基于张量列车和哈达玛超参数化的核回归

中文摘要 AI 辅助

本文介绍了一种用于多向数据插补的无训练数据、可解释且非参数的框架——基于张量列车和哈达玛超参数化的核回归（KReTTaH）。插补问题被重新表述为再生核希尔伯特空间（RKHS）中的回归，其中张量回归系数被明确约束在固定秩张量列车（TT）流形上，并通过哈达玛超参数化进行结构化以促进稀疏性和高表示效率。KReTTaH在黎曼积流形框架内联合优化TT系数张量和核协方差矩阵，实现自动核超参数选择。在高维功能磁共振成像（fMRI）数据插补和动态图中缺失边流恢复这两个具有挑战性的应用上的数值测试表明，KReTTaH在建模精度方面始终优于基于张量、贝叶斯和神经网络的现有基线。

英文摘要

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.

发表机构

• Institute of Science Tokyo（东京科学研究所）
• University of Piraeus（比雷埃克斯大学）
• Florida Atlantic University（佛罗里达亚特兰大大学）

机构由 AI 辅助整理，请以论文原文为准。