Online inference with debiased stochastic gradient descent
提出一种去偏随机梯度下降算法，用于高维数据的在线统计推断，能高效构建置信区间，并证明了估计量的渐近正态性。
Summary We propose a debiased stochastic gradient descent algorithm for online statistical inference with high-dimensional data. Our approach combines the debiasing technique developed in high-dimensional statistics with the stochastic gradient descent algorithm. It can be used to construct confidence intervals efficiently in an online fashion. Our proposed algorithm has several appealing aspects: as a one-pass algorithm, it reduces the time complexity; in addition, each update step requires only the current data together with the previous estimate, which reduces the space complexity. We establish the asymptotic normality of the proposed estimator under mild conditions on the sparsity level of the parameter and the data distribution. Numerical experiments demonstrate that the proposed debiased stochastic gradient descent algorithm attains nominal coverage probability. Furthermore, we illustrate our method with analysis of a high-dimensional text dataset.