Kernel Regression of Multi-Way Data via Tensor Trains with Hadamard Overparametrization: The Dynamic Graph Flow Case

• URL: http://arxiv.org/abs/2509.22197v1
• Date: Fri, 26 Sep 2025 11:00:05 GMT
• Title: Kernel Regression of Multi-Way Data via Tensor Trains with Hadamard Overparametrization: The Dynamic Graph Flow Case
• Authors: Duc Thien Nguyen, Konstantinos Slavakis, Eleftherios Kofidis, Dimitris Pados,
• Abstract summary: Kernel Regression via Trains with Hadamard overparametrization (KReTTaH) is a regression-based framework for interpretable multi-way data imputation.<n>KReTTaH consistently outperforms state-of-the-art alternatives.
• Score: 9.941965164307843
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: A regression-based framework for interpretable multi-way data imputation, termed Kernel Regression via Tensor Trains with Hadamard overparametrization (KReTTaH), is introduced. KReTTaH adopts a nonparametric formulation by casting imputation as regression via reproducing kernel Hilbert spaces. Parameter efficiency is achieved through tensors of fixed tensor-train (TT) rank, which reside on low-dimensional Riemannian manifolds, and is further enhanced via Hadamard overparametrization, which promotes sparsity within the TT parameter space. Learning is accomplished by solving a smooth inverse problem posed on the Riemannian manifold of fixed TT-rank tensors. As a representative application, the estimation of dynamic graph flows is considered. In this setting, KReTTaH exhibits flexibility by seamlessly incorporating graph-based (topological) priors via its inverse problem formulation. Numerical tests on real-world graph datasets demonstrate that KReTTaH consistently outperforms state-of-the-art alternatives-including a nonparametric tensor- and a neural-network-based methods-for imputing missing, time-varying edge flows.

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