The Nature of Statistical Learning Theory

By Vladimir Naumovich Vapni. 2000

45,800 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Scaling & Learning Theory

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Citations in the corpus

Deeply-Supervised Nets (2014, positive): “e the main formulation of the proposed deeply-supervised nets (DSN). We focus on building our infrastructure around supervised CNN style frameworks [12, 5, 2] by introducing classiﬁer, e.g. SVM model [29], to each layer. An early attempt to combine SVM with DL was made in [28], which however has a d”
Least-to-Most Prompting Enables Complex Reasoning in Large Language Models (2022, background): “This task is trivial for humans, but it is supposed to be impossible for even most advanced statistical learning methods: (1) models trained with two examples are not expected to generalize; (2) moreover, the length-based train-test split requires out-of-distribution generalization, while machine le”
Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information (2018, methodology): “…stochastically towards the expectation of the validation loss with respect to the distribution of the variables that are sampled in the data (e.g., Vapnik, 1999), then we can argue that this aggregation method indeed minimizes an approximation to the expected validation loss with respect to x a…”
Reconciling modern machine-learning practice and the classical bias–variance trade-off (2018, background): “Related ideas have been considered in the context of margins theory [38, 2, 35], where a larger function class H may permit the discovery of a classiﬁer with a larger margin.”
Learning Parameterized Skills (2012, methodology): “We use standard Support Vector Machines (SVM) (Vapnik, 1995) due to their good generalization capabilities and relatively low dependence on parameter tuning.”
On Network Design Spaces for Visual Recognition (2019, background): “While statistical learning theory [30, 33] has introduced theoretical notions of complexity of machine learning models, these are often not predictive of neural network behavior [36, 37].”
Seeing Stars: Exploiting Class Relationships for Sentiment Categorization with Respect to Rating Scales (2005, methodology): “In particular, we consider linear, ε -insensitive SVM regression (Vapnik, 1995; Smola and Sch¨olkopf, 1998); the idea is to ﬁnd the hyperplane that best ﬁts the training data, but where training points whose labels are within distance ε of the hyperplane incur no loss.”
LabelMe: A Database and Web-Based Tool for Image Annotation (2008, methodology): “• Perform classification: train a support vector machine classifier (Vapnik 1999) with a Gaussian kernel using the available LabelMe data and apply the classifier to each of the candidate bounding boxes extracted from each image.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “The positive definiteness of the kernel function guarantees the existence of a dot product space H and a mapping φ : X → H such that k(x,y) = 〈φ(x), φ(y)〉H (Aronszajn 1950) without needing to compute φ explicitly (Boser et al. 1992, Cortes and Vapnik 1995, Vapnik 2000, Schölkopf and Smola 2002).”
Machine Learning Models that Remember Too Much (2017, background): “The parameters foundwith themalicious regularizer will not necessarily be the same as with a conventional regularizer, but the malicious regularizer has the same effect of confining the parameter space to a less complex subspace [72].”
Deep learning in neural networks: An overview (2014, background): “In the new millennium, deep NNs have finally attracted wide-spread attention, mainly by outperforming alternative machine learning methods such as kernel machines (Schölkopf, Burges, & Smola, 1998; Vapnik, 1995) in numerous important applications.”
Training verified learners with learned verifiers (2018, methodology): “Based on the empirical risk minimization principle [29], this can be approximated with an empirical average over training samples.”
Yes, Machine Learning Can Be More Secure! A Case Study on Android Malware Detection (2017, methodology): “ different, secure variants of other linear classiﬁcation algorithm. Our Sec-SVM learning algorithm is only an instance that considers the hinge loss and ‘ 2 regularization, as the standard SVM [18], [41]. It is also worth remarking that, as the lower and upper bounds become smaller in absolute valu”
Adversarial Feature Selection Against Evasion Attacks (2016, background): “c) Nonlinear SVMs: For kernelized SVMs, the discriminant function is g(x) = ni=1 αiyik(x, xi) + b, where the parameters α and b are learned during training, k(x, xi) is the kernel function, and {xi, yi}i=1 are the training samples and their labels [65].”
Security Evaluation of Support Vector Machines in Adversarial Environments (2014, background): “While many hyperplanes may suffice for this task, the SVM hyperplane both separates the training samples of the two classes and provides a maximum distance from itself to the nearest training point (this distance is called the classifier’s margin), since maximum-margin learning generally reduces gen”
Support vector machines under adversarial label contamination (2015, background): “According to structural risk minimization [40], the learner L minimizes a sum of a regularizer and the empirical risk over the data:”
Interpreting support vector machine models for multivariate group wise analysis in neuroimaging (2015, positive): “This hyperplane minimizes ‘structural risk’ (Vapnik, 1995) which is a specific measure of label prediction accuracy that generalizes well in high dimensional space.”
An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “SVM has been first introduced by Vapnik (1995).”
Learning explanations that are hard to vary (2020, background): “The classic formalization of the problem of generalization [Vapnik, 1995] is concerned with the case of independent and i.i.d. samples.”