GroupLens: an open architecture for collaborative filtering of netnews
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Selecting weighting factors in logarithmic opinion pools
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A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Collaborative filtering with privacy via factor analysis
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Generalizing local translation models
SSST '08 Proceedings of the Second Workshop on Syntax and Structure in Statistical Translation
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Exponential family sparse coding with applications to self-taught learning
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EMNLP '09 Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing: Volume 1 - Volume 1
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Multiplicative updates for L1-regularized linear and logistic regression
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Sample complexity of linear learning machines with different restrictions over weights
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Fully corrective boosting with arbitrary loss and regularization
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Subspace clustering of high-dimensional data: a predictive approach
Data Mining and Knowledge Discovery
Heartbeat classification using disease-specific feature selection
Computers in Biology and Medicine
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We consider supervised learning in the presence of very many irrelevant features, and study two different regularization methods for preventing overfitting. Focusing on logistic regression, we show that using L1 regularization of the parameters, the sample complexity (i.e., the number of training examples required to learn "well,") grows only logarithmically in the number of irrelevant features. This logarithmic rate matches the best known bounds for feature selection, and indicates that L1 regularized logistic regression can be effective even if there are exponentially many irrelevant features as there are training examples. We also give a lower-bound showing that any rotationally invariant algorithm---including logistic regression with L2 regularization, SVMs, and neural networks trained by backpropagation---has a worst case sample complexity that grows at least linearly in the number of irrelevant features.