arXiv subjects

Hiroki Hasegawa

Publications and source records attributed to Hiroki Hasegawa.

4 recordsLinked to original sources

arXiv2026

Structural Loss Metrics for Tensor Approximation via Matrix Low-Rank Approximation

Matricized low-rank approximation via SVD is a standard surrogate for tensor decompositions, but entry-wise reconstruction error fails to capture multiway geometric degradation. Under an orthogonal Tucker model, we characterize this degradation using two metrics: cross-mode Direction Loss, measuring geometric subspace deviation from rank truncation and noise rotation, and Interaction Loss, quantifying multilinear interaction distortion in the core tensor. We prove that squared relative reconstruction error orthogonally decomposes into interaction loss and out-of-subspace energy, and derive a Wedin-type bound establishing the stability of a plug-in Direction Loss estimator. Experiments on synthetic and hyperspectral datasets demonstrate that nearly identical reconstruction errors can yield markedly different structural-loss profiles; hyperspectral patches with comparable reconstruction errors exhibit up to a 4.6-fold difference in Direction Loss, correlating with severe visual blurring.

cs.CV↗

arXiv2026

Covariance-Based Structural Equation Modeling in Small-Sample Settings with $p>n$

Factor-based Structural Equation Modeling (SEM) relies on likelihood-based estimation assuming a nonsingular sample covariance matrix, which breaks down in small-sample settings with $p>n$. To address this, we propose a novel estimation principle that reformulates the covariance structure into self-covariance and cross-covariance components. The resulting framework defines a likelihood-based feasible set combined with a relative error constraint, enabling stable estimation in small-sample settings where $p>n$ for sign and direction. Experiments on synthetic and real-world data show improved stability, particularly in recovering the sign and direction of structural parameters. These results extend covariance-based SEM to small-sample settings and provide practically useful directional information for decision-making.

cs.LG↗

arXiv2026

Interaction Tensor SHAP

This study proposes Interaction Tensor SHAP (IT-SHAP), a tensor algebraic formulation of the Shapley Taylor Interaction Index (STII) that makes its computational structure explicit. STII extends the Shapley value to higher order interactions, but its exponential combinatorial definition makes direct computation intractable at scale. We reformulate STII as a linear transformation acting on a value function and derive an explicit algebraic representation of its weight tensor. This weight tensor is shown to possess a multilinear structure induced by discrete finite difference operators. When the value function admits a Tensor Train representation, higher order interaction indices can be computed in the parallel complexity class NC squared. In contrast, under general tensor network representations without structural assumptions, the same computation is proven to be P sharp hard. The main contributions are threefold. First, we establish an exact Tensor Train representation of the STII weight tensor. Second, we develop a parallelizable evaluation algorithm with explicit complexity bounds under the Tensor Train assumption. Third, we prove that computational intractability is unavoidable in the absence of such structure. These results demonstrate that the computational difficulty of higher order interaction analysis is determined by the underlying algebraic representation rather than by the interaction index itself, providing a theoretical foundation for scalable interpretation of high dimensional models.

cs.LG↗

arXiv2025

A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor decomposition methods require predefined ranks and iterative optimization, resulting in high computational costs and dependence on analyst expertise. This study proposes a novel tensor low-rank approximation method that eliminates both prior rank specification and iterative optimization. The method applies statistical singular value hard thresholding to each mode-wise unfolded matrix to automatically extract statistically significant components, effectively reducing noise while preserving the intrinsic structure. Theoretically, the optimal thresholds for each mode are derived from the asymptotic properties of the Marcenko-Pastur distribution. Simulation experiments demonstrate that the proposed method outperforms conventional approaches (HOSVD, HOOI, and Tucker-L2E) in both estimation accuracy and computational efficiency. These results indicate that the proposed approach provides a theoretically grounded, fully automatic, and non-iterative framework for tensor decomposition.

cs.LG↗