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

2025-09-26

AI Summary

Existing methods for imputing missing values in dynamic graph streams and other multiway data suffer from low accuracy and poor interpretability. Method: We propose an interpretable nonparametric framework that integrates the low-rank Tensor Train (TT) decomposition with Reproducing Kernel Hilbert Space (RKHS) regression. To enhance parameter efficiency, we introduce Hadamard overparameterization; to encode structural priors, we optimize TT cores on the Riemannian manifold—naturally incorporating graph topology and encouraging sparsity; and we formulate missing-value estimation as a structured-constrained kernel regression problem. Results: Experiments on real-world dynamic graph edge streams demonstrate that our method significantly outperforms state-of-the-art tensor completion and graph neural network approaches in imputation accuracy, while simultaneously achieving strong interpretability and computational efficiency. The framework establishes a novel paradigm for missing-data imputation in multidimensional, time-evolving, structured data.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Imputing missing multi-way data via kernel regression
• Estimating dynamic graph flows with topological priors
• Achieving parameter efficiency through tensor train decomposition

Innovation

• Uses tensor trains with Hadamard overparametrization for efficiency
• Solves smooth inverse problems on Riemannian manifolds
• Incorporates graph-based topological priors via inverse problem