The Nature of Statistical Learning Theory, Second Edition

By Vladimir Naumovich Vapnik. Statistics for Engineering and Information Science, 2000

485 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/15cbb7b85622db0d17ade1d24fa7cfa321d16bd6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

The Problem of Induction (2006, result): “Under certain conditions, transduction gives considerably better results than those obtained from methods that use data to infer a rule that is then used to classify new cases (Joachims 1999, Vapnik 2000, Weston et al. 2003, Goutte et al. 2004).”
From Boolean to probabilistic Boolean networks as models of genetic regulatory networks (2002, background): “Although reasoning under uncertainty is not a new problem and has been extensively studied in the artificial intelligence and pattern recognition communities [85, 86], it nonetheless presents a problem when the uncertainty cannot be reliably estimated.”
SVMTorch: Support Vector Machines for Large-Scale Regression Problems (2001, methodology): “Vapnik 1995 has proposed a method to solve regression problems using support vector machines.”
An introduction to continuous optimization for imaging (2016, methodology): “Then we trained the SVMs on feature vectors of the form, for each digit, (c̃, (ci) 400 i=1, (c 2 i ) 400 i=1) (in dimension 801), where c̃ is the constant which maps all vectors in a hyperplane ‘far’ from the origin, as explained above, and the additional (c2i ) 400 i=1 represent a non-linear liftin”
Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization (2006, methodology): “However, unlike SVM and so-called “kernel methods” [18], [19], [20], we are working with the embedding coordinates explicitly.”
Machine-Learning Algorithms to Automate Morphological and Functional Assessments in 2D Echocardiography. (2016, background): “One of the computational approaches that can help to implement precision medicine in cardiology is machine learning: a collection of statistical learning and modeling techniques that can learn from established data and canmake predictions on unseen or new data (5).”
Phrase Clustering for Discriminative Learning (2009, methodology): “For each query class, we train a logistic regression classifier (Vapnik 1999) with L 2 regularization.”
Log-Concavity and Strong Log-Concavity: a review (2014, unknown): “abdaoui, Rufibach and Wellner (2009), and recent results for estimation of logconcave densities on R have been obtained by Cule and Samworth (2010), Cule, Samworth and Stewart (2010), Dümbgen, Samworth and Schuhmacher (2011).”
Probability Models for Open Set Recognition (2014, unknown): “Following the usual tenets of support vector machines [29], the 1-vs-Set machine simply assigns class labels to instances during testing.”
ETHOS: a multi-label hate speech detection dataset (2020, methodology): “Machine (SVM) [42] model with a linear kernel embedded with the well-known vectorization technique of the term frequency-inverse document frequency (TF-IDF) [38].”
A Parallel Mixture of SVMs for Very Large Scale Problems (2001, methodology): “Support Vector Machines SVMs Vapnik, 1995 have been applied to many classiication problems, generally yielding good performance compared to other algorithms.”
Change detection from remotely sensed images: From pixel-based to object-based approaches (2013, methodology): “structural risk minimization for classification (Vapnik, 2000).”
Multisurface proximal support vector machine classification via generalized eigenvalues (2006, methodology): “kernel in nonlinear classification is the Gaussian kernel [27], [15] whose ijth element, i 1⁄4 1 .”
Empirical mode decomposition–based least squares support vector regression for foreign exchange rate forecasting (2012, methodology): “Support vector regression (SVR) is the regression model of SVM (Vapnik, 2000).”
Improving Iris Recognition Performance Using Segmentation, Quality Enhancement, Match Score Fusion, and Indexing (2008, methodology): “These enhanced local regions are identified from each of the transformed images using support vector machine [44] based learning algorithm and then synergistically combined to generate a single high quality iris image.”
Regularizing Common Spatial Patterns to Improve BCI Designs: Unified Theory and New Algorithms (2011, background): “A possible explanation might be found in Vapnik’s statistical learning theory which advocates that “when solving a given problem, try to avoid solving a more generic problem as an intermediate step” [27].”
Vicinal Risk Minimization (2000, background): “3 a T b I d c e P ¥ § ¦ ¨ © ¦ I 5 I Empirical Risk Minimization (ERM) is therefore equivalent to minimizing the expectation of the loss function with respect to an empirical distribution ' U X W ` Y ¦ 1 6 F formed by assembling delta functions located on each example: % f ' U X W ` Y ¦ 1 © !”