Rank, trace-norm and max-norm

Authors:
Nathan Srebro;Adi Shraibman
Affiliations:
Department of Computer Science, University of Toronto, Toronto, ON, Canada;Institute of Computer Science, Hebrew University, Jerusalem, Israel
Venue:
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Year:
2005

Citing 9
Cited 11

Estimating the Optimal Margins of Embeddings in Euclidean Half Spaces

Machine Learning
On the Smallest Possible Dimension and the Largest Possible Margin of Linear Arrangements Representing Given Concept Classes Uniform Distribution

ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
An Algorithmic Theory of Learning: Robust Concepts and Random Projection

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Limitations of learning via embeddings in euclidean half spaces

The Journal of Machine Learning Research
The Expected Norm of Random Matrices

Combinatorics, Probability and Computing
Adaptive routing with end-to-end feedback: distributed learning and geometric approaches

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Learning with matrix factorizations

Learning with matrix factorizations
Geometrical realization of set systems and probabilistic communication complexity

SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Complexity measures of sign matrices

Combinatorica

Fast maximum margin matrix factorization for collaborative prediction

ICML '05 Proceedings of the 22nd international conference on Machine learning
Halfspace Matrices

Computational Complexity
Improving maximum margin matrix factorization

Machine Learning
Adaptive collaborative filtering

Proceedings of the 2008 ACM conference on Recommender systems
Multiverse recommendation: n-dimensional tensor factorization for context-aware collaborative filtering

Proceedings of the fourth ACM conference on Recommender systems
The Sign-Rank of AC$^0$

SIAM Journal on Computing
Increasing energy efficiency in sensor networks: blue noise sampling and non-convex matrix completion

International Journal of Sensor Networks
Collaborative temporal order modeling

Proceedings of the fifth ACM conference on Recommender systems
Music retagging using label propagation and robust principal component analysis

Proceedings of the 21st international conference companion on World Wide Web
Link label prediction in signed social networks

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Scalable hierarchical multitask learning algorithms for conversion optimization in display advertising

Proceedings of the 7th ACM international conference on Web search and data mining

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the rank, trace-norm and max-norm as complexity measures of matrices, focusing on the problem of fitting a matrix with matrices having low complexity. We present generalization error bounds for predicting unobserved entries that are based on these measures. We also consider the possible relations between these measures. We show gaps between them, and bounds on the extent of such gaps.