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"""Kernel ridge regression."""
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
from numbers import Real
import numpy as np
from .base import BaseEstimator, MultiOutputMixin, RegressorMixin, _fit_context
from .linear_model._ridge import _solve_cholesky_kernel
from .metrics.pairwise import PAIRWISE_KERNEL_FUNCTIONS, pairwise_kernels
from .utils._param_validation import Interval, StrOptions
from .utils.validation import _check_sample_weight, check_is_fitted, validate_data
class KernelRidge(MultiOutputMixin, RegressorMixin, BaseEstimator):
"""Kernel ridge regression.
Kernel ridge regression (KRR) combines ridge regression (linear least
squares with l2-norm regularization) with the kernel trick. It thus
learns a linear function in the space induced by the respective kernel and
the data. For non-linear kernels, this corresponds to a non-linear
function in the original space.
The form of the model learned by KRR is identical to support vector
regression (SVR). However, different loss functions are used: KRR uses
squared error loss while support vector regression uses epsilon-insensitive
loss, both combined with l2 regularization. In contrast to SVR, fitting a
KRR model can be done in closed-form and is typically faster for
medium-sized datasets. On the other hand, the learned model is non-sparse
and thus slower than SVR, which learns a sparse model for epsilon > 0, at
prediction-time.
This estimator has built-in support for multi-variate regression
(i.e., when y is a 2d-array of shape [n_samples, n_targets]).
Read more in the :ref:`User Guide <kernel_ridge>`.
Parameters
----------
alpha : float or array-like of shape (n_targets,), default=1.0
Regularization strength; must be a positive float. Regularization
improves the conditioning of the problem and reduces the variance of
the estimates. Larger values specify stronger regularization.
Alpha corresponds to ``1 / (2C)`` in other linear models such as
:class:`~sklearn.linear_model.LogisticRegression` or
:class:`~sklearn.svm.LinearSVC`. If an array is passed, penalties are
assumed to be specific to the targets. Hence they must correspond in
number. See :ref:`ridge_regression` for formula.
kernel : str or callable, default="linear"
Kernel mapping used internally. This parameter is directly passed to
:class:`~sklearn.metrics.pairwise.pairwise_kernels`.
If `kernel` is a string, it must be one of the metrics
in `pairwise.PAIRWISE_KERNEL_FUNCTIONS` or "precomputed".
If `kernel` is "precomputed", X is assumed to be a kernel matrix.
Alternatively, if `kernel` is a callable function, it is called on
each pair of instances (rows) and the resulting value recorded. The
callable should take two rows from X as input and return the
corresponding kernel value as a single number. This means that
callables from :mod:`sklearn.metrics.pairwise` are not allowed, as
they operate on matrices, not single samples. Use the string
identifying the kernel instead.
gamma : float, default=None
Gamma parameter for the RBF, laplacian, polynomial, exponential chi2
and sigmoid kernels. Interpretation of the default value is left to
the kernel; see the documentation for sklearn.metrics.pairwise.
Ignored by other kernels.
degree : float, default=3
Degree of the polynomial kernel. Ignored by other kernels.
coef0 : float, default=1
Zero coefficient for polynomial and sigmoid kernels.
Ignored by other kernels.
kernel_params : dict, default=None
Additional parameters (keyword arguments) for kernel function passed
as callable object.
Attributes
----------
dual_coef_ : ndarray of shape (n_samples,) or (n_samples, n_targets)
Representation of weight vector(s) in kernel space
X_fit_ : {ndarray, sparse matrix} of shape (n_samples, n_features)
Training data, which is also required for prediction. If
kernel == "precomputed" this is instead the precomputed
training matrix, of shape (n_samples, n_samples).
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
sklearn.gaussian_process.GaussianProcessRegressor : Gaussian
Process regressor providing automatic kernel hyperparameters
tuning and predictions uncertainty.
sklearn.linear_model.Ridge : Linear ridge regression.
sklearn.linear_model.RidgeCV : Ridge regression with built-in
cross-validation.
sklearn.svm.SVR : Support Vector Regression accepting a large variety
of kernels.
References
----------
* Kevin P. Murphy
"Machine Learning: A Probabilistic Perspective", The MIT Press
chapter 14.4.3, pp. 492-493
Examples
--------
>>> from sklearn.kernel_ridge import KernelRidge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> rng = np.random.RandomState(0)
>>> y = rng.randn(n_samples)
>>> X = rng.randn(n_samples, n_features)
>>> krr = KernelRidge(alpha=1.0)
>>> krr.fit(X, y)
KernelRidge(alpha=1.0)
"""
_parameter_constraints: dict = {
"alpha": [Interval(Real, 0, None, closed="left"), "array-like"],
"kernel": [
StrOptions(set(PAIRWISE_KERNEL_FUNCTIONS.keys()) | {"precomputed"}),
callable,
],
"gamma": [Interval(Real, 0, None, closed="left"), None],
"degree": [Interval(Real, 0, None, closed="left")],
"coef0": [Interval(Real, None, None, closed="neither")],
"kernel_params": [dict, None],
}
def __init__(
self,
alpha=1,
*,
kernel="linear",
gamma=None,
degree=3,
coef0=1,
kernel_params=None,
):
self.alpha = alpha
self.kernel = kernel
self.gamma = gamma
self.degree = degree
self.coef0 = coef0
self.kernel_params = kernel_params
def _get_kernel(self, X, Y=None):
if callable(self.kernel):
params = self.kernel_params or {}
else:
params = {"gamma": self.gamma, "degree": self.degree, "coef0": self.coef0}
return pairwise_kernels(X, Y, metric=self.kernel, filter_params=True, **params)
def __sklearn_tags__(self):
tags = super().__sklearn_tags__()
tags.input_tags.sparse = True
tags.input_tags.pairwise = self.kernel == "precomputed"
return tags
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y, sample_weight=None):
"""Fit Kernel Ridge regression model.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Training data. If kernel == "precomputed" this is instead
a precomputed kernel matrix, of shape (n_samples, n_samples).
y : array-like of shape (n_samples,) or (n_samples, n_targets)
Target values.
sample_weight : float or array-like of shape (n_samples,), default=None
Individual weights for each sample, ignored if None is passed.
Returns
-------
self : object
Returns the instance itself.
"""
# Convert data
X, y = validate_data(
self, X, y, accept_sparse=("csr", "csc"), multi_output=True, y_numeric=True
)
if sample_weight is not None and not isinstance(sample_weight, float):
sample_weight = _check_sample_weight(sample_weight, X)
K = self._get_kernel(X)
alpha = np.atleast_1d(self.alpha)
ravel = False
if len(y.shape) == 1:
y = y.reshape(-1, 1)
ravel = True
copy = self.kernel == "precomputed"
self.dual_coef_ = _solve_cholesky_kernel(K, y, alpha, sample_weight, copy)
if ravel:
self.dual_coef_ = self.dual_coef_.ravel()
self.X_fit_ = X
return self
def predict(self, X):
"""Predict using the kernel ridge model.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Samples. If kernel == "precomputed" this is instead a
precomputed kernel matrix, shape = [n_samples,
n_samples_fitted], where n_samples_fitted is the number of
samples used in the fitting for this estimator.
Returns
-------
C : ndarray of shape (n_samples,) or (n_samples, n_targets)
Returns predicted values.
"""
check_is_fitted(self)
X = validate_data(self, X, accept_sparse=("csr", "csc"), reset=False)
K = self._get_kernel(X, self.X_fit_)
return np.dot(K, self.dual_coef_)
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