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We introduce a new family of matrix norms, the ''local max'' norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this new family can be used to interpolate between the (weighted or unweighted) trace norm and the more conservative max norm. We test this interpolation on simulated data and on the large-scale Netflix and MovieLens ratings data, and find improved accuracy relative to the existing matrix norms. We also provide theoretical results showing learning guarantees for some of the new norms.
Author Information
Rina Foygel (Stanford University)
Nati Srebro (TTI-Chicago)
Russ Salakhutdinov (Carnegie Mellon University)
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Nati Srebro -
2010 Poster: Tight Sample Complexity of Large-Margin Learning »
Sivan Sabato · Nati Srebro · Naftali Tishby -
2010 Poster: Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm »
Russ Salakhutdinov · Nati Srebro -
2010 Poster: Extended Bayesian Information Criteria for Gaussian Graphical Models »
Rina Foygel · Mathias Drton -
2010 Poster: Practical Large-Scale Optimization for Max-norm Regularization »
Jason D Lee · Benjamin Recht · Russ Salakhutdinov · Nati Srebro · Joel A Tropp -
2010 Poster: Smoothness, Low Noise and Fast Rates »
Nati Srebro · Karthik Sridharan · Ambuj Tewari -
2009 Workshop: Approximate Learning of Large Scale Graphical Models »
Russ Salakhutdinov · Amir Globerson · David Sontag -
2009 Workshop: Understanding Multiple Kernel Learning Methods »
Brian McFee · Gert Lanckriet · Francis Bach · Nati Srebro -
2009 Poster: Statistical Analysis of Semi-Supervised Learning: The Limit of Infinite Unlabelled Data »
Boaz Nadler · Nati Srebro · Xueyuan Zhou -
2009 Poster: Replicated Softmax: an Undirected Topic Model »
Russ Salakhutdinov · Geoffrey E Hinton -
2009 Spotlight: Statistical Analysis of Semi-Supervised Learning: The Limit of Infinite Unlabelled Data »
Boaz Nadler · Nati Srebro · Xueyuan Zhou -
2009 Poster: Learning in Markov Random Fields using Tempered Transitions »
Russ Salakhutdinov -
2009 Poster: Modelling Relational Data using Bayesian Clustered Tensor Factorization »
Ilya Sutskever · Russ Salakhutdinov · Josh Tenenbaum -
2008 Poster: Fast Rates for Regularized Objectives »
Karthik Sridharan · Shai Shalev-Shwartz · Nati Srebro -
2008 Poster: Evaluating probabilities under high-dimensional latent variable models »
Iain Murray · Russ Salakhutdinov -
2008 Spotlight: Evaluating probabilities under high-dimensional latent variable models »
Iain Murray · Russ Salakhutdinov -
2007 Poster: Probabilistic Matrix Factorization »
Russ Salakhutdinov · Andriy Mnih -
2007 Oral: Probabilistic Matrix Factorization »
Russ Salakhutdinov · Andriy Mnih -
2007 Poster: Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes »
Russ Salakhutdinov · Geoffrey E Hinton