Online Tensor Inference

From Big Data to Real-Time Decisions: Online Tensor Inference Modern digital platforms, from e-commerce and online advertising to mobile health, generate massive streams of high-dimensional data that must be analyzed in real time. In their paper “Online Tensor Inference,” Xin Wen, Will Wei Sun, and Yichen Zhang develop a new statistical framework that enables both efficient learning and rigorous inference for streaming tensor data. The authors propose an online low-rank tensor estimation method based on stochastic gradient descent that processes observations sequentially without storing historical data, overcoming the memory and scalability limitations of traditional offline approaches. Beyond estimation, the paper introduces a novel online debiasing technique that delivers valid confidence intervals and hypothesis tests on the fly without data splitting. Theoretical results establish near-minimax-optimal convergence rates and asymptotic normality for general linear functionals of tensors. Together, these advances provide a principled foundation for real-time, statistically grounded decision making in fast-changing, data-rich environments.