767 lines
25 KiB
Python
767 lines
25 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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# License: Simplified BSD
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import warnings
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import numpy as np
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from .base import LinearModel
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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 _solve(A, b, solver, tol):
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# helper method for ridge_regression, A is symmetric positive
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if solver == 'auto':
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if hasattr(A, 'todense'):
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solver = 'sparse_cg'
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else:
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solver = 'dense_cholesky'
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if solver == 'sparse_cg':
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if b.ndim < 2:
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from scipy.sparse import linalg as sp_linalg
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sol, error = sp_linalg.cg(A, b, tol=tol)
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if error:
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raise ValueError("Failed with error code %d" % error)
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return sol
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else:
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# sparse_cg cannot handle a 2-d b.
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sol = []
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for j in range(b.shape[1]):
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sol.append(_solve(A, b[:, j], solver="sparse_cg", tol=tol))
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return np.array(sol).T
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elif solver == 'dense_cholesky':
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from scipy import linalg
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if hasattr(A, 'todense'):
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A = A.todense()
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return linalg.solve(A, b, sym_pos=True, overwrite_a=True)
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else:
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raise NotImplementedError('Solver %s not implemented' % solver)
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def ridge_regression(X, y, alpha, sample_weight=1.0, solver='auto', 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}, 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_responses]
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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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solver : {'auto', 'dense_cholesky', 'sparse_cg'}, optional
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Solver to use in the computational routines. 'delse_cholesky'
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will use the standard scipy.linalg.solve function, 'sparse_cg'
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will use the 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.
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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_responses, 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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is_sparse = False
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if hasattr(X, 'todense'): # lazy import of scipy.sparse
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from scipy import sparse
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is_sparse = sparse.issparse(X)
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if is_sparse:
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if n_features > n_samples or \
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isinstance(sample_weight, np.ndarray) or \
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sample_weight != 1.0:
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I = sparse.lil_matrix((n_samples, n_samples))
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I.setdiag(np.ones(n_samples) * alpha * sample_weight)
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c = _solve(X * X.T + I, y, solver, tol)
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coef = X.T * c
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else:
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I = sparse.lil_matrix((n_features, n_features))
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I.setdiag(np.ones(n_features) * alpha)
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coef = _solve(X.T * X + I, X.T * y, solver, tol)
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else:
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if n_features > n_samples or \
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isinstance(sample_weight, np.ndarray) or \
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sample_weight != 1.0:
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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 = np.dot(X, X.T)
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A.flat[::n_samples + 1] += alpha * sample_weight
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coef = np.dot(X.T, _solve(A, y, solver, tol))
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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 = np.dot(X.T, X)
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A.flat[::n_features + 1] += alpha
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coef = _solve(A, np.dot(X.T, y), solver, tol)
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return coef.T
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class Ridge(LinearModel):
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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_responses]).
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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
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problem and reduce the variance of the estimates.
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Alpha corresponds to (2*C)^-1 in other linear models such as
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LogisticRegression or LinearSVC.
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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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normalize : boolean, optional
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If True, the regressors X are normalized
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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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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_responses, 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, normalize=False,
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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, tol=1e-3):
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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.tol = tol
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def fit(self, X, y, sample_weight=1.0, solver='auto'):
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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_responses]
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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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solver : {'auto', 'dense_cholesky', 'sparse_cg'}
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Solver to use in the computational
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routines. 'delse_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.
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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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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 = \
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self._center_data(X, y, self.fit_intercept,
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self.normalize, self.copy_X)
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self.coef_ = ridge_regression(X, y, self.alpha, sample_weight,
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solver, 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 RidgeClassifier(Ridge):
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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
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problem and reduce the variance of the estimates.
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Alpha corresponds to (2*C)^-1 in other linear models such as
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LogisticRegression or LinearSVC.
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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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normalize : boolean, optional
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If True, the regressors X are normalized
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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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tol: float
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Precision of the solution.
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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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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, tol=1e-3, class_weight=None):
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super(RidgeClassifier, self).__init__(alpha=alpha,
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fit_intercept=fit_intercept, normalize=normalize,
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copy_X=copy_X, tol=tol)
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self.class_weight = class_weight
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def fit(self, X, y, solver='auto'):
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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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solver : {'auto', 'dense_cholesky', 'sparse_cg'}
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Solver to use in the computational
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routines. 'delse_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.
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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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sample_weight_classes = np.array([class_weight.get(k, 1.0) for k in y])
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self.label_binarizer = LabelBinarizer()
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Y = self.label_binarizer.fit_transform(y)
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Ridge.fit(self, X, Y, solver=solver, sample_weight=sample_weight_classes)
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return self
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def decision_function(self, X):
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return Ridge.decision_function(self, X)
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def predict(self, X):
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"""Predict target values according to the fitted model.
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Parameters
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----------
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X : array-like, shape = [n_samples, n_features]
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Returns
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-------
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y : array, shape = [n_samples]
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"""
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Y = self.decision_function(X)
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return self.label_binarizer.inverse_transform(Y)
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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, copy_X=True,
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gcv_mode=None):
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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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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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from scipy import linalg
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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]
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return (c / G_diag) ** 2, c
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def _values(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]
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return y - (c / G_diag), c
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def _pre_compute_svd(self, X, y):
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from scipy import sparse
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if sparse.issparse(X) and hasattr(X, 'toarray'):
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X = X.toarray()
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U, s, _ = np.linalg.svd(X, full_matrices=0)
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v = s ** 2
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UT_y = np.dot(U.T, y)
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return v, U, UT_y
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def _errors_svd(self, alpha, y, v, U, UT_y):
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w = ((v + alpha) ** -1) - (alpha ** -1)
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c = np.dot(U, self._diag_dot(w, UT_y)) + (alpha ** -1) * y
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G_diag = self._decomp_diag(w, U) + (alpha ** -1)
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if len(y.shape) != 1:
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# handle case where y is 2-d
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G_diag = G_diag[:, np.newaxis]
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return (c / G_diag) ** 2, c
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def _values_svd(self, alpha, y, v, U, UT_y):
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w = ((v + alpha) ** -1) - (alpha ** -1)
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c = np.dot(U, self._diag_dot(w, UT_y)) + (alpha ** -1) * y
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G_diag = self._decomp_diag(w, U) + (alpha ** -1)
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if len(y.shape) != 1:
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# handle case when y is 2-d
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G_diag = G_diag[:, np.newaxis]
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return y - (c / G_diag), c
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def fit(self, X, y, sample_weight=1.0):
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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_responses]
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Target values
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sample_weight : float or array-like of shape [n_samples]
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Sample weight
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Returns
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-------
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self : Returns self.
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"""
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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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n_samples, n_features = X.shape
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X, y, X_mean, y_mean, X_std = LinearModel._center_data(X, y,
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self.fit_intercept, self.normalize, self.copy_X)
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gcv_mode = self.gcv_mode
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with_sw = len(np.shape(sample_weight))
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if gcv_mode is None or gcv_mode == 'auto':
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if n_features > n_samples or with_sw:
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gcv_mode = 'eigen'
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else:
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gcv_mode = 'svd'
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elif gcv_mode == "svd" and with_sw:
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# FIXME non-uniform sample weights not yet supported
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warnings.warn("non-uniform sample weights unsupported for svd, "
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"forcing usage of eigen")
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gcv_mode = 'eigen'
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if gcv_mode == 'eigen':
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_pre_compute = self._pre_compute
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_errors = self._errors
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_values = self._values
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elif gcv_mode == 'svd':
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# assert n_samples >= n_features
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_pre_compute = self._pre_compute_svd
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_errors = self._errors_svd
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_values = self._values_svd
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else:
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raise ValueError('bad gcv_mode "%s"' % gcv_mode)
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v, Q, QT_y = _pre_compute(X, y)
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n_y = 1 if len(y.shape) == 1 else y.shape[1]
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M = 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)
|
|
M[:, i] = out.ravel()
|
|
C.append(c)
|
|
|
|
if error:
|
|
best = M.mean(axis=0).argmin()
|
|
else:
|
|
func = self.score_func if self.score_func else self.loss_func
|
|
out = [func(y.ravel(), M[:, i]) for i in range(len(self.alphas))]
|
|
best = np.argmax(out) if self.score_func else np.argmin(out)
|
|
|
|
self.best_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)
|
|
|
|
return self
|
|
|
|
|
|
class RidgeCV(LinearModel):
|
|
"""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_alpha]
|
|
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.
|
|
|
|
|
|
Attributes
|
|
----------
|
|
`coef_` : array, shape = [n_features] or [n_classes, n_features]
|
|
Weight vector(s).
|
|
|
|
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 svd 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.
|
|
|
|
See also
|
|
--------
|
|
Ridge: Ridge regression
|
|
RidgeClassifier: Ridge classifier
|
|
RidgeCV: Ridge regression with built-in cross validation
|
|
"""
|
|
|
|
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):
|
|
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
|
|
|
|
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_responses]
|
|
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, self.fit_intercept,
|
|
self.score_func, self.loss_func, gcv_mode=self.gcv_mode)
|
|
estimator.fit(X, y, sample_weight=sample_weight)
|
|
self.best_alpha = estimator.best_alpha
|
|
else:
|
|
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.best_alpha = gs.best_estimator_.alpha
|
|
|
|
self.coef_ = estimator.coef_
|
|
self.intercept_ = estimator.intercept_
|
|
|
|
return self
|
|
|
|
|
|
class RidgeClassifierCV(RidgeCV):
|
|
"""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_alpha]
|
|
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.
|
|
|
|
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
|
|
|
|
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.
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
if class_weight != None:
|
|
warnings.warn("'class_weight' is now an initialization parameter."
|
|
"Using it in the 'fit' method is deprecated.",
|
|
DeprecationWarning)
|
|
self.class_weight_ = class_weight
|
|
else:
|
|
self.class_weight_ = self.class_weight
|
|
|
|
if self.class_weight_ is None:
|
|
self.class_weight_ = {}
|
|
|
|
sample_weight2 = np.array([self.class_weight_.get(k, 1.0) for k in y])
|
|
self.label_binarizer = LabelBinarizer()
|
|
Y = self.label_binarizer.fit_transform(y)
|
|
RidgeCV.fit(self, X, Y, sample_weight=sample_weight * sample_weight2)
|
|
return self
|
|
|
|
def decision_function(self, X):
|
|
return RidgeCV.decision_function(self, X)
|
|
|
|
def predict(self, X):
|
|
"""Predict target values according to the fitted model.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape = [n_samples, n_features]
|
|
|
|
Returns
|
|
-------
|
|
y : array, shape = [n_samples]
|
|
"""
|
|
Y = self.decision_function(X)
|
|
return self.label_binarizer.inverse_transform(Y)
|