Kernel Regression with Tensor Trains and Hadamard Overparameterization

Abstract:Kernel regression with tensor trains and Hadamard overparameterization (KReTTaH) is introduced as a training-data-free, interpretable, and nonparametric framework for multi-way data imputation. The imputation problem is reformulated as regression in reproducing kernel Hilbert spaces (RKHS), where the tensor regression coefficients are explicitly constrained to lie on fixed-rank tensor-train (TT) manifolds and structured via Hadamard overparameterization to promote sparsity and high representational efficiency. Rather than relying on costly cross-validation, KReTTaH jointly optimizes the TT coefficient tensors and the kernel covariance matrices within a Riemannian product-manifold framework -- the former on fixed-rank TT manifolds, the latter on the manifold of positive-definite matrices -- thereby enabling automated kernel-hyperparameter selection. Numerical tests on two challenging applications -- imputation of high-dimensional functional magnetic resonance imaging (fMRI) data and recovery of missing edge flows in dynamic graphs -- demonstrate that KReTTaH consistently outperforms state-of-the-art tensor-, Bayesian-, and neural-network-based baselines in terms of modeling accuracy.

Machine Learning (stat.ML); Machine Learning (cs.LG); Signal Processing (eess.SP)

arXiv:2607.17390 [stat.ML]

(or arXiv:2607.17390v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.17390 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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