题目：HiGrad: Statistical Inference for Stochastic Approximation and Online Learning

报告人：Professor Weijie Su（University of Pennsylvania）

地点：致远楼101室

时间：2018年7月10日（周二）下午3:00开始

摘要

Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of works on SGD, much less is known about the statistical inferential properties of predictions based on SGD solutions. In this talk, we introduce a novel procedure termedHiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with the vanilla SGD. The HiGrad procedure begins by performing SGD iterations for a while and then split the single thread into a few, and this procedure hierarchically operates in this fashion along each thread. With predictions provided by multiple threads in place, a t-based confidence interval is constructed by decorrelating predictions using covariance structures given by the Ruppert–Polyak averaging scheme. Under certain regularity conditions, the HiGrad confidence interval is shown to attain asymptotically exact coverage probability. Finally, the performance of HiGrad is evaluated through extensive simulation studies and a real data example.

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