Structured Adaptive Tensor Prediction for Streaming Data

• URL: http://arxiv.org/abs/2606.10085v1
• Date: Mon, 08 Jun 2026 19:09:58 GMT
• Title: Structured Adaptive Tensor Prediction for Streaming Data
• Abstract summary: Matrix-valued time series arise in a wide range of applications, such as adaptability of medical imaging data.<n>Existing methods are mainly designed for static settings and lack to streaming and time-varying environments.<n>We develop an adaptive regression framework that includes Matrix-on-Matrix (MoM) and gradient-on-Matrix (ToM)<n>We show that ToM achieves lower steady-state error and stronger denoising capability than MoM.
• Score: 12.618068868826512
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Matrix-valued time series arise in a wide range of applications, such as spatio-temporal data from medical imaging and geophysics. Existing methods are mainly designed for static settings and lack adaptability to streaming and time-varying environments. Adaptive filtering techniques have also been largely limited to data with scalar or vector values, leaving adaptive forecasting for matrix-valued time series inadequately understood. To bridge these gaps, we develop an adaptive tensor regression framework that includes Matrix-on-Matrix (MoM) and Tensor-on-Matrix (ToM) formulations for streaming matrix-valued prediction. The two formulations differ in whether to directly model matrix-valued outputs or to exploit temporal structure via higher-order tensor representations. For the proposed tensor regression framework, we develop stochastic gradient descent (SGD) algorithms for online learning. We show that stacking multiple responses across time into higher-order tensors improves performance; in particular, the ToM achieves lower steady-state error and stronger denoising capability than MoM, motivating our focus on the ToM model. We further characterize the tracking behavior of SGD under time-varying dynamics. From a statistical perspective, we establish fixed-time recovery guarantees for ToM under general low-dimensional structures, including sparsity, low-rankness, and their joint sparselow-rank models.

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