Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm

2010/02/14 by Ruslan Salakhutdinov, Nathan Srebro, Salakhutdinov, Ruslan +1 · 68 citations
Chemistry · Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #Algorithm #Applied mathematics #Artificial intelligence #Chemistry #Computer science #Epistemology #FOS: Computer and information sciences #Indoor and Outdoor Localization Technologies #Machine Learning (cs.LG) #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix norm #Norm (philosophy) #Physics #Regularization (linguistics) #Sparse and Compressive Sensing Techniques #TRACE (psycholinguistics) #cs.LG

paper · pdf · doi:10.48550/arxiv.1002.2780

published in arXiv (Cornell University) (Cornell University) · 9 pages

arxiv created 2010/02/14 · openalex publication_date 2010/02/14 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that matrix completion with trace-norm regularization can be significantly hurt when entries of the matrix are sampled non-uniformly. We introduce a weighted version of the trace-norm regularizer that works well also with non-uniform sampling. Our experimental results demonstrate that the weighted trace-norm regularization indeed yields significant gains on the (highly non-uniformly sampled) Netflix dataset.

Citations

• Local Minima and Convergence in Low-Rank Semidefinite Programming
• Matrix Completion With Noise

Cited by

• On the Benefits of Weight Normalization for Overparameterized Matrix Sensing
• Structured Matrix Completion with Applications to Genomic Data Integration
• Gap Filling in the Plant Kingdom---Trait Prediction Using Hierarchical Probabilistic Matrix Factorization
• Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision
• Matrix Completion from Noisy Entries

Related

• Matrix reconstruction with the local max norm
• Learning with the Weighted Trace-norm under Arbitrary Sampling Distributions
• A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization
• Trace norm regularization for multi-task learning with scarce data
• Learning Parameters for Weighted Matrix Completion via Empirical Estimation