Convex Optimization
Feature selection, L1 vs. L2 regularization, and rotational invariance
ICML '04 Proceedings of the twenty-first international conference on Machine learning
IEEE Transactions on Neural Networks
Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches
ECML '07 Proceedings of the 18th European conference on Machine Learning
Domain Adaptation of Conditional Probability Models Via Feature Subsetting
PKDD 2007 Proceedings of the 11th European conference on Principles and Practice of Knowledge Discovery in Databases
Large-scale sparse logistic regression
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning dynamic temporal graphs for oil-production equipment monitoring system
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Exponential family sparse coding with applications to self-taught learning
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Stochastic gradient descent training for L1-regularized log-linear models with cumulative penalty
ACL '09 Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP: Volume 1 - Volume 1
A Fast Hybrid Algorithm for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
Multiplicative updates for L1-regularized linear and logistic regression
IDA'07 Proceedings of the 7th international conference on Intelligent data analysis
Efficient learning and feature selection in high-dimensional regression
Neural Computation
Effective structure learning for EDA via L1-regularizedbayesian networks
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Learning to combine discriminative classifiers: confidence based
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Expert Systems with Applications: An International Journal
The Journal of Machine Learning Research
A coordinate gradient descent method for l1-regularized convex minimization
Computational Optimization and Applications
Classification and feature selection for craniosynostosis
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
An improved GLMNET for L1-regularized logistic regression
The Journal of Machine Learning Research
Coupled Matrix Factorization with Sparse Factors to Identify Potential Biomarkers in Metabolomics
International Journal of Knowledge Discovery in Bioinformatics
Coupled Matrix Factorization with Sparse Factors to Identify Potential Biomarkers in Metabolomics
International Journal of Knowledge Discovery in Bioinformatics
Embedded local feature selection within mixture of experts
Information Sciences: an International Journal
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L1 regularized logistic regression is now a workhorse of machine learning: it is widely used for many classification problems, particularly ones with many features. L1 regularized logistic regression requires solving a convex optimization problem. However, standard algorithms for solving convex optimization problems do not scale well enough to handle the large datasets encountered in many practical settings. In this paper, we propose an efficient algorithm for L1 regularized logistic regression. Our algorithm iteratively approximates the objective function by a quadratic approximation at the current point, while maintaining the L1 constraint. In each iteration, it uses the efficient LARS (Least Angle Regression) algorithm to solve the resulting L1 constrained quadratic optimization problem. Our theoretical results show that our algorithm is guaranteed to converge to the global optimum. Our experiments show that our algorithm significantly outperforms standard algorithms for solving convex optimization problems. Moreover, our algorithm outperforms four previously published algorithms that were specifically designed to solve the L1 regularized logistic regression problem.