211 lines
8.3 KiB
Python
211 lines
8.3 KiB
Python
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"""Module :mod:`sklearn.kernel_ridge` implements kernel ridge regression."""
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# Authors: Mathieu Blondel <mathieu@mblondel.org>
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# Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
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# License: BSD 3 clause
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import numpy as np
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from .base import BaseEstimator, RegressorMixin, MultiOutputMixin
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from .metrics.pairwise import pairwise_kernels
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from .linear_model._ridge import _solve_cholesky_kernel
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from .utils.validation import check_is_fitted, _check_sample_weight
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from .utils.validation import _deprecate_positional_args
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from .utils.deprecation import deprecated
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class KernelRidge(MultiOutputMixin, RegressorMixin, BaseEstimator):
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"""Kernel ridge regression.
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Kernel ridge regression (KRR) combines ridge regression (linear least
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squares with l2-norm regularization) with the kernel trick. It thus
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learns a linear function in the space induced by the respective kernel and
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the data. For non-linear kernels, this corresponds to a non-linear
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function in the original space.
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The form of the model learned by KRR is identical to support vector
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regression (SVR). However, different loss functions are used: KRR uses
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squared error loss while support vector regression uses epsilon-insensitive
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loss, both combined with l2 regularization. In contrast to SVR, fitting a
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KRR model can be done in closed-form and is typically faster for
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medium-sized datasets. On the other hand, the learned model is non-sparse
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and thus slower than SVR, which learns a sparse model for epsilon > 0, at
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prediction-time.
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This estimator has built-in support for multi-variate regression
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(i.e., when y is a 2d-array of shape [n_samples, n_targets]).
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Read more in the :ref:`User Guide <kernel_ridge>`.
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Parameters
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----------
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alpha : float or array-like of shape (n_targets,), default=1.0
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Regularization strength; must be a positive float. Regularization
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improves the conditioning of the problem and reduces the variance of
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the estimates. Larger values specify stronger regularization.
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Alpha corresponds to ``1 / (2C)`` in other linear models such as
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:class:`~sklearn.linear_model.LogisticRegression` or
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:class:`~sklearn.svm.LinearSVC`. If an array is passed, penalties are
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assumed to be specific to the targets. Hence they must correspond in
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number. See :ref:`ridge_regression` for formula.
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kernel : string or callable, default="linear"
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Kernel mapping used internally. This parameter is directly passed to
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:class:`~sklearn.metrics.pairwise.pairwise_kernel`.
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If `kernel` is a string, it must be one of the metrics
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in `pairwise.PAIRWISE_KERNEL_FUNCTIONS`.
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If `kernel` is "precomputed", X is assumed to be a kernel matrix.
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Alternatively, if `kernel` is a callable function, it is called on
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each pair of instances (rows) and the resulting value recorded. The
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callable should take two rows from X as input and return the
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corresponding kernel value as a single number. This means that
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callables from :mod:`sklearn.metrics.pairwise` are not allowed, as
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they operate on matrices, not single samples. Use the string
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identifying the kernel instead.
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gamma : float, default=None
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Gamma parameter for the RBF, laplacian, polynomial, exponential chi2
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and sigmoid kernels. Interpretation of the default value is left to
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the kernel; see the documentation for sklearn.metrics.pairwise.
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Ignored by other kernels.
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degree : float, default=3
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Degree of the polynomial kernel. Ignored by other kernels.
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coef0 : float, default=1
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Zero coefficient for polynomial and sigmoid kernels.
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Ignored by other kernels.
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kernel_params : mapping of string to any, default=None
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Additional parameters (keyword arguments) for kernel function passed
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as callable object.
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Attributes
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----------
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dual_coef_ : ndarray of shape (n_samples,) or (n_samples, n_targets)
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Representation of weight vector(s) in kernel space
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X_fit_ : {ndarray, sparse matrix} of shape (n_samples, n_features)
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Training data, which is also required for prediction. If
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kernel == "precomputed" this is instead the precomputed
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training matrix, of shape (n_samples, n_samples).
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References
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----------
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* Kevin P. Murphy
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"Machine Learning: A Probabilistic Perspective", The MIT Press
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chapter 14.4.3, pp. 492-493
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See Also
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--------
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sklearn.linear_model.Ridge : Linear ridge regression.
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sklearn.svm.SVR : Support Vector Regression implemented using libsvm.
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Examples
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--------
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>>> from sklearn.kernel_ridge import KernelRidge
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>>> import numpy as np
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>>> n_samples, n_features = 10, 5
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>>> rng = np.random.RandomState(0)
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>>> y = rng.randn(n_samples)
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>>> X = rng.randn(n_samples, n_features)
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>>> clf = KernelRidge(alpha=1.0)
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>>> clf.fit(X, y)
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KernelRidge(alpha=1.0)
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"""
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@_deprecate_positional_args
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def __init__(self, alpha=1, *, kernel="linear", gamma=None, degree=3,
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coef0=1, kernel_params=None):
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self.alpha = alpha
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self.kernel = kernel
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self.gamma = gamma
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self.degree = degree
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self.coef0 = coef0
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self.kernel_params = kernel_params
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def _get_kernel(self, X, Y=None):
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if callable(self.kernel):
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params = self.kernel_params or {}
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else:
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params = {"gamma": self.gamma,
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"degree": self.degree,
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"coef0": self.coef0}
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return pairwise_kernels(X, Y, metric=self.kernel,
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filter_params=True, **params)
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def _more_tags(self):
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return {'pairwise': self.kernel == 'precomputed'}
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# TODO: Remove in 1.1
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# mypy error: Decorated property not supported
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@deprecated("Attribute _pairwise was deprecated in " # type: ignore
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"version 0.24 and will be removed in 1.1 (renaming of 0.26).")
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@property
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def _pairwise(self):
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return self.kernel == "precomputed"
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def fit(self, X, y, sample_weight=None):
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"""Fit Kernel Ridge regression model
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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Training data. If kernel == "precomputed" this is instead
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a precomputed kernel matrix, of shape (n_samples, n_samples).
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y : array-like of shape (n_samples,) or (n_samples, n_targets)
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Target values
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sample_weight : float or array-like of shape (n_samples,), default=None
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Individual weights for each sample, ignored if None is passed.
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Returns
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-------
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self : returns an instance of self.
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"""
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# Convert data
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X, y = self._validate_data(X, y, accept_sparse=("csr", "csc"),
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multi_output=True, y_numeric=True)
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if sample_weight is not None and not isinstance(sample_weight, float):
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sample_weight = _check_sample_weight(sample_weight, X)
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K = self._get_kernel(X)
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alpha = np.atleast_1d(self.alpha)
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ravel = False
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if len(y.shape) == 1:
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y = y.reshape(-1, 1)
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ravel = True
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copy = self.kernel == "precomputed"
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self.dual_coef_ = _solve_cholesky_kernel(K, y, alpha,
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sample_weight,
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copy)
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if ravel:
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self.dual_coef_ = self.dual_coef_.ravel()
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self.X_fit_ = X
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return self
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def predict(self, X):
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"""Predict using the kernel ridge model
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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Samples. If kernel == "precomputed" this is instead a
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precomputed kernel matrix, shape = [n_samples,
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n_samples_fitted], where n_samples_fitted is the number of
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samples used in the fitting for this estimator.
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Returns
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-------
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C : ndarray of shape (n_samples,) or (n_samples, n_targets)
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Returns predicted values.
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"""
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check_is_fitted(self)
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X = self._validate_data(X, accept_sparse=("csr", "csc"), reset=False)
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K = self._get_kernel(X, self.X_fit_)
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return np.dot(K, self.dual_coef_)
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