明日讲座速递 | 大湾区数据科学与统计云讲堂

We investigate a generalized framework in online setting to estimate a latent low-rank tensor. This framework covers both linear and generalized linear models, and can easily handle continuous or categorical variables in online setting. Meanwhile, we also consider online tensor completion and online binary tensor learning. We propose the online Riemannian gradient descent algorithm, which is proved to converge linearly and can recover the low-rank part under suitable conditions in all the applications. Moreover, a sharp entry-wise error bound is provided in the online tensor completion. To the best of our knowledge, our results are the first that take noise into consideration in the online low-rank tensor (even low-rank matrix) recovery task. In the noise case, a surprising computational and statistical tradeoff is observed: a larger stepsize leads to a faster convergence speed while the output has a larger statistical error; a smaller stepsize gives rise to a statistical optimal estimator but has slower convergence.