Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis

• URL: http://arxiv.org/abs/2607.22262v1
• Date: Fri, 24 Jul 2026 12:55:09 GMT
• Title: Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis
• Abstract summary: We introduce a spatial variational tensor decomposition (ST-VTD) framework that combines a tensor factorization generative model with structured priors.<n>The proposed approach significantly improves latent factor recovery compared with representative classical and probabilistic decomposition benchmarks.
• Score: 2.3799118675414226
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modeling shared and subject-specific structure in multisubject spatiotemporal data remains challenging, particularly in neuroimaging, where both spatial and temporal patterns exhibit rich variability across subjects. Existing matrix and tensor decompositions provide interpretable factorizations, but rely on fixed multilinear structures or coupling schemes that may limit their flexibility in capturing complex variability. In this work, we introduce a spatiotemporal variational tensor decomposition (ST-VTD) framework that combines a tensor factorization generative model with structured priors to jointly represent spatial maps and temporal dynamics. Spatial factors are regularized to promote a low-rank structure inspired by the LL1 decomposition, while temporal factors are modeled using a learned Long short-term memory (LSTM)-based prior, enabling flexible and adaptive dynamics. Posterior inference is performed using an amortized variational formulation by unrolling iterations of an optimization algorithm, leading to an interpretable and parameter-efficient architecture. The proposed inference framework employs a warm-start strategy based on group independent component analysis, which we found to improve optimization performance. Experiments on a realistic synthetic functional MRI (fMRI) dataset demonstrate that the proposed approach significantly improves latent factor recovery compared with representative classical and probabilistic decomposition benchmarks.

Related papers

• Structured Neural Chaos: An Adaptive Surrogate Modeling Framework for Functional Uncertainty Quantification and Global Sensitivity Analysis [3.4686904619645866]
  We introduce the Structured Neural Chaos (sNC) expansion as a surrogate modeling framework for variance-based global sensitivity analysis.<n>The proposed framework retains the interpretability of structured decompositions while leveraging the power of neural networks.
  arXiv  Detail & Related papers  (2026-07-31T00:03:07Z)
• Learning Spatio-Temporal Foundation Models from Pure Synthetic Data [85.23980441738811]
  NeoST is a scalable synthetic-training corpus to real-world bias, a latent-space reasoning architecture that generates and iteratively refines multiple future trajectories, and latent-space objectives that emphasize structural dynamics and enable inference-time correction under distribution shifts.<n>Extensive experiments across diverse real-world benchmarks show that NeoST consistently outperforms existing STFMs in diverse real-worldtemporal systems.
  arXiv  Detail & Related papers  (2026-06-27T02:56:46Z)
• Factorize to Generalize: Retrieval-Guided Invariant-Dynamic Decomposition for Time Series Forecasting [64.2640656619583]
  Time series foundation models (TSFMs) have recently achieved strong zero-shot forecasting performance through large-scale pretraining and retrieval-augmented prediction.<n>We propose a Retrieval-guided Invariant-Dynamic DEcomposition framework for time series forecasting.
  arXiv  Detail & Related papers  (2026-05-24T07:31:55Z)
• SPaRSe-TIME: Saliency-Projected Low-Rank Temporal Modeling for Efficient and Interpretable Time Series Prediction [0.0]
  SPaRSe-TIME is a framework that models time series through a decomposition into three complementary components: saliency, memory, and trend.<n>Experiments on diverse real-world datasets demonstrate that SPaRSe-TIME achieves competitive performance.<n>Overall, SPaRSe-TIME offers a principled alternative to monolithic sequence models, bridging efficiency, interpretability, and performance, and providing a scalable framework for time series learning.
  arXiv  Detail & Related papers  (2026-04-19T09:55:28Z)
• ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equations [54.886931928255564]
  Low-rank adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning method in deep transfer learning.<n>We propose a novel continuous-time optimization dynamic for LoRA factor matrices in the form of an ordinary differential equation (ODE)<n>We show that ODELoRA achieves stable feature learning, a property that is crucial for training deep neural networks at different scales of problem dimensionality.
  arXiv  Detail & Related papers  (2026-02-07T10:19:36Z)
• Graph Neural Regularizers for PDE Inverse Problems [62.49743146797144]
  We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs)<n>The forward problem is numerically solved using the finite element method (FEM)<n>We employ physics-inspired graph neural networks as learned regularizers, providing a robust, interpretable, and generalizable alternative to standard approaches.
  arXiv  Detail & Related papers  (2025-10-23T21:43:25Z)
• Multivariate Long-term Time Series Forecasting with Fourier Neural Filter [42.60778405812048]
  We introduce FNF as the backbone and DBD as architecture to provide excellent learning capabilities and optimal learning pathways for spatial-temporal modeling.<n>We show that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling.
  arXiv  Detail & Related papers  (2025-06-10T18:40:20Z)
• High-Fidelity Scientific Simulation Surrogates via Adaptive Implicit Neural Representations [51.90920900332569]
  Implicit neural representations (INRs) offer a compact and continuous framework for modeling spatially structured data.<n>Recent approaches address this by introducing additional features along rigid geometric structures.<n>We propose a simple yet effective alternative: Feature-Adaptive INR (FA-INR)
  arXiv  Detail & Related papers  (2025-06-07T16:45:17Z)
• A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems [8.206685537936078]
  This study introduces a stepwise data-driven framework for discovering fractional differential equations (FDEs) directly from data.<n>Our framework applies deep neural networks as surrogate models for denoising and reconstructing sparse and noisy observations.<n>We validate the framework across various datasets, including synthetic anomalous diffusion data and experimental data on the creep behavior of frozen soils.
  arXiv  Detail & Related papers  (2024-12-05T08:38:30Z)
• Factorized Fusion Shrinkage for Dynamic Relational Data [16.531262817315696]
  We consider a factorized fusion shrinkage model in which all decomposed factors are dynamically shrunk towards group-wise fusion structures. The proposed priors enjoy many favorable properties in comparison and clustering of the estimated dynamic latent factors. We present a structured mean-field variational inference framework that balances optimal posterior inference with computational scalability.
  arXiv  Detail & Related papers  (2022-09-30T21:03:40Z)
• Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression [17.158289775348063]
  Kernelized tensor Regression (BKTR) can be considered a new and scalable approach to modeling processes with low-rank cotemporal structure. We conduct extensive experiments on both synthetic and real-world data sets, and our results confirm the superior performance and efficiency of BKTR for model estimation and inference.
  arXiv  Detail & Related papers  (2021-08-31T19:22:23Z)
• Optimization with Momentum: Dynamical, Control-Theoretic, and Symplectic Perspectives [97.16266088683061]
  The article rigorously establishes why symplectic discretization schemes are important for momentum-based optimization algorithms. It provides a characterization of algorithms that exhibit accelerated convergence.
  arXiv  Detail & Related papers  (2020-02-28T00:32:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.