11.. _kernel_ridge :
22
33===========================
4- Kernelized ridge regression
4+ Kernel ridge regression
55===========================
66
77.. currentmodule :: sklearn.kernel_ridge
88
9- Kernelized ridge regression (KRR) [M2012 ]_ combines :ref: `ridge_regression `
10- (linear least squares plus l2-norm regularization) with the kernel trick. It
9+ Kernel ridge regression (KRR) [M2012 ]_ combines :ref: `ridge_regression `
10+ (linear least squares with l2-norm regularization) with the kernel trick. It
1111thus learns a linear function in the space induced by the respective kernel and
1212the data. For non-linear kernels, this corresponds to a non-linear
1313function in the original space.
@@ -16,9 +16,9 @@ The form of the model learned by :class:`KernelRidge` is identical to support
1616vector regression (:class: `SVR `). However, different loss functions are used:
1717KRR uses squared error loss while support vector regression uses
1818:math: `\epsilon `-insensitive loss, both combined with l2 regularization. In
19- contrast to :class: `SVR `, fitting :class: `KernelRidge ` can be done in
20- closed-form and is typically faster for medium-sized datasets. On the other
21- hand, the learned model is non-sparse and thus slower than SVR, which learns
19+ contrast to :class: `SVR `, fitting :class: `KernelRidge ` can be done in
20+ closed-form and is typically faster for medium-sized datasets. On the other
21+ hand, the learned model is non-sparse and thus slower than SVR, which learns
2222a sparse model for :math: `\epsilon > 0 `, at prediction-time.
2323
2424The following figure compares :class: `KernelRidge ` and :class: `SVR ` on
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