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NonAsymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning
"... We consider the minimization of a convex objective function defined on a Hilbert space, which is only available through unbiased estimates of its gradients. This problem includes standard machine learning algorithms such as kernel logistic regression and leastsquares regression, and is commonly ref ..."
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Cited by 45 (10 self)
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referred to as a stochastic approximation problem in the operations research community. We provide a nonasymptotic analysis of the convergence of two wellknown algorithms, stochastic gradient descent (a.k.a. RobbinsMonro algorithm) as well as a simple modification where iterates are averaged (a
Benchmarking Least Squares Support Vector Machine Classifiers
 NEURAL PROCESSING LETTERS
, 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
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Cited by 456 (46 self)
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in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LSSVM sparse approximation procedure can be successfully applied.
From Data Mining to Knowledge Discovery in Databases.
 AI Magazine,
, 1996
"... ■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in database ..."
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Cited by 516 (0 self)
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in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular realworld applications, specific datamining techniques, challenges involved in realworld applications of knowledge discovery, and current and future
Dictionary Learning and NonAsymptotic Bounds for the Geometric MultiResolution Analysis
"... Abstract: Highdimensional data sets arising in a wide variety of applications often exhibit inherently lowdimensional structure. Detecting, measuring, and exploiting such low intrinsic dimensionality has been the focus of much research in the past decade, with implications and applications in many ..."
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nonasymptotic probabilistic bounds for GMRA approximation error under certain assumptions on the geometry of the underlying distribution. In particular, our results imply that if the data is supported near a lowdimensional manifold, the proposed sparse representations result in an error primarily
Nonasymptotic mixing of the MALA algorithm
 IMA J of Numer Anal
"... The MetropolisAdjusted Langevin Algorithm (MALA), originally introduced to sample exactly the invariant measure of certain stochastic differential equations (SDE) on infinitely long time intervals, can also be used to approximate pathwise the solution of these SDEs on finite time intervals. However ..."
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Cited by 8 (1 self)
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The MetropolisAdjusted Langevin Algorithm (MALA), originally introduced to sample exactly the invariant measure of certain stochastic differential equations (SDE) on infinitely long time intervals, can also be used to approximate pathwise the solution of these SDEs on finite time intervals
Nonasymptotic Oracle Inequalities for the Lasso and
, 2015
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Nonasymptotic calibration and resolution
, 2005
"... We analyze a new algorithm for probability forecasting of binary observations on the basis of the available data, without making any assumptions about the way the observations are generated. The algorithm is shown to be well calibrated and to have good resolution for long enough sequences of observa ..."
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Cited by 1 (1 self)
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of observations and for a suitable choice of its parameter, a kernel on the Cartesian product of the forecast space [0, 1] and the data space. Our main results are nonasymptotic: we establish explicit inequalities, shown to be tight, for the performance of the algorithm. 1
Online learning for matrix factorization and sparse coding
, 2010
"... Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the largescale matrix factorization problem that consists of learning the basis set in order to ad ..."
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Cited by 318 (30 self)
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to adapt it to specific data. Variations of this problem include dictionary learning in signal processing, nonnegative matrix factorization and sparse principal component analysis. In this paper, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations
Sparse Greedy Matrix Approximation for Machine Learning
, 2000
"... In kernel based methods such as Regularization Networks large datasets pose signi cant problems since the number of basis functions required for an optimal solution equals the number of samples. We present a sparse greedy approximation technique to construct a compressed representation of the ..."
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Cited by 221 (10 self)
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of the design matrix. Experimental results are given and connections to KernelPCA, Sparse Kernel Feature Analysis, and Matching Pursuit are pointed out. 1. Introduction Many recent advances in machine learning such as Support Vector Machines [Vapnik, 1995], Regularization Networks [Girosi et al., 1995
Results 1  10
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