Bayesian Methods for Support Vector Machines: Evidence and Predictive Class Probabilities

By Peter Sollich. 2002

218 citations recorded by the source corpus.

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In Artificial Intelligence

Citations in the corpus

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, neutral): “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.”
When Training and Test Sets are Different: Characterising Learning Transfer (2013, background): “In [21, 22], it is shown that in order for the support vector machine to be defined as a probabilistic model, a global compensation factor needs to be made due to the fact that the SVM classifier does not include a normalisation term in its optimisation.”
The kernel recursive least-squares algorithm (2004, background): “2 It should be noted that support vector machines may also be cast within a probabilistic Bayesian framework, see [ 32 ].”
Bayesian Gaussian Process Classification with the EM-EP Algorithm (2006, background): “Bayesian versions of SVMs which have sparse solutions have also been proposed in [33], [34], [35], [36], [37].”
Probabilistic programming (2014, methodology): “I Classical algorithm: Support Vector Machines I Bayesian model I See: Sollich, P. (2002). Bayesian Methods for Support Vector Machines: Evidence and Predictive Class Probabilities.”
Incorporating Prior Knowledge on Features into Learning (2007, background): “The link between Gaussian process and SVM has been pointed out by a number of authors (see e.g., Sollich, 2002).”
Semiparametric Regression of Multidimensional Genetic Pathway Data: Least‐Squares Kernel Machines and Linear Mixed Models (2007, unknown): “It is not strictly equivalent to a continuous Bayesian Gaussian process (Rasmussen and Williams, 2006), because the ﬁnite-dimensional representation of h ( · ) does not lead to a coherent Bayesian model (Green and Silverman, 1994; Tipping, 2001; Sollich, 2002.”
Nonparametric Bayesian Kernel Models (2007, background): “Bayesian versions of kernel models, in particular Bayesian SVMs, have been proposed before [7, 8, 9].”
PKLot - A robust dataset for parking lot classification (2015, methodology): “The classifier used for the experiments was the Support Vector Machine (SVM) introduced by Vapnik (1998). Normalisation was performed by linearly scaling each attribute to the range [ 1, +1].”
Bayesian reasoning and machine learning (2012, unknown): “Whilst, arguably, no fully satisfactory direct match between the SVM and a related probabilistic model has been achieved, approximate matches have been obtained[255].”
Support Vector Machines as Probabilistic Models (2011, background): “For instance, (Sollich, 2002) interprets the hinge loss as − log p(y|x), which necessitates to artificially introduce a “don’tknow” class.”