By Olivier Bousquet, Ulrike von Luxburg, Gunnar Rätsch
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Extra info for Advanced Lectures On Machine Learning: Revised Lectures
So the conditional probability now becomes and the dependency of the probability of B on the parameter settings, as well as A, is made explicit. Rather than ‘learning’ comprising the optimisation of some quality measure, a distribution over the parameters w is inferred from Bayes’ rule. We will demonstrate this concept by means of a simple example regression task in Section 2. To obtain this ‘posterior’ distribution over w alluded to above, it is necessary to specify a ‘prior’ distribution before we observe the data.
We wish to find the function that minimizes subject to the four constraints 3 In fact Lagrange first suggested the use of the symbol to denote the variation of a whole function, rather than that at a point, in 1755 . Some Notes on Applied Mathematics for Machine Learning 27 Note that the last two constraints, which specify the first and second moments, is equivalent to specifying the mean and variance. Our Lagrangian is therefore: where we’ll try the free constraint gambit and skip the positivity constraint.
Smola. Leaning with kernels: Support vector machines, regularization, optimization, and beyond. MIT Press, Cambridge, MA, USA, 2002. 47. J. W. Duin. Data domain description by support vectors. In M. Verleysen, editor, Proceedings of the European symposium on artificial neural networks, pages 251–256, Brussel, 1999. 48. J. W. Duin. Combining one-class classifiers. In J. Kittler and F. Roli, editors, Proceedings of the Second International Workshop on Multiple Classifier Systems, MCS 2001, Heidelberg, Germany, 2001.
Advanced Lectures On Machine Learning: Revised Lectures by Olivier Bousquet, Ulrike von Luxburg, Gunnar Rätsch
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