Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis

2026-07-27 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

A novel spatiotemporal variational tensor decomposition (ST-VTD) framework is introduced to analyze multisubject spatiotemporal data, addressing challenges in modeling shared and subject-specific structures, especially in neuroimaging fMRI. ST-VTD integrates a tensor factorization generative model with structured priors, employing a low-rank prior for spatial factors (inspired by LL1 decomposition) and a learned Long short-term memory (LSTM)-based prior for flexible temporal dynamics. Posterior inference is achieved through an amortized variational formulation by unrolling iterations of a Linearized Proximal Alternating Least-squares Minimization (LPALM) optimization algorithm, enhanced by a Group Independent Component Analysis (GICA) warm-start strategy. Evaluated on a synthetic fMRI dataset of 100 subjects, 150 time points, and 30x30 pixels, ST-VTD demonstrates superior latent factor recovery, achieving spatial and temporal correlations of 0.9829 and 0.9845, and factor errors of 0.1578 and 0.1605, outperforming GICA, LL1, BCPF, and PARAFAC2 benchmarks. The model contains approximately 19,300 trainable parameters and trains in about 6 minutes on CPU.

Key takeaway

For AI Scientists analyzing complex multisubject spatiotemporal data like fMRI, you should consider ST-VTD to achieve superior latent factor recovery and interpretability. Its combination of low-rank spatial and LSTM-based temporal priors, coupled with an unrolled LPALM optimization, offers a flexible framework. Ensure you use a robust warm-start strategy, such as GICA, to mitigate the non-convexity challenges during optimization and achieve stable, high-performance solutions.

Key insights

Combining structured priors with unrolled optimization in variational tensor decomposition improves spatiotemporal data analysis.

Principles

• Structured priors enhance interpretability and flexibility in tensor models.
• Amortized variational inference can leverage unrolled optimization for efficiency.
• Warm-start strategies are crucial for stable optimization in non-convex problems.

Method

ST-VTD uses a tensor factorization generative model with low-rank spatial priors and LSTM-based temporal priors. Inference employs an amortized variational formulation via unrolled LPALM optimization, initialized with GICA.

In practice

• Use GICA for warm-starting tensor decomposition inference networks.
• Apply low-rank priors for structured spatial representations in fMRI data.
• Incorporate LSTM priors for modeling complex nonlinear temporal dynamics.

Topics

• Variational Tensor Decomposition
• Spatiotemporal Data Analysis
• fMRI
• LSTM Networks
• Low-rank Priors
• Amortized Variational Inference

Code references

• lmontaldo/stvtd

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

Related on AIssential

• Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization — Primal-dual optimization with preconditioning offers scalable, robust, and faster convergence for large-scale mean-field variational inference.
• Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling — Tensor Train Diffusion efficiently samples high-dimensional distributions by solving HJB PDEs using low-rank functional tensor train approximations.
• On-Manifold Variational Learning with Heat-Kernel Priors — Manifold-anchored variational learning improves medical image representation by keeping prototypes on the data manifold.
• Efficient frequent directions algorithms for approximate decomposition of matrices and higher-order tensors — New frequent directions algorithms enhance low-rank matrix and tensor approximations for efficiency and accuracy.
• Separable Neural Architectures as Physical World Models: from Mathematical Theory to Applications — The SNA combines neural networks with tensor decomposition to efficiently model high-dimensional PDEs, enabling rapid simulations and inversions.
• Kernel Regression with Tensor Trains and Hadamard Overparameterization — KReTTaH integrates kernel regression, tensor trains, and Hadamard overparameterization via Riemannian optimization for efficient, interpretable multi-way data imputation.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.