Title: On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent via Batch Means Show Chinese title

Title: 通过批次均值构建随机梯度下降模型参数的置信区域

Abstract: In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level functional central limit theorem for Polyak-Ruppert averaging based stochastic gradient descent estimators. We also extend the batch means method to accommodate more general batch size specifications. Show Chinese abstract

Abstract: 在本文中，我们研究一种简单的算法，使用批均值方法构建模型参数的渐近有效置信区域。 主要思想是消除难以/昂贵估计的协方差矩阵。 在开发该算法的过程中，我们建立了基于Polyak-Ruppert平均的随机梯度下降估计量的过程级功能中心极限定理。 我们还将批均值方法扩展以适应更一般的批次大小规范。