整精确矩阵估算问题。 没有重新抽样的假设,我们证明这一算法不仅具有线性趋同率,而且达到了最佳统计率(即微缩指数 ) 。 此外,我们的分析还描述了共变调整精确矩阵估算问题的时间数据取舍。提供了数字实验以验证我们的理论结果。