# Kernel Regression with Tensor Trains and Hadamard Overparameterization

arXiv: https://arxiv.org/abs/2607.17390 · HTML: https://mlsanity.com/paper/2607.17390/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 66 references that are in the map.
- First posted on arXiv 19 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [BOLD5000: A public fMRI dataset of 5000 images](https://mlsanity.com/paper/1809.01281/) (2018)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Simplicial Convolutional Neural Networks](https://mlsanity.com/paper/2110.02585/) (2021)
- [HodgeNet: Graph Neural Networks for Edge Data](https://mlsanity.com/paper/1912.02354/) (2019)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Smoothing the Edges: Smooth Optimization for Sparse Regularization using Hadamard Overparametrization](https://mlsanity.com/paper/2307.03571/) (2023)
- [Data adaptive RKHS Tikhonov regularization for learning kernels in operators](https://mlsanity.com/paper/2203.03791/) (2022)
- [Gradient-based Optimization for Regression in the Functional Tensor-Train Format](https://mlsanity.com/paper/1801.00885/) (2018)
- [Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data](https://mlsanity.com/paper/2408.05677/) (2024)
- [Riemannian preconditioned algorithms for tensor completion via tensor ring decomposition](https://mlsanity.com/paper/2302.14456/) (2023)
- [Signal Processing on Product Spaces](https://mlsanity.com/paper/2303.10495/) (2023)
- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning](https://mlsanity.com/paper/2409.05135/) (2024)
- [When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning](https://mlsanity.com/paper/2512.21486/) (2025)

## Abstract (arXiv)

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.