Nuclear Norm Minimization

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3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Nuclear Norm-Regularized Bayesian Matrix Completion
Sep 24, 2026Calvin TolbertNuclear Norm Minimization Posterior Sampling
School of Operations Research and Information Engineering Cornell University
Regularized Least Squares Training of Quadratic Neural Networks with Applications to System Identification
Sep 15, 2026Luis Rodrigues, Zachary Yetman Van Egmond, Mohammad R. Amiri FardNeural Network Optimization Nuclear Norm Minimization
Department of Electrical and Computer Engineering Concordia University Montr´eal, QC, Canada
On the Regularization Landscape for the Linear Recommendation Models
Sep 12, 2026Dong Li, Zhenming Liu, Ruoming Jin +4Nuclear Norm Minimization Low-Rank Approximation
Kent State University, USA · College of William and Mary, USA · iLambda, USA
Three-Pronged Spectral Control for Federated Parameter Efficient Fine Tuning
Jul 23, 2026Shiva Raj Pokhrel, Dipsan Bhattarai, Anwar WalidFederated Learning Aggregation Nuclear Norm Minimization
School of IT, Deakin University, Australia · Columbia University, USA
SLORR: Simple and Efficient In-Training Low-Rank Regularization
Jul 9, 2026David González-Martínez, Shiwei LiuLLM Compression Low-Rank Matrix Decomposition
Max Planck Institute for Intelligent Systems · University of Tübingen · ELLIS Institute Tübingen +1
Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View
Jun 3, 2026Mingyu LiSpectral Regularization Weight Decay
Beijing Normal University
Group-Aware Matrix Estimation and Latent Subspace Recovery
May 19, 2026Hamza Golubovic, Matthew Shen, Genevera I. Allen +1Low-Rank Matrix Decomposition Nuclear Norm Minimization
Department of Statistics, Columbia University New York, NY 10027 · Department of Statistics, Irving Institute for Cellular Dynamics, Zuckerman Institute Columbia University New York, NY 10027 · School of Data and Information Sciences, University of North Carolina at Chapel Hill Chapel Hill, NC 27599
Low Rank Tensor Completion via Adaptive ADMM
May 5, 2026Niclas Führling, Getuar Rexhepi, Giuseppe Thadeu Freitas de AbreuTensor Completion Nuclear Norm Minimization
School of Computer Science and Engineering, Constructor University, Bremen, Germany
Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling
Apr 18, 2026Wei Li, Yuyang Li, Kaile Du +2Tensor Completion Tensor Decomposition
The authors are with the School of Automation, Southeast University, Nanjing, China 210018.

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Nuclear Norm-Regularized Bayesian Matrix Completion

Calvin Tolbert

School of Operations Research and Information Engineering Cornell University

Nuclear Norm Minimization Posterior Sampling Matrix Completion

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Matrix completion, the problem of estimating missing entries in a matrix from noisily observed ones, underlies a diverse array of problems such as recommender systems and counterfactual outcome estimation in panel data. Many algorithms address the problem using regularized least squares, often with the nuclear norm as a regularizer, but this method yields a point estimate with no built-in uncertainty quantification. A Bayesian formulation is a natural alternative, and if the noise variance is known, the nuclear norm-based prior yields a log-concave posterior. Unfortunately, in practice, the noise variance will not be known a priori, so for a fully Bayesian approach, a prior must be imposed on it. We give the first sampler for this model with an explicit non-asymptotic guarantee: polynomial in the matrix dimensions and in the reciprocal of the target accuracy. Our technique is to discretize the distribution of the noise precision onto a grid and build a categorical posterior via thermodynamic integration. This extension is not specific to matrix completion and may be useful in other non-log-concave sampling problems where the non-log-concavity is restricted to a single variable and the joint distribution of the remaining variables is nonsmooth. Our contribution is a feasibility result: we show that a polynomial-time Bayesian sampler for this model exists at all, and the resulting complexity, while polynomial, is not intended as a deployable algorithm at current problem scales.

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