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Tag: tensor

  • Near-Universal Multiplicative Updates for Nonnegative Einsum Factorization

    Near-Universal Multiplicative Updates for Nonnegative Einsum Factorization arXiv:2602.02759v1 Announce Type: new Abstract: Despite the ubiquity of multiway data across scientific domains, there are few user-friendly tools that fit tailored nonnegative tensor factorizations. Researchers may use gradient-based automatic differentiation (which often struggles in nonnegative settings), choose between a limited set of methods with mature implementations, or…

  • Laplace Approximation For Tensor Train Kernel Machines In System Identification

    Laplace Approximation For Tensor Train Kernel Machines In System Identification arXiv:2512.02532v1 Announce Type: new Abstract: To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this…

  • A Fully Probabilistic Tensor Network for Regularized Volterra System Identification

    A Fully Probabilistic Tensor Network for Regularized Volterra System Identification arXiv:2511.20457v1 Announce Type: new Abstract: Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the Bayesian Tensor Network framework to Volterra system identification.…

  • Graphical model for tensor factorization by sparse sampling

    Graphical model for tensor factorization by sparse sampling arXiv:2510.17886v1 Announce Type: new Abstract: We consider tensor factorizations based on sparse measurements of the tensor components. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful in cases where a substantial amount of data…

  • The Nondecreasing Rank

    The Nondecreasing Rank arXiv:2509.00265v1 Announce Type: new Abstract: In this article the notion of the nondecreasing (ND) rank of a matrix or tensor is introduced. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each vector satisfying a monotonicity constraint. It…

  • Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selection

    Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selection arXiv:2507.11136v1 Announce Type: new Abstract: Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further, they require manual tuning of model…

  • Performance of Rank-One Tensor Approximation on Incomplete Data

    Performance of Rank-One Tensor Approximation on Incomplete Data arXiv:2504.07818v1 Announce Type: new Abstract: We are interested in the estimation of a rank-one tensor signal when only a portion $varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral…

  • Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems

    Quantile-Based Randomized Kaczmarz for Corrupted Tensor Linear Systems arXiv:2503.18190v1 Announce Type: new Abstract: The reconstruction of tensor-valued signals from corrupted measurements, known as tensor regression, has become essential in many multi-modal applications such as hyperspectral image reconstruction and medical imaging. In this work, we address the tensor linear system problem $mathcal{A} mathcal{X}=mathcal{B}$, where $mathcal{A}$ is…

  • Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent

    Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent arXiv:2501.01696v1 Announce Type: new Abstract: Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data are often accompanied by arbitrary signal corruptions,…

  • Generalized Least Squares Kernelized Tensor Factorization

    Generalized Least Squares Kernelized Tensor Factorization arXiv:2412.07041v1 Announce Type: new Abstract: Real-world datasets often contain missing or corrupted values. Completing multidimensional tensor-structured data with missing entries is essential for numerous applications. Smoothness-constrained low-rank factorization models have shown superior performance with reduced computational costs. While effective at capturing global and long-range correlations, these models struggle to…