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861
Adaptive Subgradient Methods for Online Learning and Stochastic Optimization
, 2010
"... Stochastic subgradient methods are widely used, well analyzed, and constitute effective tools for optimization and online learning. Stochastic gradient methods ’ popularity and appeal are largely due to their simplicity, as they largely follow predetermined procedural schemes. However, most common s ..."
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Cited by 276 (3 self)
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Stochastic subgradient methods are widely used, well analyzed, and constitute effective tools for optimization and online learning. Stochastic gradient methods ’ popularity and appeal are largely due to their simplicity, as they largely follow predetermined procedural schemes. However, most common subgradient approaches are oblivious to the characteristics of the data being observed. We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradientbased learning. The adaptation, in essence, allows us to find needles in haystacks in the form of very predictive but rarely seenfeatures. Ourparadigmstemsfromrecentadvancesinstochasticoptimizationandonlinelearning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. In a companion paper, we validate experimentally our theoretical analysis and show that the adaptive subgradient approach outperforms stateoftheart, but nonadaptive, subgradient algorithms. 1
An extension on ―statistical comparisons of classifiers over multiple data sets‖ for all pairwise comparisons
 Journal of Machine Learning Research
"... In a recently published paper in JMLR, Demˇsar (2006) recommends a set of nonparametric statistical tests and procedures which can be safely used for comparing the performance of classifiers over multiple data sets. After studying the paper, we realize that the paper correctly introduces the basic ..."
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Cited by 140 (35 self)
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In a recently published paper in JMLR, Demˇsar (2006) recommends a set of nonparametric statistical tests and procedures which can be safely used for comparing the performance of classifiers over multiple data sets. After studying the paper, we realize that the paper correctly introduces the basic procedures and some of the most advanced ones when comparing a control method. However, it does not deal with some advanced topics in depth. Regarding these topics, we focus on more powerful proposals of statistical procedures for comparing n×n classifiers. Moreover, we illustrate an easy way of obtaining adjusted and comparable pvalues in multiple comparison procedures.
Sparse Online Learning via Truncated Gradient
"... We propose a general method called truncated gradient to induce sparsity in the weights of onlinelearning algorithms with convex loss. This method has several essential properties. First, the degree of sparsity is continuous—a parameter controls the rate of sparsification from no sparsification to ..."
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Cited by 106 (4 self)
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We propose a general method called truncated gradient to induce sparsity in the weights of onlinelearning algorithms with convex loss. This method has several essential properties. First, the degree of sparsity is continuous—a parameter controls the rate of sparsification from no sparsification to total sparsification. Second, the approach is theoretically motivated, and an instance of it can be regarded as an online counterpart of the popular L1regularization method in the batch setting. We prove small rates of sparsification result in only small additional regret with respect to typical onlinelearning guarantees. Finally, the approach works well empirically. We apply it to several datasets and find for datasets with large numbers of features, substantial sparsity is discoverable. 1
On smoothing and inference for topic models
 In Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence
, 2009
"... Latent Dirichlet analysis, or topic modeling, is a flexible latent variable framework for modeling highdimensional sparse count data. Various learning algorithms have been developed in recent years, including collapsed Gibbs sampling, variational inference, and maximum a posteriori estimation, and ..."
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Cited by 101 (8 self)
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Latent Dirichlet analysis, or topic modeling, is a flexible latent variable framework for modeling highdimensional sparse count data. Various learning algorithms have been developed in recent years, including collapsed Gibbs sampling, variational inference, and maximum a posteriori estimation, and this variety motivates the need for careful empirical comparisons. In this paper, we highlight the close connections between these approaches. We find that the main differences are attributable to the amount of smoothing applied to the counts. When the hyperparameters are optimized, the differences in performance among the algorithms diminish significantly. The ability of these algorithms to achieve solutions of comparable accuracy gives us the freedom to select computationally efficient approaches. Using the insights gained from this comparative study, we show how accurate topic models can be learned in several seconds on text corpora with thousands of documents. 1
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 90 (21 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
Fast Support Vector Machine Training and Classification
 on Graphics Processors, Proc. 25th Int. Conf. Machine Learning
, 2008
"... Recent developments in programmable, highly parallel Graphics Processing Units (GPUs) have enabled high performance implementations of machine learning algorithms. We describe a solver for Support Vector Machine training running on a GPU, using the Sequential Minimal Optimization algorithm and an ad ..."
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Cited by 76 (2 self)
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Recent developments in programmable, highly parallel Graphics Processing Units (GPUs) have enabled high performance implementations of machine learning algorithms. We describe a solver for Support Vector Machine training running on a GPU, using the Sequential Minimal Optimization algorithm and an adaptive first and second order working set selection heuristic, which achieves speedups of 935 × over LIBSVM running on a traditional processor. We also present a GPUbased system for SVM classification which achieves speedups of 81138 × over LIBSVM (524 × over our own CPU based SVM classifier). 1.
Bolasso: model consistent lasso estimation through the bootstrap
 In Proceedings of the Twentyfifth International Conference on Machine Learning (ICML
, 2008
"... We consider the leastsquare linear regression problem with regularization by the ℓ1norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various decays of the regularization parameter, we compute asymptotic ..."
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Cited by 74 (14 self)
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We consider the leastsquare linear regression problem with regularization by the ℓ1norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various decays of the regularization parameter, we compute asymptotic equivalents of the probability of correct model selection (i.e., variable selection). For a specific rate decay, we show that the Lasso selects all the variables that should enter the model with probability tending to one exponentially fast, while it selects all other variables with strictly positive probability. We show that this property implies that if we run the Lasso for several bootstrapped replications of a given sample, then intersecting the supports of the Lasso bootstrap estimates leads to consistent model selection. This novel variable selection algorithm, referred to as the Bolasso, is compared favorably to other linear regression methods on synthetic data and datasets from the UCI machine learning repository. 1.
Nonlinear causal discovery with additive noise models
"... The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In ..."
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Cited by 72 (27 self)
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The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the datagenerating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true datagenerating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1
Conditional random fields for activity recognition
 In Proceedings of the Sixth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2007
, 2007
"... of any sponsoring institution, the U.S. government or any other entity. ..."
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Cited by 69 (0 self)
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of any sponsoring institution, the U.S. government or any other entity.
Differentially private empirical risk minimization
 In
, 2011
"... Privacypreserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacypreserving approximations of classifiers learned via (regularized) empirical ris ..."
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Cited by 67 (5 self)
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Privacypreserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacypreserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the ǫdifferential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacypreserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. We prove theoretical results showing that our algorithms preserve privacy and give generalization bounds for linear and nonlinear kernels. We further present a privacypreserving technique for tuning the parameters in general machine learning algorithms, thereby providing endtoend privacy guarantees for the training process. We apply these results to produce privacypreserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous stateoftheart, output perturbation, in managing the inherent tradeoff between privacy and learning performance. 1