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An Efficient Projection for l1, ∞ Regularization

by Ariadna Quattoni, Xavier Carreras, Michael Collins, Trevor Darrell
"... In recent years the l1, ∞ norm has been proposed for joint regularization. In essence, this type of regularization aims at extending the l1 framework for learning sparse models to a setting where the goal is to learn a set of jointly sparse models. In this paper we derive a simple and effective proj ..."
Abstract - Cited by 18 (0 self) - Add to MetaCart
In recent years the l1, ∞ norm has been proposed for joint regularization. In essence, this type of regularization aims at extending the l1 framework for learning sparse models to a setting where the goal is to learn a set of jointly sparse models. In this paper we derive a simple and effective

An interior-point method for large-scale l1-regularized logistic regression

by Kwangmoo Koh, Seung-jean Kim, Stephen Boyd, Yi Lin - Journal of Machine Learning Research , 2007
"... Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interior-point method for solving large-scale ℓ1-regularized logistic regression problems. Small problems with up to a thousand ..."
Abstract - Cited by 290 (9 self) - Add to MetaCart
Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interior-point method for solving large-scale ℓ1-regularized logistic regression problems. Small problems with up to a thousand

Efficient l1 regularized logistic regression

by Su-in Lee, Honglak Lee, Pieter Abbeel, Andrew Y. Ng - In AAAI-06 , 2006
"... 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 opti ..."
Abstract - Cited by 68 (4 self) - Add to MetaCart
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

Scalable training of L1-regularized log-linear models

by Galen Andrew, Jianfeng Gao - In ICML ’07 , 2007
"... The l-bfgs limited-memory quasi-Newton method is the algorithm of choice for optimizing the parameters of large-scale log-linear models with L2 regularization, but it cannot be used for an L1-regularized loss due to its non-differentiability whenever some parameter is zero. Efficient algorithms have ..."
Abstract - Cited by 178 (5 self) - Add to MetaCart
The l-bfgs limited-memory quasi-Newton method is the algorithm of choice for optimizing the parameters of large-scale log-linear models with L2 regularization, but it cannot be used for an L1-regularized loss due to its non-differentiability whenever some parameter is zero. Efficient algorithms

Bregman Distance to L1 Regularized Logistic Regression

by Mithun Das Gupta, Thomas S. Huang
"... In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We convert L1-regularized logistic regression (LR) into more general Bregman divergence framework and propose a primal-dual method based algorithm for learning the parameters of the mode ..."
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In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We convert L1-regularized logistic regression (LR) into more general Bregman divergence framework and propose a primal-dual method based algorithm for learning the parameters

Some sharp performance bounds for least squares regression with L1 regularization

by Tong Zhang - Rutgers Univ. MODEL SELECTION 35 Applied and Computational Mathematics California Institute of Technology 300 Firestone, Mail Code 217-50 Pasadena, California 91125 E-mail: emmanuel@acm.caltech.edu plan@acm.caltech.edu , 2009
"... We derive sharp performance bounds for least squares regression with L1 regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [Ann. Statist. 35 (2007) 2313–2351] for the Dantzig selector. ..."
Abstract - Cited by 92 (7 self) - Add to MetaCart
We derive sharp performance bounds for least squares regression with L1 regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [Ann. Statist. 35 (2007) 2313–2351] for the Dantzig selector

Learning combination features with L1 regularization

by Daisuke Okanohara - In Proc. NAACL HLT 2009, Short Papers , 2009
"... When linear classifiers cannot successfully classify data, we often add combination features, which are products of several original features. The searching for effective combination features, namely feature engineering, requires domain-specific knowledge and hard work. We present herein an efficien ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
an efficient algorithm for learning an L1 regularized logistic regression model with combination features. We propose to use the grafting algorithm with efficient computation of gradients. This enables us to find optimal weights efficiently without enumerating all combination features. By using L1

Efficient structure learning of Markov networks using L1regularization

by Su-in Lee, Varun Ganapathi, Daphne Koller - In NIPS , 2006
"... Markov networks are widely used in a wide variety of applications, in problems ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to ..."
Abstract - Cited by 144 (3 self) - Add to MetaCart
to the lack of effective algorithms for learning Markov network structure from data. In this paper, we provide a computationally effective method for learning Markov network structure from data. Our method is based on the use of L1 regularization on the weights of the log-linear model, which has the effect

L1 regularized linear temporal difference learning

by Christopher Painter-wakefield, Ronald Parr , 2012
"... Several recent efforts in the field of reinforcement learning have focused attention on the importance of regularization, but the techniques for incorporating regularization into reinforcement learning algorithms, and the effects of these changes upon the convergence of these algorithms, are ongoing ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
, are ongoing areas of research. In particular, little has been written about the use of regularization in online reinforcement learning. In this paper, we describe a novel online stochastic approximation algorithm for reinforcement learning. We prove convergence of the online algorithm and show that the L1

Parallel Coordinate Descent for L1-Regularized Loss Minimization

by Joseph K. Bradley, Aapo Kyrola, Danny Bickson, Carlos Guestrin
"... We propose Shotgun, a parallel coordinate descent algorithm for minimizing L1regularized losses. Though coordinate descent seems inherently sequential, we prove convergence bounds for Shotgun which predict linear speedups, up to a problemdependent limit. We present a comprehensive empirical study of ..."
Abstract - Cited by 77 (1 self) - Add to MetaCart
We propose Shotgun, a parallel coordinate descent algorithm for minimizing L1regularized losses. Though coordinate descent seems inherently sequential, we prove convergence bounds for Shotgun which predict linear speedups, up to a problemdependent limit. We present a comprehensive empirical study
Results 1 - 10 of 4,577