239 lines
8.9 KiB
Python
239 lines
8.9 KiB
Python
|
"""Module :mod:`sklearn.kernel_ridge` implements kernel ridge regression."""
|
||
|
|
|
||
|
|
# Authors: Mathieu Blondel <mathieu@mblondel.org>
|
||
|
|
# Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
|
||
|
|
# License: BSD 3 clause
|
||
|
|
from numbers import Integral, Real
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
|
||
|
|
from .base import BaseEstimator, RegressorMixin, MultiOutputMixin
|
||
|
|
from .utils._param_validation import Interval, StrOptions
|
||
|
|
from .metrics.pairwise import PAIRWISE_KERNEL_FUNCTIONS, pairwise_kernels
|
||
|
|
from .linear_model._ridge import _solve_cholesky_kernel
|
||
|
|
from .utils.validation import check_is_fitted, _check_sample_weight
|
||
|
|
|
||
|
|
|
||
|
|
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_kernel`.
|
||
|
|
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 : int, 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(Integral, 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 _more_tags(self):
|
||
|
|
return {"pairwise": self.kernel == "precomputed"}
|
||
|
|
|
||
|
|
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.
|
||
|
|
"""
|
||
|
|
self._validate_params()
|
||
|
|
|
||
|
|
# Convert data
|
||
|
|
X, y = self._validate_data(
|
||
|
|
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 = self._validate_data(X, accept_sparse=("csr", "csc"), reset=False)
|
||
|
|
K = self._get_kernel(X, self.X_fit_)
|
||
|
|
return np.dot(K, self.dual_coef_)
|