mlsanityData to 7 Oct 2026

Structured Adaptive Tensor Prediction for Streaming Data

arXiv 2606.10085 ↗First posted 8 Jun 2026cs.LG eess.SP math.OCcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 88 references that are in the map. First posted on arXiv 8 Jun 2026.

Builds on

31 of 88 references.

References · 31

  1. 2017Tensor SVD: Statistical and Computational Limitscited by 52
  2. 2020An Optimal Statistical and Computational Framework for Generalized Tensor Estimationcited by 39
  3. 2019Nonconvex Low-Rank Tensor Completion from Noisy Datacited by 35
  4. 2021Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscited by 28
  5. 2017On Polynomial Time Methods for Exact Low Rank Tensor Completioncited by 27
  6. 2021Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimizationcited by 24
  7. 2017Tensor-on-tensor regressioncited by 22
  8. 2018Autoregressive Models for Matrix-Valued Time Seriescited by 18
  9. 2022Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplaycited by 15
  10. 2019Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filtercited by 13
  11. 2016STORE: Sparse Tensor Response Regression and Neuroimaging Analysiscited by 11
  12. 2020Reduced-Rank Tensor-on-Tensor Regression and Tensor-variate Analysis of Variancecited by 10
19 more
  1. 2015Generalized Correntropy for Robust Adaptive Filteringcited by 9
  2. 2022Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Reviewcited by 9
  3. 2023Quantum State Tomography for Matrix Product Density Operatorscited by 9
  4. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  5. 2019Sparse Tensor Additive Regressioncited by 5
  6. 2021High-Dimensional Low-Rank Tensor Autoregressive Time Series Modelingcited by 5
  7. 2021Multi-linear Tensor Autoregressive Modelscited by 4
  8. 2022A machine learning-based framework for high resolution mapping of PM2.5 in Tehran, Iran, using MAIAC AOD datacited by 4
  9. 2024Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decompositioncited by 4
  10. 2025A Scalable Factorization Approach for High-Order Structured Tensor Recoverycited by 4
  11. 2019Maximum Correntropy Criterion with Variable Centercited by 3
  12. 2020Matrix Completion Methods for the Total Electron Content Video Reconstructioncited by 3
  13. 2024Robust Low-rank Tensor Train Recoverycited by 2
  14. 2016Constrained Maximum Correntropy Adaptive Filteringcited by 1
  15. 2020Regularized Estimation in High-Dimensional Vector Auto-Regressive Models using Spatio-Temporal Informationcited by 1
  16. 2022Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysiscited by 1
  17. 2023Matrix Autoregressive Model with Vector Time Series Covariates for Spatio-Temporal Datacited by 1
  18. 2025Enhancing Quantum State Reconstruction with Structured Classical Shadowscited by 1
  19. 2025Fourier Low-rank and Sparse Tensor for Efficient Tensor Completioncited by 1

Built on by

Not cited yet.