Regularization perspectives on support vector machines: Difference between revisions

Revision as of 13:13, 26 May 2012

Revision as of 13:36, 29 May 2012

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==Theoretical background==

In the [[statistical learning theory]] framework, an [[algorithm]] is a strategy for choosing a [[function]] <math> f:\mathbf X \to \mathbf Y </math> given a training set <math> S = \{(x_1,y_1),\ldots, (x_n,y_n)\}</math> of inputs, <math>x_i</math>, and their labels, <math>y_i</math> (the labels are usually <math>\pm1</math>). [[Regularization]] strategies avoid [[overfitting]] by choosing a function that fits the data, but is not too complex. Specifically:

<math>f = \text{arg}\min_{f\in\mathcal{H}}\left\{\frac{1}{n}\sum_{i=1}^n V(y_i,f(x_i))+\lambda||f||^2_\mathcal{H}\right\} </math>,