892 lines
31 KiB
Python
892 lines
31 KiB
Python
"""
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Ridge regression
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"""
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# Author: Mathieu Blondel <mathieu@mblondel.org>
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# Reuben Fletcher-Costin <reuben.fletchercostin@gmail.com>
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# Fabian Pedregosa <fabian@fseoane.net>
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# License: Simplified BSD
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from abc import ABCMeta, abstractmethod
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import warnings
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import numpy as np
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from scipy import linalg
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from scipy import sparse
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from scipy.sparse import linalg as sp_linalg
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from .base import LinearClassifierMixin, LinearModel
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from ..base import RegressorMixin
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from ..utils.extmath import safe_sparse_dot
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from ..utils import safe_asarray
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from ..preprocessing import LabelBinarizer
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from ..grid_search import GridSearchCV
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def ridge_regression(X, y, alpha, sample_weight=1.0, solver='auto',
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max_iter=None, tol=1e-3):
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"""Solve the ridge equation by the method of normal equations.
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Parameters
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----------
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X : {array-like, sparse matrix, LinearOperator},
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shape = [n_samples, n_features]
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Training data
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y : array-like, shape = [n_samples] or [n_samples, n_targets]
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Target values
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max_iter : int, optional
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Maximum number of iterations for conjugate gradient solver.
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The default value is determined by scipy.sparse.linalg.
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sample_weight : float or numpy array of shape [n_samples]
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Individual weights for each sample
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solver : {'auto', 'dense_cholesky', 'lsqr', 'sparse_cg'}
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Solver to use in the computational routines:
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- 'auto' chooses the solver automatically based on the type of data.
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- 'dense_cholesky' uses the standard scipy.linalg.solve function to
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obtain a closed-form solution.
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- 'sparse_cg' uses the conjugate gradient solver as found in
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scipy.sparse.linalg.cg. As an iterative algorithm, this solver is
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more appropriate than 'dense_cholesky' for large-scale data
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(possibility to set `tol` and `max_iter`).
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- 'lsqr' uses the dedicated regularized least-squares routine
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scipy.sparse.linalg.lsqr. It is the fatest but may not be available
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in old scipy versions. It also uses an iterative procedure.
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All three solvers support both dense and sparse data.
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tol: float
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Precision of the solution.
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Returns
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-------
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coef: array, shape = [n_features] or [n_targets, n_features]
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Weight vector(s).
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Notes
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-----
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This function won't compute the intercept.
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"""
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n_samples, n_features = X.shape
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has_sw = isinstance(sample_weight, np.ndarray) or sample_weight != 1.0
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if solver == 'auto':
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# cholesky if it's a dense array and cg in
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# any other case
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if hasattr(X, '__array__'):
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solver = 'dense_cholesky'
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else:
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solver = 'sparse_cg'
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elif solver == 'lsqr' and not hasattr(sp_linalg, 'lsqr'):
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warnings.warn("""lsqr not available on this machine, falling back
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to sparse_cg.""")
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solver = 'sparse_cg'
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if has_sw:
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solver = 'dense_cholesky'
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if solver == 'sparse_cg':
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# gradient descent
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X1 = sp_linalg.aslinearoperator(X)
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if y.ndim == 1:
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y1 = np.reshape(y, (-1, 1))
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else:
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y1 = y
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coefs = np.empty((y1.shape[1], n_features))
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if n_features > n_samples:
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def mv(x):
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return X1.matvec(X1.rmatvec(x)) + alpha * x
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else:
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def mv(x):
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return X1.rmatvec(X1.matvec(x)) + alpha * x
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for i in range(y1.shape[1]):
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y_column = y1[:, i]
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if n_features > n_samples:
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# kernel ridge
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# w = X.T * inv(X X^t + alpha*Id) y
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C = sp_linalg.LinearOperator(
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(n_samples, n_samples), matvec=mv, dtype=X.dtype)
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coef, info = sp_linalg.cg(C, y_column, tol=tol)
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coefs[i] = X1.rmatvec(coef)
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else:
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# ridge
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# w = inv(X^t X + alpha*Id) * X.T y
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y_column = X1.rmatvec(y_column)
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C = sp_linalg.LinearOperator(
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(n_features, n_features), matvec=mv, dtype=X.dtype)
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coefs[i], info = sp_linalg.cg(C, y_column, maxiter=max_iter,
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tol=tol)
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if info != 0:
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raise ValueError("Failed with error code %d" % info)
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if y.ndim == 1:
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coefs = np.ravel(coefs)
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return coefs
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elif solver == "lsqr":
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if y.ndim == 1:
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y1 = np.reshape(y, (-1, 1))
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else:
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y1 = y
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coefs = np.empty((y1.shape[1], n_features))
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# According to the lsqr documentation, alpha = damp^2.
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sqrt_alpha = np.sqrt(alpha)
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for i in range(y1.shape[1]):
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y_column = y1[:, i]
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coefs[i] = sp_linalg.lsqr(X, y_column, damp=sqrt_alpha,
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atol=tol, btol=tol, iter_lim=max_iter)[0]
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if y.ndim == 1:
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coefs = np.ravel(coefs)
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return coefs
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else:
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# normal equations (cholesky) method
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if n_features > n_samples or has_sw:
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# kernel ridge
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# w = X.T * inv(X X^t + alpha*Id) y
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A = safe_sparse_dot(X, X.T, dense_output=True)
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A.flat[::n_samples + 1] += alpha * sample_weight
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Axy = linalg.solve(A, y, sym_pos=True, overwrite_a=True)
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coef = safe_sparse_dot(X.T, Axy, dense_output=True)
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else:
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# ridge
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# w = inv(X^t X + alpha*Id) * X.T y
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A = safe_sparse_dot(X.T, X, dense_output=True)
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A.flat[::n_features + 1] += alpha
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Xy = safe_sparse_dot(X.T, y, dense_output=True)
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coef = linalg.solve(A, Xy, sym_pos=True, overwrite_a=True)
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return coef.T
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class _BaseRidge(LinearModel):
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__metaclass__ = ABCMeta
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@abstractmethod
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def __init__(self, alpha=1.0, fit_intercept=True, normalize=False,
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copy_X=True, max_iter=None, tol=1e-3, solver="auto"):
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self.alpha = alpha
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self.fit_intercept = fit_intercept
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self.normalize = normalize
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self.copy_X = copy_X
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self.max_iter = max_iter
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self.tol = tol
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self.solver = solver
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def fit(self, X, y, sample_weight=1.0, solver=None):
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X = safe_asarray(X, dtype=np.float)
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y = np.asarray(y, dtype=np.float)
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X, y, X_mean, y_mean, X_std = self._center_data(
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X, y, self.fit_intercept, self.normalize, self.copy_X)
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self.coef_ = ridge_regression(X, y,
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alpha=self.alpha,
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sample_weight=sample_weight,
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solver=solver,
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max_iter=self.max_iter,
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tol=self.tol)
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self._set_intercept(X_mean, y_mean, X_std)
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return self
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class Ridge(_BaseRidge, RegressorMixin):
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"""Linear least squares with l2 regularization.
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This model solves a regression model where the loss function is
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the linear least squares function and regularization is given by
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the l2-norm. Also known as Ridge Regression or Tikhonov regularization.
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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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Parameters
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----------
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alpha : float
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Small positive values of alpha improve the conditioning of the problem
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and reduce the variance of the estimates. Alpha corresponds to
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``(2*C)^-1`` in other linear models such as LogisticRegression or
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LinearSVC.
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copy_X : boolean, optional, default True
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If True, X will be copied; else, it may be overwritten.
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fit_intercept : boolean
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Whether to calculate the intercept for this model. If set
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to false, no intercept will be used in calculations
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(e.g. data is expected to be already centered).
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max_iter : int, optional
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Maximum number of iterations for conjugate gradient solver.
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The default value is determined by scipy.sparse.linalg.
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normalize : boolean, optional
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If True, the regressors X are normalized
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solver : {'auto', 'dense_cholesky', 'lsqr', 'sparse_cg'}
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Solver to use in the computational routines:
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- 'auto' chooses the solver automatically based on the type of data.
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- 'dense_cholesky' uses the standard scipy.linalg.solve function to
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obtain a closed-form solution.
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- 'sparse_cg' uses the conjugate gradient solver as found in
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scipy.sparse.linalg.cg. As an iterative algorithm, this solver is
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more appropriate than 'dense_cholesky' for large-scale data
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(possibility to set `tol` and `max_iter`).
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- 'lsqr' uses the dedicated regularized least-squares routine
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scipy.sparse.linalg.lsqr. It is the fatest but may not be available
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in old scipy versions. It also uses an iterative procedure.
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All three solvers support both dense and sparse data.
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tol : float
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Precision of the solution.
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Attributes
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----------
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`coef_` : array, shape = [n_features] or [n_targets, n_features]
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Weight vector(s).
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See also
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--------
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RidgeClassifier, RidgeCV
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Examples
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--------
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>>> from sklearn.linear_model import Ridge
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>>> import numpy as np
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>>> n_samples, n_features = 10, 5
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>>> np.random.seed(0)
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>>> y = np.random.randn(n_samples)
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>>> X = np.random.randn(n_samples, n_features)
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>>> clf = Ridge(alpha=1.0)
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>>> clf.fit(X, y) # doctest: +NORMALIZE_WHITESPACE
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Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,
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normalize=False, solver='auto', tol=0.001)
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"""
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def __init__(self, alpha=1.0, fit_intercept=True, normalize=False,
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copy_X=True, max_iter=None, tol=1e-3, solver="auto"):
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super(Ridge, self).__init__(alpha=alpha, fit_intercept=fit_intercept,
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normalize=normalize, copy_X=copy_X,
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max_iter=max_iter, tol=tol, solver=solver)
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def fit(self, X, y, sample_weight=1.0, solver=None):
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"""Fit Ridge regression model
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Parameters
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----------
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X : {array-like, sparse matrix}, shape = [n_samples, n_features]
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Training data
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y : array-like, shape = [n_samples] or [n_samples, n_targets]
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Target values
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sample_weight : float or numpy array of shape [n_samples]
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Individual weights for each sample
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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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if solver is None:
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solver = self.solver
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else:
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# The fit method should be removed from Ridge when this warning is
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# removed
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warnings.warn("""solver option in fit is deprecated and will be
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removed in v0.14.""")
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return _BaseRidge.fit(self, X, y, solver=solver,
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sample_weight=sample_weight)
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class RidgeClassifier(LinearClassifierMixin, _BaseRidge):
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"""Classifier using Ridge regression.
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Parameters
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----------
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alpha : float
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Small positive values of alpha improve the conditioning of the problem
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and reduce the variance of the estimates. Alpha corresponds to
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``(2*C)^-1`` in other linear models such as LogisticRegression or
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LinearSVC.
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class_weight : dict, optional
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Weights associated with classes in the form
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{class_label : weight}. If not given, all classes are
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supposed to have weight one.
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copy_X : boolean, optional, default True
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If True, X will be copied; else, it may be overwritten.
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fit_intercept : boolean
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Whether to calculate the intercept for this model. If set to false, no
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intercept will be used in calculations (e.g. data is expected to be
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already centered).
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max_iter : int, optional
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Maximum number of iterations for conjugate gradient solver.
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The default value is determined by scipy.sparse.linalg.
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normalize : boolean, optional
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If True, the regressors X are normalized
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solver : {'auto', 'dense_cholesky', 'lsqr', 'sparse_cg'}
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Solver to use in the computational
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routines. 'dense_cholesky' will use the standard
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scipy.linalg.solve function, 'sparse_cg' will use the
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conjugate gradient solver as found in
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scipy.sparse.linalg.cg while 'auto' will chose the most
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appropriate depending on the matrix X. 'lsqr' uses
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a direct regularized least-squares routine provided by scipy.
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tol : float
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Precision of the solution.
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Attributes
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----------
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`coef_` : array, shape = [n_features] or [n_classes, n_features]
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Weight vector(s).
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See also
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--------
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Ridge, RidgeClassifierCV
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Notes
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-----
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For multi-class classification, n_class classifiers are trained in
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a one-versus-all approach. Concretely, this is implemented by taking
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advantage of the multi-variate response support in Ridge.
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"""
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def __init__(self, alpha=1.0, fit_intercept=True, normalize=False,
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copy_X=True, max_iter=None, tol=1e-3, class_weight=None,
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solver="auto"):
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super(RidgeClassifier, self).__init__(
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alpha=alpha, fit_intercept=fit_intercept, normalize=normalize,
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copy_X=copy_X, max_iter=max_iter, tol=tol, solver=solver)
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self.class_weight = class_weight
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def fit(self, X, y, solver=None):
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"""Fit Ridge regression model.
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Parameters
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----------
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X : {array-like, sparse matrix}, shape = [n_samples,n_features]
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Training data
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y : array-like, shape = [n_samples]
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Target values
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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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if self.class_weight is None:
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class_weight = {}
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else:
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class_weight = self.class_weight
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if solver is None:
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solver = self.solver
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else:
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warnings.warn("""solver option in fit is deprecated and will be
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removed in v0.14.""")
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sample_weight_classes = np.array([class_weight.get(k, 1.0) for k in y])
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self._label_binarizer = LabelBinarizer(pos_label=1, neg_label=-1)
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Y = self._label_binarizer.fit_transform(y)
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_BaseRidge.fit(self, X, Y, solver=solver,
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sample_weight=sample_weight_classes)
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return self
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@property
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def classes_(self):
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return self._label_binarizer.classes_
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class _RidgeGCV(LinearModel):
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"""Ridge regression with built-in Generalized Cross-Validation
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It allows efficient Leave-One-Out cross-validation.
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This class is not intended to be used directly. Use RidgeCV instead.
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Notes
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-----
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We want to solve (K + alpha*Id)c = y,
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where K = X X^T is the kernel matrix.
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Let G = (K + alpha*Id)^-1.
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Dual solution: c = Gy
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Primal solution: w = X^T c
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Compute eigendecomposition K = Q V Q^T.
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Then G = Q (V + alpha*Id)^-1 Q^T,
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where (V + alpha*Id) is diagonal.
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It is thus inexpensive to inverse for many alphas.
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Let loov be the vector of prediction values for each example
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when the model was fitted with all examples but this example.
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loov = (KGY - diag(KG)Y) / diag(I-KG)
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Let looe be the vector of prediction errors for each example
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when the model was fitted with all examples but this example.
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looe = y - loov = c / diag(G)
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References
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----------
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http://cbcl.mit.edu/projects/cbcl/publications/ps/MIT-CSAIL-TR-2007-025.pdf
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http://www.mit.edu/~9.520/spring07/Classes/rlsslides.pdf
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"""
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def __init__(self, alphas=[0.1, 1.0, 10.0], fit_intercept=True,
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normalize=False, score_func=None, loss_func=None,
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copy_X=True, gcv_mode=None, store_cv_values=False):
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self.alphas = np.asarray(alphas)
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self.fit_intercept = fit_intercept
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self.normalize = normalize
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self.score_func = score_func
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self.loss_func = loss_func
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self.copy_X = copy_X
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self.gcv_mode = gcv_mode
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self.store_cv_values = store_cv_values
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def _pre_compute(self, X, y):
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# even if X is very sparse, K is usually very dense
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K = safe_sparse_dot(X, X.T, dense_output=True)
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v, Q = linalg.eigh(K)
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QT_y = np.dot(Q.T, y)
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return v, Q, QT_y
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def _decomp_diag(self, v_prime, Q):
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# compute diagonal of the matrix: dot(Q, dot(diag(v_prime), Q^T))
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return (v_prime * Q ** 2).sum(axis=-1)
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def _diag_dot(self, D, B):
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# compute dot(diag(D), B)
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if len(B.shape) > 1:
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# handle case where B is > 1-d
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D = D[(slice(None), ) + (np.newaxis, ) * (len(B.shape) - 1)]
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return D * B
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def _errors(self, alpha, y, v, Q, QT_y):
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# don't construct matrix G, instead compute action on y & diagonal
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w = 1.0 / (v + alpha)
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c = np.dot(Q, self._diag_dot(w, QT_y))
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G_diag = self._decomp_diag(w, Q)
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# handle case where y is 2-d
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if len(y.shape) != 1:
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|
G_diag = G_diag[:, np.newaxis]
|
|
return (c / G_diag) ** 2, c
|
|
|
|
def _values(self, alpha, y, v, Q, QT_y):
|
|
# don't construct matrix G, instead compute action on y & diagonal
|
|
w = 1.0 / (v + alpha)
|
|
c = np.dot(Q, self._diag_dot(w, QT_y))
|
|
G_diag = self._decomp_diag(w, Q)
|
|
# handle case where y is 2-d
|
|
if len(y.shape) != 1:
|
|
G_diag = G_diag[:, np.newaxis]
|
|
return y - (c / G_diag), c
|
|
|
|
def _pre_compute_svd(self, X, y):
|
|
if sparse.issparse(X) and hasattr(X, 'toarray'):
|
|
X = X.toarray()
|
|
U, s, _ = np.linalg.svd(X, full_matrices=0)
|
|
v = s ** 2
|
|
UT_y = np.dot(U.T, y)
|
|
return v, U, UT_y
|
|
|
|
def _errors_svd(self, alpha, y, v, U, UT_y):
|
|
w = ((v + alpha) ** -1) - (alpha ** -1)
|
|
c = np.dot(U, self._diag_dot(w, UT_y)) + (alpha ** -1) * y
|
|
G_diag = self._decomp_diag(w, U) + (alpha ** -1)
|
|
if len(y.shape) != 1:
|
|
# handle case where y is 2-d
|
|
G_diag = G_diag[:, np.newaxis]
|
|
return (c / G_diag) ** 2, c
|
|
|
|
def _values_svd(self, alpha, y, v, U, UT_y):
|
|
w = ((v + alpha) ** -1) - (alpha ** -1)
|
|
c = np.dot(U, self._diag_dot(w, UT_y)) + (alpha ** -1) * y
|
|
G_diag = self._decomp_diag(w, U) + (alpha ** -1)
|
|
if len(y.shape) != 1:
|
|
# handle case when y is 2-d
|
|
G_diag = G_diag[:, np.newaxis]
|
|
return y - (c / G_diag), c
|
|
|
|
def fit(self, X, y, sample_weight=1.0):
|
|
"""Fit Ridge regression model
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
|
|
Training data
|
|
|
|
y : array-like, shape = [n_samples] or [n_samples, n_targets]
|
|
Target values
|
|
|
|
sample_weight : float or array-like of shape [n_samples]
|
|
Sample weight
|
|
|
|
Returns
|
|
-------
|
|
self : Returns self.
|
|
"""
|
|
X = safe_asarray(X, dtype=np.float)
|
|
y = np.asarray(y, dtype=np.float)
|
|
|
|
n_samples, n_features = X.shape
|
|
|
|
X, y, X_mean, y_mean, X_std = LinearModel._center_data(
|
|
X, y, self.fit_intercept, self.normalize, self.copy_X)
|
|
|
|
gcv_mode = self.gcv_mode
|
|
with_sw = len(np.shape(sample_weight))
|
|
|
|
if gcv_mode is None or gcv_mode == 'auto':
|
|
if n_features > n_samples or with_sw:
|
|
gcv_mode = 'eigen'
|
|
else:
|
|
gcv_mode = 'svd'
|
|
elif gcv_mode == "svd" and with_sw:
|
|
# FIXME non-uniform sample weights not yet supported
|
|
warnings.warn("non-uniform sample weights unsupported for svd, "
|
|
"forcing usage of eigen")
|
|
gcv_mode = 'eigen'
|
|
|
|
if gcv_mode == 'eigen':
|
|
_pre_compute = self._pre_compute
|
|
_errors = self._errors
|
|
_values = self._values
|
|
elif gcv_mode == 'svd':
|
|
# assert n_samples >= n_features
|
|
_pre_compute = self._pre_compute_svd
|
|
_errors = self._errors_svd
|
|
_values = self._values_svd
|
|
else:
|
|
raise ValueError('bad gcv_mode "%s"' % gcv_mode)
|
|
|
|
v, Q, QT_y = _pre_compute(X, y)
|
|
n_y = 1 if len(y.shape) == 1 else y.shape[1]
|
|
cv_values = np.zeros((n_samples * n_y, len(self.alphas)))
|
|
C = []
|
|
|
|
error = self.score_func is None and self.loss_func is None
|
|
|
|
for i, alpha in enumerate(self.alphas):
|
|
if error:
|
|
out, c = _errors(sample_weight * alpha, y, v, Q, QT_y)
|
|
else:
|
|
out, c = _values(sample_weight * alpha, y, v, Q, QT_y)
|
|
cv_values[:, i] = out.ravel()
|
|
C.append(c)
|
|
|
|
if error:
|
|
best = cv_values.mean(axis=0).argmin()
|
|
else:
|
|
func = self.score_func if self.score_func else self.loss_func
|
|
out = [func(y.ravel(), cv_values[:, i])
|
|
for i in range(len(self.alphas))]
|
|
best = np.argmax(out) if self.score_func else np.argmin(out)
|
|
|
|
self.alpha_ = self.alphas[best]
|
|
self.dual_coef_ = C[best]
|
|
self.coef_ = safe_sparse_dot(self.dual_coef_.T, X)
|
|
|
|
self._set_intercept(X_mean, y_mean, X_std)
|
|
|
|
if self.store_cv_values:
|
|
if len(y.shape) == 1:
|
|
cv_values_shape = n_samples, len(self.alphas)
|
|
else:
|
|
cv_values_shape = n_samples, n_y, len(self.alphas)
|
|
self.cv_values_ = cv_values.reshape(cv_values_shape)
|
|
|
|
return self
|
|
|
|
@property
|
|
def best_alpha(self):
|
|
warnings.warn("Use alpha_. Using best_alpha is deprecated"
|
|
"since version 0.12, and backward compatibility "
|
|
"won't be maintained from version 0.14 onward. ",
|
|
DeprecationWarning, stacklevel=2)
|
|
return self.alpha_
|
|
|
|
|
|
class _BaseRidgeCV(LinearModel):
|
|
|
|
def __init__(self, alphas=np.array([0.1, 1.0, 10.0]),
|
|
fit_intercept=True, normalize=False, score_func=None,
|
|
loss_func=None, cv=None, gcv_mode=None,
|
|
store_cv_values=False):
|
|
self.alphas = alphas
|
|
self.fit_intercept = fit_intercept
|
|
self.normalize = normalize
|
|
self.score_func = score_func
|
|
self.loss_func = loss_func
|
|
self.cv = cv
|
|
self.gcv_mode = gcv_mode
|
|
self.store_cv_values = store_cv_values
|
|
|
|
def fit(self, X, y, sample_weight=1.0):
|
|
"""Fit Ridge regression model
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape = [n_samples, n_features]
|
|
Training data
|
|
|
|
y : array-like, shape = [n_samples] or [n_samples, n_targets]
|
|
Target values
|
|
|
|
sample_weight : float or array-like of shape [n_samples]
|
|
Sample weight
|
|
|
|
Returns
|
|
-------
|
|
self : Returns self.
|
|
"""
|
|
if self.cv is None:
|
|
estimator = _RidgeGCV(self.alphas,
|
|
fit_intercept=self.fit_intercept,
|
|
normalize=self.normalize,
|
|
score_func=self.score_func,
|
|
loss_func=self.loss_func,
|
|
gcv_mode=self.gcv_mode,
|
|
store_cv_values=self.store_cv_values)
|
|
estimator.fit(X, y, sample_weight=sample_weight)
|
|
self.alpha_ = estimator.alpha_
|
|
if self.store_cv_values:
|
|
self.cv_values_ = estimator.cv_values_
|
|
else:
|
|
if self.store_cv_values:
|
|
raise ValueError("cv!=None and store_cv_values=True "
|
|
" are incompatible")
|
|
parameters = {'alpha': self.alphas}
|
|
# FIXME: sample_weight must be split into training/validation data
|
|
# too!
|
|
#fit_params = {'sample_weight' : sample_weight}
|
|
fit_params = {}
|
|
gs = GridSearchCV(Ridge(fit_intercept=self.fit_intercept),
|
|
parameters, fit_params=fit_params, cv=self.cv)
|
|
gs.fit(X, y)
|
|
estimator = gs.best_estimator_
|
|
self.alpha_ = gs.best_estimator_.alpha
|
|
|
|
self.coef_ = estimator.coef_
|
|
self.intercept_ = estimator.intercept_
|
|
|
|
return self
|
|
|
|
|
|
class RidgeCV(_BaseRidgeCV, RegressorMixin):
|
|
"""Ridge regression with built-in cross-validation.
|
|
|
|
By default, it performs Generalized Cross-Validation, which is a form of
|
|
efficient Leave-One-Out cross-validation.
|
|
|
|
Parameters
|
|
----------
|
|
alphas: numpy array of shape [n_alphas]
|
|
Array of alpha values to try.
|
|
Small positive values of alpha improve the conditioning of the
|
|
problem and reduce the variance of the estimates.
|
|
Alpha corresponds to ``(2*C)^-1`` in other linear models such as
|
|
LogisticRegression or LinearSVC.
|
|
|
|
fit_intercept : boolean
|
|
Whether to calculate the intercept for this model. If set
|
|
to false, no intercept will be used in calculations
|
|
(e.g. data is expected to be already centered).
|
|
|
|
normalize : boolean, optional
|
|
If True, the regressors X are normalized
|
|
|
|
score_func: callable, optional
|
|
function that takes 2 arguments and compares them in
|
|
order to evaluate the performance of prediction (big is good)
|
|
if None is passed, the score of the estimator is maximized
|
|
|
|
loss_func: callable, optional
|
|
function that takes 2 arguments and compares them in
|
|
order to evaluate the performance of prediction (small is good)
|
|
if None is passed, the score of the estimator is maximized
|
|
|
|
cv : cross-validation generator, optional
|
|
If None, Generalized Cross-Validation (efficient Leave-One-Out)
|
|
will be used.
|
|
|
|
gcv_mode : {None, 'auto', 'svd', eigen'}, optional
|
|
Flag indicating which strategy to use when performing
|
|
Generalized Cross-Validation. Options are::
|
|
|
|
'auto' : use svd if n_samples > n_features, otherwise use eigen
|
|
'svd' : force computation via singular value decomposition of X
|
|
'eigen' : force computation via eigendecomposition of X^T X
|
|
|
|
The 'auto' mode is the default and is intended to pick the cheaper \
|
|
option of the two depending upon the shape of the training data.
|
|
|
|
store_cv_values : boolean, default=False
|
|
Flag indicating if the cross-validation values corresponding to
|
|
each alpha should be stored in the `cv_values_` attribute (see
|
|
below). This flag is only compatible with `cv=None` (i.e. using
|
|
Generalized Cross-Validation).
|
|
|
|
Attributes
|
|
----------
|
|
`cv_values_` : array, shape = [n_samples, n_alphas] or \
|
|
shape = [n_samples, n_targets, n_alphas], optional
|
|
Cross-validation values for each alpha (if `store_cv_values=True` and \
|
|
`cv=None`). After `fit()` has been called, this attribute will \
|
|
contain the mean squared errors (by default) or the values of the \
|
|
`{loss,score}_func` function (if provided in the constructor).
|
|
|
|
`coef_` : array, shape = [n_features] or [n_targets, n_features]
|
|
Weight vector(s).
|
|
|
|
`alpha_` : float
|
|
Estimated regularization parameter.
|
|
|
|
See also
|
|
--------
|
|
Ridge: Ridge regression
|
|
RidgeClassifier: Ridge classifier
|
|
RidgeClassifierCV: Ridge classifier with built-in cross validation
|
|
"""
|
|
pass
|
|
|
|
|
|
class RidgeClassifierCV(LinearClassifierMixin, _BaseRidgeCV):
|
|
"""Ridge classifier with built-in cross-validation.
|
|
|
|
By default, it performs Generalized Cross-Validation, which is a form of
|
|
efficient Leave-One-Out cross-validation. Currently, only the n_features >
|
|
n_samples case is handled efficiently.
|
|
|
|
Parameters
|
|
----------
|
|
alphas: numpy array of shape [n_alphas]
|
|
Array of alpha values to try.
|
|
Small positive values of alpha improve the conditioning of the
|
|
problem and reduce the variance of the estimates.
|
|
Alpha corresponds to (2*C)^-1 in other linear models such as
|
|
LogisticRegression or LinearSVC.
|
|
|
|
fit_intercept : boolean
|
|
Whether to calculate the intercept for this model. If set
|
|
to false, no intercept will be used in calculations
|
|
(e.g. data is expected to be already centered).
|
|
|
|
normalize : boolean, optional
|
|
If True, the regressors X are normalized
|
|
|
|
score_func: callable, optional
|
|
function that takes 2 arguments and compares them in
|
|
order to evaluate the performance of prediction (big is good)
|
|
if None is passed, the score of the estimator is maximized
|
|
|
|
loss_func: callable, optional
|
|
function that takes 2 arguments and compares them in
|
|
order to evaluate the performance of prediction (small is good)
|
|
if None is passed, the score of the estimator is maximized
|
|
|
|
cv : cross-validation generator, optional
|
|
If None, Generalized Cross-Validation (efficient Leave-One-Out)
|
|
will be used.
|
|
|
|
class_weight : dict, optional
|
|
Weights associated with classes in the form
|
|
{class_label : weight}. If not given, all classes are
|
|
supposed to have weight one.
|
|
|
|
Attributes
|
|
----------
|
|
`cv_values_` : array, shape = [n_samples, n_alphas] or \
|
|
shape = [n_samples, n_responses, n_alphas], optional
|
|
Cross-validation values for each alpha (if `store_cv_values=True` and
|
|
`cv=None`). After `fit()` has been called, this attribute will contain \
|
|
the mean squared errors (by default) or the values of the \
|
|
`{loss,score}_func` function (if provided in the constructor).
|
|
|
|
`coef_` : array, shape = [n_features] or [n_targets, n_features]
|
|
Weight vector(s).
|
|
|
|
`alpha_` : float
|
|
Estimated regularization parameter
|
|
|
|
See also
|
|
--------
|
|
Ridge: Ridge regression
|
|
RidgeClassifier: Ridge classifier
|
|
RidgeCV: Ridge regression with built-in cross validation
|
|
|
|
Notes
|
|
-----
|
|
For multi-class classification, n_class classifiers are trained in
|
|
a one-versus-all approach. Concretely, this is implemented by taking
|
|
advantage of the multi-variate response support in Ridge.
|
|
"""
|
|
def __init__(self, alphas=np.array([0.1, 1.0, 10.0]), fit_intercept=True,
|
|
normalize=False, score_func=None, loss_func=None, cv=None,
|
|
class_weight=None):
|
|
super(RidgeClassifierCV, self).__init__(
|
|
alphas=alphas, fit_intercept=fit_intercept, normalize=normalize,
|
|
score_func=score_func, loss_func=loss_func, cv=cv)
|
|
self.class_weight = class_weight
|
|
|
|
def fit(self, X, y, sample_weight=1.0, class_weight=None):
|
|
"""Fit the ridge classifier.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape = [n_samples, n_features]
|
|
Training vectors, where n_samples is the number of samples
|
|
and n_features is the number of features.
|
|
|
|
y : array-like, shape = [n_samples]
|
|
Target values.
|
|
|
|
sample_weight : float or numpy array of shape [n_samples]
|
|
Sample weight
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
if self.class_weight is not None:
|
|
get_cw = self.class_weight.get
|
|
sample_weight = (sample_weight
|
|
* np.array([get_cw(k, 1.0) for k in y]))
|
|
self._label_binarizer = LabelBinarizer(pos_label=1, neg_label=-1)
|
|
Y = self._label_binarizer.fit_transform(y)
|
|
_BaseRidgeCV.fit(self, X, Y, sample_weight=sample_weight)
|
|
return self
|
|
|
|
@property
|
|
def classes_(self):
|
|
return self._label_binarizer.classes_
|