Consistency and Convergence Rates of One-Class SVM and Related Algorithms

By Régis Vert, Jean-Philippe Vert. 2005

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Citations in the corpus

Minimax Estimation of Kernel Mean Embeddings (2016, background): “The continuous inclusion of Hk in L 2(Rd) is known for Gaussian kernels on Rd (e.g., see Vert and Vert, 2006, Lemma 11).”
Patch SVDD: Patch-level SVDD for Anomaly Detection and Segmentation (2020, background): “[3] showed their equivalence in the case of a Gaussian kernel.”
A bagging SVM to learn from positive and unlabeled examples (2010, methodology): “, by ranking the unlabeled examples by decreasing similarity to the mean positive example (Joachims, 1997) or using more advanced learning methods such as 1-class SVM (Schölkopf et al., 2001; Manevitz and Yousef, 2001; Vert and Vert, 2006; De Bie et al., 2007) Alternatively, the problem of inductive”
A Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data (2016, background): “In particular, it has been shown that they converge to the true density level set [57].”
Deep One-Class Classification (2018, methodology): “In the case of the widely used Gaussian kernel, the two methods are equivalent and are asymptotically consistent density level set estimators (Tsybakov, 1997; Vert & Vert, 2006).”
Asymptotic normality of plug-in level set estimates. (2009, background): “Relevant published work (not yet mentioned above) include Hartigan (1987), Polonik (1995), Cavalier (1997), Tsybakov (1997), Walther (1997), Baíllo, Cuevas and Justel (2000), Baíllo, Cuestas-Albertos and Cuevas (2001), Cuevas, Febrero and Fraiman (2000), Baíllo (2003), Tsybakov (2004), Steinwart,…”
A Unifying Review of Deep and Shallow Anomaly Detection (2020, background): “is, in fact, an asymptotically consistent ν-density level set estimator [311].”
Anomaly Detection with Score functions based on Nearest Neighbor Graphs (2009, background): “It is also r efer ed to as novelty detection [1, 2], outlier detection [3], one-class classification [4, 5] and s ingle-class classification [6] in the literature.”
Learning Sets with Separating Kernels (2012, methodology): “In this context, some algorithms inspired by Support Vector Machine (SVM) have been studied in [56, 64, 69].”
SHIV: Reducing supervisor burden in DAgger using support vectors for efficient learning from demonstrations in high dimensional state spaces (2016, methodology): “Here, the parameter ν controls the penalty or ‘slack term’ and is equivalent to the quantile of the probability density of X [34] , as the number of samples increases.”