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Bayesian tensor regression using the Tucker decomposition for sparse spatial modeling

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arxiv 2203.04733 v3 pith:YLVQ45MI submitted 2022-03-09 stat.ME

Daniel Spencer , Rajarshi Guhaniyogi , Russell Shinohara , Raquel Prado This is my paper · ORCID
classification stat.ME
keywords tensormodeldatamethodsbayesiancovariatedecompositionmodeling
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Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize an association between a tensor covariate and a scalar response. We propose a Bayesian method to efficiently model a scalar response with a tensor covariate using the Tucker tensor decomposition in order to retain the spatial relationship within a tensor coefficient, while reducing the number of parameters varying within the model and applying regularization methods. Simulated data are analyzed to compare the model to recently proposed methods. A neuroimaging analysis using data from the Alzheimer's Data Neuroimaging Initiative is included to illustrate the benefits of the model structure in making inference.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Functional Tensor Regression

    stat.ME 2025-06 conditional novelty 7.0 of 10

    A new regression framework models scalar responses against functional tensor covariates using low Tucker rank and spline smoothness, with a provably quadratically convergent Riemannian Gauss-Newton algorithm.

  2. Statistical Inference for Low-Rank Tensor Models

    math.ST 2025-01 conditional novelty 7.0 of 10

    A debiased tangent-space projection estimator yields asymptotically normal and minimax-optimal confidence intervals for general linear functionals of low-Tucker-rank tensors.

  3. Time-varying Parameter Tensor Vector Autoregression

    stat.ME 2025-05 conditional novelty 6.0 of 10

    Time-varying tensor VARs with one evolving CP loading and a conditional DIC plus knee point rule recover true configurations in simulations and reveal time-varying fMRI connectivity.

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