Probabilistic Methods for Support Vector Machines

By Peter Sollich. 1999

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Citations in the corpus

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, positive): “This is the case of [248] and [247] , which are studies where SVMs are interpreted as MAP (Maximum A Posteriori) solutions to inference problems with Gaussian Process priors.”
Conformal Transformation of Kernel Functions: A Data-Dependent Way to Improve Support Vector Machine Classifiers (2002, methodology): “We can also understand the method intuitively in the Bayesian framework developed recently [9^11].”
Personalized handwriting recognition via biased regularization (2006, background): “Finally, biased regularization can also be motivated from a MAP (maximum a posteriori) interpretation of SVMs (Sollich, 2000), where the L 2 -regularizer comes from a Gaussian process prior on w .”
Artificial Neural Networks — ICANN 2001 (2001, methodology): “The starting point is the following result [4].”
Mixtures of Gaussian Processes (2000, methodology): “Finally, we use a set of M Gaussian processes Fσ(x) = {fσ1 (x), . . . , fσM (x)} to model the input-dependent noise variance of the GPR models.”
Bayesian Methods for Support Vector Machines: Evidence and Predictive Class Probabilities (2002, unknown): “Abriefsummaryofsomeoftheaboveresultscanbefoundintheconference proceedings(Sollich,2000);anearlierversionoftheprobabilisticframework(Sollich,1999) disregardedtheissueofnormalizationandshouldthereforeberegardedassuperseded.”
Fast Marginal Likelihood Maximisation for Sparse Bayesian Models (2003, background): “An alternative perspective is to consider the linear model (1) directly within a ‘sparse Bayesian’ framework, which leads to a model such as the ‘relevance vector machine’ (RVM) [10, 11].”
Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis (2002, background): “Observe that the result of (24) is equivalent with the Gaussian Process (GP) formulation (Gibbs, 1997; Neal, 1997; Rasmussen, 1996; Sollich, 2000; Williams, 1998; Williams & Barber, 1998) for regression.”