# Structured Adaptive Tensor Prediction for Streaming Data

arXiv: https://arxiv.org/abs/2606.10085 · HTML: https://mlsanity.com/paper/2606.10085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 88 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [Nonconvex Low-Rank Tensor Completion from Noisy Data](https://mlsanity.com/paper/1911.04436/) (2019)
- [Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements](https://mlsanity.com/paper/2104.14526/) (2021)
- [On Polynomial Time Methods for Exact Low Rank Tensor Completion](https://mlsanity.com/paper/1702.06980/) (2017)
- [Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization](https://mlsanity.com/paper/2103.08895/) (2021)
- [Tensor-on-tensor regression](https://mlsanity.com/paper/1701.01037/) (2017)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay](https://mlsanity.com/paper/2206.08756/) (2022)
- [Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filter](https://mlsanity.com/paper/1905.00406/) (2019)
- [STORE: Sparse Tensor Response Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1609.04523/) (2016)
- [Generalized Correntropy for Robust Adaptive Filtering](https://mlsanity.com/paper/1504.02931/) (2015)
- [Reduced-Rank Tensor-on-Tensor Regression and Tensor-variate Analysis of Variance](https://mlsanity.com/paper/2012.10249/) (2020)
- [Quantum State Tomography for Matrix Product Density Operators](https://mlsanity.com/paper/2306.09432/) (2023)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery](https://mlsanity.com/paper/2401.02592/) (2024)
- [Sparse Tensor Additive Regression](https://mlsanity.com/paper/1904.00479/) (2019)
- [High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling](https://mlsanity.com/paper/2101.04276/) (2021)
- [Multi-linear Tensor Autoregressive Models](https://mlsanity.com/paper/2110.00928/) (2021)
- [A machine learning-based framework for high resolution mapping of PM2.5 in Tehran, Iran, using MAIAC AOD data](https://mlsanity.com/paper/2204.02093/) (2022)
- [Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decomposition](https://mlsanity.com/paper/2406.06002/) (2024)
- [A Scalable Factorization Approach for High-Order Structured Tensor Recovery](https://mlsanity.com/paper/2506.16032/) (2025)
- [Maximum Correntropy Criterion with Variable Center](https://mlsanity.com/paper/1904.06501/) (2019)
- [Matrix Completion Methods for the Total Electron Content Video Reconstruction](https://mlsanity.com/paper/2012.01618/) (2020)
- [Robust Low-rank Tensor Train Recovery](https://mlsanity.com/paper/2410.15224/) (2024)
- [Constrained Maximum Correntropy Adaptive Filtering](https://mlsanity.com/paper/1610.01766/) (2016)
- [Regularized Estimation in High-Dimensional Vector Auto-Regressive Models using Spatio-Temporal Information](https://mlsanity.com/paper/2012.10030/) (2020)
- [Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis](https://mlsanity.com/paper/2210.12311/) (2022)
- [Matrix Autoregressive Model with Vector Time Series Covariates for Spatio-Temporal Data](https://mlsanity.com/paper/2305.15671/) (2023)
- [Enhancing Quantum State Reconstruction with Structured Classical Shadows](https://mlsanity.com/paper/2501.03144/) (2025)

## 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.