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Asymptotics in empirical risk minimization
, 2006
"... In this paper, we study a twocategory classification problem. We indicate the categories by labels Y = 1 and Y = −1. We observe a covariate, or feature, X ∈ X ⊂ Rd. Consider a collection {ha} of classifiers indexed by a finitedimensional parameter a, and the classifier ha ∗ that minimizes the pre ..."
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Cited by 1 (1 self)
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the prediction error over this class. The parameter a ∗ is estimated by the empirical risk minimizer ân over the class, where the empirical risk is calculated on a training sample of size n. We apply the Kim Pollard Theorem to show that under certain differentiability assumptions, ân converges to a ∗ with rate
Differentially private empirical risk minimization
, 2010
"... 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 77 (6 self)
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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
Penalized empirical risk minimalization Penalized empirical risk minimization
"... Abstract In a twocategory classification problem labeled by Y = 1 and Y = −1, we observe a covariate, or feature, X ∈ X ⊂ R d . We first consider a general loss function and a general penalty and obtain an upper bound for the penalizedrisk of the penalized empirical risk minimizer. As an example, ..."
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Abstract In a twocategory classification problem labeled by Y = 1 and Y = −1, we observe a covariate, or feature, X ∈ X ⊂ R d . We first consider a general loss function and a general penalty and obtain an upper bound for the penalizedrisk of the penalized empirical risk minimizer. As an example
Private Empirical Risk Minimization, Revisited
, 2014
"... In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower bounds for private ERM assuming only that each data point’ ..."
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In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower bounds for private ERM assuming only that each data point
Empirical risk minimization for heavytailed losses
, 2014
"... The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess ri ..."
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Cited by 1 (0 self)
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The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess
Local Complexities for Empirical Risk Minimization
 In Proceedings of the 17th Annual Conference on Learning Theory (COLT
, 2004
"... Abstract. We present sharp bounds on the risk of the empirical minimization algorithm under mild assumptions on the class. We introduce the notion of isomorphic coordinate projections and show that this leads to a sharper error bound than the best previously known. The quantity which governs this bo ..."
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Cited by 9 (2 self)
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Abstract. We present sharp bounds on the risk of the empirical minimization algorithm under mild assumptions on the class. We introduce the notion of isomorphic coordinate projections and show that this leads to a sharper error bound than the best previously known. The quantity which governs
Aggregation via Empirical Risk Minimization
, 2008
"... Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show tha ..."
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Cited by 8 (3 self)
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Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show
Aggregation versus Empirical Risk Minimization
, 2007
"... Given a finite set F of estimators, the problem of aggregation is to construct a new estimator that has a risk as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show t ..."
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Given a finite set F of estimators, the problem of aggregation is to construct a new estimator that has a risk as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show
Ranking and scoring using empirical risk minimization
 Proceedings of the Eighteenth Annual Conference on Computational Learning Theory (COLT
, 2005
"... Abstract. A general model is proposed for studying ranking problems. We investigate learning methods based on empirical minimization of the natural estimates of the ranking risk. The empirical estimates are of the form of a Ustatistic. Inequalities from the theory of Ustatistics and Uprocesses are ..."
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Cited by 29 (8 self)
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Abstract. A general model is proposed for studying ranking problems. We investigate learning methods based on empirical minimization of the natural estimates of the ranking risk. The empirical estimates are of the form of a Ustatistic. Inequalities from the theory of Ustatistics and Uprocesses
Results 1  10
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1,380,509