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70
An interiorpoint method for largescale l1regularized logistic regression
 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 interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand ..."
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Cited by 153 (6 self)
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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 interiorpoint method for solving largescale ℓ1regularized logistic regression problems. Small problems with up to a thousand or so features and examples can be solved in seconds on a PC; medium sized problems, with tens of thousands of features and examples, can be solved in tens of seconds (assuming some sparsity in the data). A variation on the basic method, that uses a preconditioned conjugate gradient method to compute the search step, can solve very large problems, with a million features and examples (e.g., the 20 Newsgroups data set), in a few minutes, on a PC. Using warmstart techniques, a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently.
A Dual Coordinate Descent Method for Largescale Linear SVM
"... In many applications, data appear with a huge number of instances as well as features. Linear Support Vector Machines (SVM) is one of the most popular tools to deal with such largescale sparse data. This paper presents a novel dual coordinate descent method for linear SVM with L1 and L2loss functi ..."
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Cited by 96 (10 self)
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In many applications, data appear with a huge number of instances as well as features. Linear Support Vector Machines (SVM) is one of the most popular tools to deal with such largescale sparse data. This paper presents a novel dual coordinate descent method for linear SVM with L1 and L2loss functions. The proposed method is simple and reaches an ɛaccurate solution in O(log(1/ɛ)) iterations. Experiments indicate that our method is much faster than state of the art solvers such as Pegasos, TRON, SVM perf, and a recent primal coordinate descent implementation. 1.
Training a support vector machine in the primal
 Neural Computation
, 2007
"... Most literature on Support Vector Machines (SVMs) concentrate on the dual optimization problem. In this paper, we would like to point out that the primal problem can also be solved efficiently, both for linear and nonlinear SVMs, and that there is no reason for ignoring this possibilty. On the cont ..."
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Cited by 91 (5 self)
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Most literature on Support Vector Machines (SVMs) concentrate on the dual optimization problem. In this paper, we would like to point out that the primal problem can also be solved efficiently, both for linear and nonlinear SVMs, and that there is no reason for ignoring this possibilty. On the contrary, from the primal point of view new families of algorithms for large scale SVM training can be investigated.
Trust region Newton method for largescale logistic regression
 In Proceedings of the 24th International Conference on Machine Learning (ICML
, 2007
"... Largescale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the loglikelihood of the logistic regression model. The proposed method uses only approximate Newton steps in ..."
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Cited by 64 (10 self)
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Largescale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the loglikelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than the commonly used quasi Newton approach for logistic regression. We also compare it with existing linear SVM implementations. 1
Large scale transductive svms
 JMLR
"... We show how the ConcaveConvex Procedure can be applied to Transductive SVMs, which traditionally require solving a combinatorial search problem. This provides for the first time a highly scalable algorithm in the nonlinear case. Detailed experiments verify the utility of our approach. Software is a ..."
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Cited by 62 (5 self)
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We show how the ConcaveConvex Procedure can be applied to Transductive SVMs, which traditionally require solving a combinatorial search problem. This provides for the first time a highly scalable algorithm in the nonlinear case. Detailed experiments verify the utility of our approach. Software is available at
A scalable modular convex solver for regularized risk minimization
 In KDD. ACM
, 2007
"... A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Logistic Regression, Conditional Random Fields (CRFs ..."
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Cited by 59 (14 self)
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A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Logistic Regression, Conditional Random Fields (CRFs), and Lasso amongst others. This paper describes the theory and implementation of a highly scalable and modular convex solver which solves all these estimation problems. It can be parallelized on a cluster of workstations, allows for datalocality, and can deal with regularizers such as ℓ1 and ℓ2 penalties. At present, our solver implements 20 different estimation problems, can be easily extended, scales to millions of observations, and is up to 10 times faster than specialized solvers for many applications. The open source code is freely available as part of the ELEFANT toolbox.
Building Support Vector Machines with Reduced Classifier Complexity
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... Support vector machines (SVMs), though accurate, are not preferred in applications requiring great classification speed, due to the number of support vectors being large. To overcome this problem we devise a primal method with the following properties: (1) it decouples the idea of basis functions ..."
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Cited by 58 (1 self)
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Support vector machines (SVMs), though accurate, are not preferred in applications requiring great classification speed, due to the number of support vectors being large. To overcome this problem we devise a primal method with the following properties: (1) it decouples the idea of basis functions from the concept of support vectors; (2) it greedily finds a set of kernel basis functions of a specified maximum size (d max ) to approximate the SVM primal cost function well; (3) it is efficient and roughly scales as O(nd max ) where n is the number of training examples; and, (4) the number of basis functions it requires to achieve an accuracy close to the SVM accuracy is usually far less than the number of SVM support vectors.
Large Scale Semisupervised Linear SVMs
, 2006
"... Large scale learning is often realistic only in a semisupervised setting where a small set of labeled examples is available together with a large collection of unlabeled data. In many information retrieval and data mining applications, linear classifiers are strongly preferred because of their ease ..."
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Cited by 51 (9 self)
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Large scale learning is often realistic only in a semisupervised setting where a small set of labeled examples is available together with a large collection of unlabeled data. In many information retrieval and data mining applications, linear classifiers are strongly preferred because of their ease of implementation, interpretability and empirical performance. In this work, we present a family of semisupervised linear support vector classifiers that are designed to handle partiallylabeled sparse datasets with possibly very large number of examples and features. At their core, our algorithms employ recently developed modified finite Newton techniques. Our contributions in this paper are as follows: (a) We provide an implementation of Transductive SVM (TSVM) that is significantly more efficient and scalable than currently used dual techniques, for linear classification problems involving large, sparse datasets. (b) We propose a variant of TSVM that involves multiple switching of labels. Experimental results show that this variant provides an order of magnitude further improvement in training efficiency. (c) We present a new algorithm for semisupervised learning based on a Deterministic Annealing (DA) approach. This algorithm alleviates the problem of local minimum in the TSVM optimization procedure while also being computationally attractive. We conduct an empirical study on several document classification tasks which confirms the value of our methods in large scale semisupervised settings.
Bundle Methods for Regularized Risk Minimization
"... A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Gaussian Processes, Logistic Regression, Conditional ..."
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Cited by 36 (2 self)
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A wide variety of machine learning problems can be described as minimizing a regularized risk functional, with different algorithms using different notions of risk and different regularizers. Examples include linear Support Vector Machines (SVMs), Gaussian Processes, Logistic Regression, Conditional Random Fields (CRFs), and Lasso amongst others. This paper describes the theory and implementation of a scalable and modular convex solver which solves all these estimation problems. It can be parallelized on a cluster of workstations, allows for datalocality, and can deal with regularizers such as L1 and L2 penalties. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1/ɛ) steps to ɛ precision for general convex problems and in O(log(1/ɛ)) steps for continuously differentiable problems. We demonstrate the performance of our general purpose solver on a variety of publicly available datasets.
A continuation method for semisupervised svms
 In International Conference on Machine Learning
, 2006
"... SemiSupervised Support Vector Machines (S3VMs) are an appealing method for using unlabeled data in classification: their objective function favors decision boundaries which do not cut clusters. However their main problem is that the optimization problem is nonconvex and has many local minima, whic ..."
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Cited by 31 (3 self)
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SemiSupervised Support Vector Machines (S3VMs) are an appealing method for using unlabeled data in classification: their objective function favors decision boundaries which do not cut clusters. However their main problem is that the optimization problem is nonconvex and has many local minima, which often results in suboptimal performances. In this paper we propose to use a global optimization technique known as continuation to alleviate this problem. Compared to other algorithms minimizing the same objective function, our continuation method often leads to lower test errors. 1.