The paper treats large language model (LLM) evaluation as a tensor completion problem, modeling noisy, sparse, and non‑uniform pairwise human judgments through a low‑rank latent score tensor under Bradley‑Terry‑Luce‑type models. It derives the efficient influence function and semiparametric efficiency bound for smooth functionals of the true tensor, and proposes a one‑step debiased estimator with asymptotic normality. A key innovation is a score‑whitening technique that equalizes local Fisher information, overcoming anisotropy in the information operator and enabling stable inference at optimal sample‑complexity.
By Jiachun Li, David Simchi-Levi, Will Wei Sun
arXiv:2410. 06329v4 Announce Type: replace-cross Abstract: Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning.
By Joseph K. Chege, Arie Yeredor, Martin Haardt
Tensor Completion using Subspace Information (TCSI) is an algorithm that leverages side information by estimating a subspace and reformulating tensor completion as a matrix regression problem. Theoretical analysis shows that accurate subspace information reduces sample complexity to nearly linear in the uncoupled ambient dimensions and relaxes signal-to-noise ratio requirements compared to existing guarantees. Numerical simulations and an application to reconstructing global Total Electron Content (TEC) maps demonstrate lower reconstruction errors than competing methods.
By Jingyang Li, Michael K. Ng
arXiv:2109. 11057v2 Announce Type: replace-cross Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights.
By Elena Tuzhilina, Trevor Hastie
The paper introduces Coupled Tensor‑Tensor Completion (CTTC), a new framework that incorporates side information in tensor form to enhance tensor completion tasks. CTTC leverages hidden connections among multimodal tensors and is grounded in distance metric learning and group theory. Experiments on the DTD and LINCS datasets show that CTTC outperforms existing methods such as HaLRTC, CTRC, Cell, and NTDDR in both run‑time and root‑sum‑of‑errors accuracy for predicting drug effects.
The paper introduces Coupled Tensor‑Tensor Completion (CTTC), a new framework that incorporates side information in tensor form to enhance tensor completion tasks. CTTC leverages hidden connections among multimodal tensors and is grounded in distance metric learning and group theory. Experiments on the DTD and LINCS datasets show that CTTC outperforms existing methods such as HaLRTC, CTRC, Cell, and NTDDR in both runtime and root‑sum‑of‑squares error for drug effect prediction.
By Maryam Bagherian, Albert Hung, Ivo Dinov, Joshua Welch
The paper introduces a functional Tucker decomposition (FTD) that incorporates a mode-wise continuity constraint into tensor factorization, modeling continuous modes as functions in a reproducing kernel Hilbert space (RKHS) without requiring a predefined basis. It preserves the multilinear subspace structure of the Tucker model and provides a reconstruction error bound for continuous modes, quantifying approximation quality when a subspace estimated on one domain is reused on another. The authors demonstrate the practical value of this subspace transfer on cross-domain classification tasks in hyperspectral imaging and multivariate time-series analysis.
By Noah Steidle, Joppe De Jonghe, Mariya Ishteva
arXiv:2607. 13919v1 Announce Type: new Abstract: Nonnegative Matrix Factorization (NMF) is a fundamental tool in unsupervised learning, which approximates a nonnegative matrix by the product of two low-rank nonnegative factors.
By Damien Lesens, J\'er\'emy E. Cohen, Bora U\c{c}ar
arXiv:2606. 15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products.
By Zvonimir Bujanovi\'c, Daniel Kressner, Hrvoje Oli\'c
arXiv:2412. 07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications.
By Mengying Lei, Lijun Sun
arXiv:2405. 18220v4 Announce Type: replace-cross Abstract: Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power terms in the objective function, which hinder the derivation of closed-form update rules.
By Kazu Ghalamkari, Jesper L{\o}ve Hinrich, Morten M{\o}rup
arXiv:2607. 09546v1 Announce Type: new Abstract: We address the low-rank matrix completion problem by incorporating graph regularization into the existing Riemannian Trust-Region Matrix Completion (RTRMC) framework.
By Beno\^it Loucheur, P. -A. Absil, Michel Journ\'ee