Estimating the Support of a High-Dimensional Distribution

By Bernhard Schölkopf, John C. Platt, John Shawe-Taylor, Alex Smola, Robert C. Williamson. 2001

6,482 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Security analysis of online centroid anomaly detection (2010, methodology): “Hence several direct methods have been proposed for anomaly detection, e.g., oneclass SVM (Schölkopf et al., 2001), support vector data description (SVDD) (Tax and Duin, 1999a,b), and density level set estimation (Polonik, 1995; Tsybakov, 1997; Steinwart et al., 2005).”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “It was pointed out that the kernel map of a set of points corresponds to a kernel density estimator in the input domain (Schölkopf and Smola 2002; Schölkopf et al. 2001), provided the kernel is nonnegative and integrates to 1.”
One-Class Support Measure Machines for Group Anomaly Detection (2013, background): “When ν = 1, it is well-known that, under some technical assumptions, the OCSVM corresponds exactly to the KDE (Schölkopf et al. 2001).”
Scalable Kernel Methods via Doubly Stochastic Gradients (2014, background): “f u> y ˝ if u<y and the step 5 in Algorithm. 1. becomes i i= ( i(˝ 1)˚ !(x i) if f(x i) > y i i˝˚ ! i (x i) if f(x i) <y i : Kernel Novelty Detection. The loss function l(u;˝) = maxf0;˝ ug[23] is proposed for novelty detection. Since ˝is also a variable which needs to be optimized, the o”
Kernel methods in machine learning (2007, neutral): “ﬃne copy of the Parzen windows classiﬁer (5). 3.2. Estimating the support of a density. We now extend the notion of linear separation to that of estimating the support of a density (Scho¨lkopf et al. [117] and Tax and Duin [134]). Denote by X= {x 1,...,xn}⊆Xthe sample drawn from P(x). Let Cbe a clas”
Improving Generalization via Scalable Neighborhood Component Analysis (2018, background): “Each training image i only has to look for a few supporting neighbors [34] to embed the features.”
Learning Cumulatively to Become More Knowledgeable (2016, background): “[33] and SVDD [37] are two representative one-class classifiers.”
Recent Advances in Open Set Recognition: A Survey (2018, methodology): “Additionally, the one-class classiﬁer [33]–[40] usually used for anomaly detection seems suitable for OSR problem, in which the empirical distribution of training data is modeled such that it can be separated from the surrounding open space (the space far from known/training data) in all directions…”
Open Category Detection with PAC Guarantees (2018, background): “One-class SVMs (OCSVMs) (Sch¨olkopf et al., 2001) are popular for this problem.”
OCGAN: One-Class Novelty Detection Using GANs With Constrained Latent Representations (2019, methodology): “Earlier work of this nature used one-class modeling tools such as One-class SVM [26] and Support Vector Data Descriptor (SVDD) [27] on top of an obtained latent representation.”
Dataset Shift in Machine Learning (2009, methodology): “Hence the SVM classifier is in some way dependent on the covariate density, as it is dependent purely on the observation of covariates themselves.”
Learning with Kernels: support vector machines, regularization, optimization, and beyond (2001, neutral): “• present case [54]: λ(C) ∝ 1 margin2 , where C := {half-spaces in H, not containing the origin}”