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[2312.17111] Online Tensor Inference
Summary
The paper presents a novel framework for online tensor inference, addressing the challenges of real-time data processing in applications like recommendation systems and health monitoring.
Why It Matters
As the demand for real-time data analysis grows, traditional offline learning methods become impractical. This research offers a solution that enhances the efficiency and applicability of low-rank tensor methods, making it crucial for industries relying on timely decision-making.
Key Takeaways
- Introduces an online inference framework for low-rank tensors.
- Utilizes Stochastic Gradient Descent for efficient real-time processing.
- Eliminates the need for historical data storage, facilitating on-the-fly hypothesis testing.
- Establishes a non-asymptotic convergence result nearly matching offline models.
- Proposes a novel debiasing approach for sequential statistical inference.
Statistics > Machine Learning arXiv:2312.17111 (stat) [Submitted on 28 Dec 2023 (v1), last revised 12 Feb 2026 (this version, v2)] Title:Online Tensor Inference Authors:Xin Wen, Will Wei Sun, Yichen Zhang View a PDF of the paper titled Online Tensor Inference, by Xin Wen and 2 other authors View PDF Abstract:Contemporary applications, such as recommendation systems and mobile health monitoring, require real-time processing and analysis of sequentially arriving high-dimensional tensor data. Traditional offline learning, involving the storage and utilization of all data in each computational iteration, becomes impractical for these tasks. Furthermore, existing low-rank tensor methods lack the capability for online statistical inference, which is essential for real-time predictions and informed decision-making. This paper addresses these challenges by introducing a novel online inference framework for low-rank tensors. Our approach employs Stochastic Gradient Descent (SGD) to enable efficient real-time data processing without extensive memory requirements. We establish a non-asymptotic convergence result for the online low-rank SGD estimator, nearly matches the minimax optimal estimation error rate of offline models. Furthermore, we propose a simple yet powerful online debiasing approach for sequential statistical inference. The entire online procedure, covering both estimation and inference, eliminates the need for data splitting or storing historical data, making it suitabl...
