1462 lines
54 KiB
Python
1462 lines
54 KiB
Python
"""
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Logistic Regression
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"""
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# Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
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# Fabian Pedregosa <f@bianp.net>
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# Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
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# Manoj Kumar <manojkumarsivaraj334@gmail.com>
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# Lars Buitinck
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# Simon Wu <s8wu@uwaterloo.ca>
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import numbers
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import warnings
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import numpy as np
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from scipy import optimize, sparse
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from .base import LinearClassifierMixin, SparseCoefMixin, BaseEstimator
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from ..feature_selection.from_model import _LearntSelectorMixin
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from ..preprocessing import LabelEncoder, LabelBinarizer
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from ..svm.base import _fit_liblinear
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from ..utils import check_array, check_consistent_length, compute_class_weight
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from ..utils.extmath import (logsumexp, log_logistic, safe_sparse_dot,
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squared_norm)
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from ..utils.optimize import newton_cg
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from ..utils.validation import (as_float_array, DataConversionWarning,
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check_X_y)
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from ..utils.fixes import expit
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from ..externals.joblib import Parallel, delayed
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from ..cross_validation import _check_cv
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from ..externals import six
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from ..metrics import SCORERS
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# .. some helper functions for logistic_regression_path ..
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def _intercept_dot(w, X, y):
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"""Computes y * np.dot(X, w).
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It takes into consideration if the intercept should be fit or not.
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Parameters
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----------
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w : ndarray, shape (n_features,) or (n_features + 1,)
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Coefficient vector.
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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 : ndarray, shape (n_samples,)
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Array of labels.
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"""
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c = 0.
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if w.size == X.shape[1] + 1:
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c = w[-1]
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w = w[:-1]
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z = safe_sparse_dot(X, w) + c
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return w, c, y * z
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def _logistic_loss_and_grad(w, X, y, alpha, sample_weight=None):
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"""Computes the logistic loss and gradient.
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Parameters
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----------
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w : ndarray, shape (n_features,) or (n_features + 1,)
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Coefficient vector.
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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 : ndarray, shape (n_samples,)
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Array of labels.
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alpha : float
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Regularization parameter. alpha is equal to 1 / C.
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sample_weight : ndarray, shape (n_samples,) optional
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Array of weights that are assigned to individual samples.
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If not provided, then each sample is given unit weight.
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Returns
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-------
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out : float
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Logistic loss.
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grad : ndarray, shape (n_features,) or (n_features + 1,)
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Logistic gradient.
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"""
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_, n_features = X.shape
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grad = np.empty_like(w)
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w, c, yz = _intercept_dot(w, X, y)
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if sample_weight is None:
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sample_weight = np.ones(y.shape[0])
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# Logistic loss is the negative of the log of the logistic function.
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out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w)
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z = expit(yz)
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z0 = sample_weight * (z - 1) * y
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grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w
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# Case where we fit the intercept.
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if grad.shape[0] > n_features:
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grad[-1] = z0.sum()
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return out, grad
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def _logistic_loss(w, X, y, alpha, sample_weight=None):
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"""Computes the logistic loss.
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Parameters
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----------
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w : ndarray, shape (n_features,) or (n_features + 1,)
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Coefficient vector.
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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 : ndarray, shape (n_samples,)
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Array of labels.
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alpha : float
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Regularization parameter. alpha is equal to 1 / C.
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sample_weight : ndarray, shape (n_samples,) optional
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Array of weights that are assigned to individual samples.
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If not provided, then each sample is given unit weight.
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Returns
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-------
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out : float
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Logistic loss.
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"""
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w, c, yz = _intercept_dot(w, X, y)
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if sample_weight is None:
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sample_weight = np.ones(y.shape[0])
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# Logistic loss is the negative of the log of the logistic function.
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out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w)
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return out
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def _logistic_loss_grad_hess(w, X, y, alpha, sample_weight=None):
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"""Computes the logistic loss, gradient and the Hessian.
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Parameters
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----------
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w : ndarray, shape (n_features,) or (n_features + 1,)
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Coefficient vector.
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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 : ndarray, shape (n_samples,)
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Array of labels.
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alpha : float
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Regularization parameter. alpha is equal to 1 / C.
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sample_weight : ndarray, shape (n_samples,) optional
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Array of weights that are assigned to individual samples.
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If not provided, then each sample is given unit weight.
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Returns
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-------
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out : float
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Logistic loss.
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grad : ndarray, shape (n_features,) or (n_features + 1,)
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Logistic gradient.
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Hs : callable
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Function that takes the gradient as a parameter and returns the
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matrix product of the Hessian and gradient.
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"""
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n_samples, n_features = X.shape
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grad = np.empty_like(w)
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fit_intercept = grad.shape[0] > n_features
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w, c, yz = _intercept_dot(w, X, y)
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if sample_weight is None:
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sample_weight = np.ones(y.shape[0])
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# Logistic loss is the negative of the log of the logistic function.
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out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w)
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z = expit(yz)
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z0 = sample_weight * (z - 1) * y
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grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w
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# Case where we fit the intercept.
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if fit_intercept:
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grad[-1] = z0.sum()
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# The mat-vec product of the Hessian
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d = sample_weight * z * (1 - z)
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if sparse.issparse(X):
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dX = safe_sparse_dot(sparse.dia_matrix((d, 0),
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shape=(n_samples, n_samples)), X)
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else:
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# Precompute as much as possible
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dX = d[:, np.newaxis] * X
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if fit_intercept:
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# Calculate the double derivative with respect to intercept
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# In the case of sparse matrices this returns a matrix object.
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dd_intercept = np.squeeze(np.array(dX.sum(axis=0)))
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def Hs(s):
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ret = np.empty_like(s)
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ret[:n_features] = X.T.dot(dX.dot(s[:n_features]))
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ret[:n_features] += alpha * s[:n_features]
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# For the fit intercept case.
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if fit_intercept:
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ret[:n_features] += s[-1] * dd_intercept
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ret[-1] = dd_intercept.dot(s[:n_features])
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ret[-1] += d.sum() * s[-1]
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return ret
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return out, grad, Hs
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def _multinomial_loss(w, X, Y, alpha, sample_weight):
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"""Computes multinomial loss and class probabilities.
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Parameters
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----------
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w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features + 1),)
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Coefficient vector.
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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 : ndarray, shape (n_samples, n_classes)
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Transformed labels according to the output of LabelBinarizer.
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alpha : float
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Regularization parameter. alpha is equal to 1 / C.
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sample_weight : ndarray, shape (n_samples,) optional
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Array of weights that are assigned to individual samples.
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If not provided, then each sample is given unit weight.
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Returns
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-------
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loss : float
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Multinomial loss.
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p : ndarray, shape (n_samples, n_classes)
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Estimated class probabilities.
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w : ndarray, shape (n_classes, n_features)
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Reshaped param vector excluding intercept terms.
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"""
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n_classes = Y.shape[1]
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n_features = X.shape[1]
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fit_intercept = w.size == (n_classes * (n_features + 1))
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w = w.reshape(n_classes, -1)
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sample_weight = sample_weight[:, np.newaxis]
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if fit_intercept:
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intercept = w[:, -1]
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w = w[:, :-1]
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else:
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intercept = 0
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p = safe_sparse_dot(X, w.T)
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p += intercept
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p -= logsumexp(p, axis=1)[:, np.newaxis]
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loss = -(sample_weight * Y * p).sum()
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loss += 0.5 * alpha * squared_norm(w)
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p = np.exp(p, p)
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return loss, p, w
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def _multinomial_loss_grad(w, X, Y, alpha, sample_weight):
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"""Computes the multinomial loss, gradient and class probabilities.
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Parameters
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----------
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w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features + 1),)
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Coefficient vector.
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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 : ndarray, shape (n_samples, n_classes)
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Transformed labels according to the output of LabelBinarizer.
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alpha : float
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Regularization parameter. alpha is equal to 1 / C.
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sample_weight : ndarray, shape (n_samples,) optional
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Array of weights that are assigned to individual samples.
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Returns
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-------
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loss : float
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Multinomial loss.
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grad : ndarray, shape (n_classes * n_features,) or
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(n_classes * (n_features + 1),)
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Ravelled gradient of the multinomial loss.
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p : ndarray, shape (n_samples, n_classes)
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Estimated class probabilities
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"""
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n_classes = Y.shape[1]
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n_features = X.shape[1]
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fit_intercept = (w.size == n_classes * (n_features + 1))
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grad = np.zeros((n_classes, n_features + bool(fit_intercept)))
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loss, p, w = _multinomial_loss(w, X, Y, alpha, sample_weight)
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sample_weight = sample_weight[:, np.newaxis]
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diff = sample_weight * (p - Y)
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grad[:, :n_features] = safe_sparse_dot(diff.T, X)
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grad[:, :n_features] += alpha * w
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if fit_intercept:
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grad[:, -1] = diff.sum(axis=0)
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return loss, grad.ravel(), p
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def _multinomial_loss_grad_hess(w, X, Y, alpha, sample_weight):
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"""
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Provides multinomial loss, gradient, and a function for computing hessian
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vector product.
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Parameters
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----------
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w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features + 1),)
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Coefficient vector.
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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 : ndarray, shape (n_samples, n_classes)
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Transformed labels according to the output of LabelBinarizer.
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alpha : float
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Regularization parameter. alpha is equal to 1 / C.
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sample_weight : ndarray, shape (n_samples,) optional
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Array of weights that are assigned to individual samples.
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Returns
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-------
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loss : float
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Multinomial loss.
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grad : array, shape (n_classes * n_features,) or
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(n_classes * (n_features + 1),)
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Ravelled gradient of the multinomial loss.
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hessp : callable
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Function that takes in a vector input of shape (n_classes * n_features)
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or (n_classes * (n_features + 1)) and returns matrix-vector product
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with hessian.
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References
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----------
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Barak A. Pearlmutter (1993). Fast Exact Multiplication by the Hessian.
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http://www.bcl.hamilton.ie/~barak/papers/nc-hessian.pdf
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"""
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n_features = X.shape[1]
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n_classes = Y.shape[1]
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fit_intercept = w.size == (n_classes * (n_features + 1))
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loss, grad, p = _multinomial_loss_grad(w, X, Y, alpha, sample_weight)
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sample_weight = sample_weight[:, np.newaxis]
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# Hessian-vector product derived by applying the R-operator on the gradient
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# of the multinomial loss function.
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def hessp(v):
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v = v.reshape(n_classes, -1)
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if fit_intercept:
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inter_terms = v[:, -1]
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v = v[:, :-1]
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else:
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inter_terms = 0
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# r_yhat holds the result of applying the R-operator on the multinomial
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# estimator.
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r_yhat = safe_sparse_dot(X, v.T)
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r_yhat += inter_terms
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r_yhat += (-p * r_yhat).sum(axis=1)[:, np.newaxis]
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r_yhat *= p
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r_yhat *= sample_weight
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hessProd = np.zeros((n_classes, n_features + bool(fit_intercept)))
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hessProd[:, :n_features] = safe_sparse_dot(r_yhat.T, X)
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hessProd[:, :n_features] += v * alpha
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if fit_intercept:
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hessProd[:, -1] = r_yhat.sum(axis=0)
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return hessProd.ravel()
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return loss, grad, hessp
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def logistic_regression_path(X, y, pos_class=None, Cs=10, fit_intercept=True,
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max_iter=100, tol=1e-4, verbose=0,
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solver='lbfgs', coef=None, copy=True,
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class_weight=None, dual=False, penalty='l2',
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intercept_scaling=1., multi_class='ovr'):
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"""Compute a Logistic Regression model for a list of regularization
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parameters.
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This is an implementation that uses the result of the previous model
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to speed up computations along the set of solutions, making it faster
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than sequentially calling LogisticRegression for the different parameters.
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Parameters
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----------
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X : array-like or sparse matrix, shape (n_samples, n_features)
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Input data.
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y : array-like, shape (n_samples,)
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Input data, target values.
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Cs : int | array-like, shape (n_cs,)
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List of values for the regularization parameter or integer specifying
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the number of regularization parameters that should be used. In this
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case, the parameters will be chosen in a logarithmic scale between
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1e-4 and 1e4.
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pos_class : int, None
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The class with respect to which we perform a one-vs-all fit.
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If None, then it is assumed that the given problem is binary.
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fit_intercept : bool
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Whether to fit an intercept for the model. In this case the shape of
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the returned array is (n_cs, n_features + 1).
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max_iter : int
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Maximum number of iterations for the solver.
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tol : float
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Stopping criterion. For the newton-cg and lbfgs solvers, the iteration
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will stop when ``max{|g_i | i = 1, ..., n} <= tol``
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where ``g_i`` is the i-th component of the gradient.
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verbose : int
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For the liblinear and lbfgs solvers set verbose to any positive
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number for verbosity.
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solver : {'lbfgs', 'newton-cg', 'liblinear'}
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Numerical solver to use.
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coef : array-like, shape (n_features,), default None
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Initialization value for coefficients of logistic regression.
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copy : bool, default True
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Whether or not to produce a copy of the data. Setting this to
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True will be useful in cases, when logistic_regression_path
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is called repeatedly with the same data, as y is modified
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along the path.
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class_weight : {dict, 'auto'}, optional
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Over-/undersamples the samples of each class according to the given
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weights. If not given, all classes are supposed to have weight one.
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The 'auto' mode selects weights inversely proportional to class
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frequencies in the training set.
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dual : bool
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Dual or primal formulation. Dual formulation is only implemented for
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l2 penalty with liblinear solver. Prefer dual=False when
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n_samples > n_features.
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penalty : str, 'l1' or 'l2'
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Used to specify the norm used in the penalization. The newton-cg and
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lbfgs solvers support only l2 penalties.
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intercept_scaling : float, default 1.
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This parameter is useful only when the solver 'liblinear' is used
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and self.fit_intercept is set to True. In this case, x becomes
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[x, self.intercept_scaling],
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i.e. a "synthetic" feature with constant value equals to
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intercept_scaling is appended to the instance vector.
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The intercept becomes intercept_scaling * synthetic feature weight
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Note! the synthetic feature weight is subject to l1/l2 regularization
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as all other features.
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To lessen the effect of regularization on synthetic feature weight
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(and therefore on the intercept) intercept_scaling has to be increased.
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multi_class : str, {'ovr', 'multinomial'}
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Multiclass option can be either 'ovr' or 'multinomial'. If the option
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chosen is 'ovr', then a binary problem is fit for each label. Else
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the loss minimised is the multinomial loss fit across
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the entire probability distribution. Works only for the 'lbfgs'
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solver.
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Returns
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-------
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coefs : ndarray, shape (n_cs, n_features) or (n_cs, n_features + 1)
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List of coefficients for the Logistic Regression model. If
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fit_intercept is set to True then the second dimension will be
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n_features + 1, where the last item represents the intercept.
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Cs : ndarray
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Grid of Cs used for cross-validation.
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Notes
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-----
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You might get slighly different results with the solver liblinear than
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with the others since this uses LIBLINEAR which penalizes the intercept.
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"""
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if isinstance(Cs, numbers.Integral):
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Cs = np.logspace(-4, 4, Cs)
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if multi_class not in ['multinomial', 'ovr']:
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raise ValueError("multi_class can be either 'multinomial' or 'ovr'"
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"got %s" % multi_class)
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|
|
if solver not in ['liblinear', 'newton-cg', 'lbfgs']:
|
|
raise ValueError("Logistic Regression supports only liblinear,"
|
|
" newton-cg and lbfgs solvers. got %s" % solver)
|
|
|
|
if multi_class == 'multinomial' and solver == 'liblinear':
|
|
raise ValueError("Solver %s cannot solve problems with "
|
|
"a multinomial backend." % solver)
|
|
|
|
if solver != 'liblinear':
|
|
if penalty != 'l2':
|
|
raise ValueError("newton-cg and lbfgs solvers support only "
|
|
"l2 penalties, got %s penalty." % penalty)
|
|
if dual:
|
|
raise ValueError("newton-cg and lbfgs solvers support only "
|
|
"dual=False, got dual=%s" % dual)
|
|
# Preprocessing.
|
|
X = check_array(X, accept_sparse='csr', dtype=np.float64)
|
|
y = check_array(y, ensure_2d=False, copy=copy)
|
|
_, n_features = X.shape
|
|
check_consistent_length(X, y)
|
|
classes = np.unique(y)
|
|
|
|
if pos_class is None and multi_class != 'multinomial':
|
|
if (classes.size > 2):
|
|
raise ValueError('To fit OvR, use the pos_class argument')
|
|
# np.unique(y) gives labels in sorted order.
|
|
pos_class = classes[1]
|
|
|
|
# If class_weights is a dict (provided by the user), the weights
|
|
# are assigned to the original labels. If it is "auto", then
|
|
# the class_weights are assigned after masking the labels with a OvR.
|
|
sample_weight = np.ones(X.shape[0])
|
|
le = LabelEncoder()
|
|
|
|
if isinstance(class_weight, dict):
|
|
if solver == "liblinear":
|
|
if classes.size == 2:
|
|
# Reconstruct the weights with keys 1 and -1
|
|
temp = {1: class_weight[pos_class],
|
|
-1: class_weight[classes[0]]}
|
|
class_weight = temp.copy()
|
|
else:
|
|
raise ValueError("In LogisticRegressionCV the liblinear "
|
|
"solver cannot handle multiclass with "
|
|
"class_weight of type dict. Use the lbfgs, "
|
|
"newton-cg solvers or set "
|
|
"class_weight='auto'")
|
|
else:
|
|
class_weight_ = compute_class_weight(class_weight, classes, y)
|
|
sample_weight = class_weight_[le.fit_transform(y)]
|
|
|
|
# For doing a ovr, we need to mask the labels first. for the
|
|
# multinomial case this is not necessary.
|
|
if multi_class == 'ovr':
|
|
w0 = np.zeros(n_features + int(fit_intercept))
|
|
mask_classes = [-1, 1]
|
|
mask = (y == pos_class)
|
|
y[mask] = 1
|
|
y[~mask] = -1
|
|
# To take care of object dtypes, i.e 1 and -1 are in the form of
|
|
# strings.
|
|
y = as_float_array(y, copy=False)
|
|
|
|
else:
|
|
lbin = LabelBinarizer()
|
|
Y_bin = lbin.fit_transform(y)
|
|
if Y_bin.shape[1] == 1:
|
|
Y_bin = np.hstack([1 - Y_bin, Y_bin])
|
|
w0 = np.zeros((Y_bin.shape[1], n_features + int(fit_intercept)),
|
|
order='F')
|
|
mask_classes = classes
|
|
|
|
if class_weight == "auto":
|
|
class_weight_ = compute_class_weight(class_weight, mask_classes, y)
|
|
sample_weight = class_weight_[le.fit_transform(y)]
|
|
|
|
if coef is not None:
|
|
# it must work both giving the bias term and not
|
|
if multi_class == 'ovr':
|
|
if not coef.size in (n_features, w0.size):
|
|
raise ValueError(
|
|
'Initialization coef is of shape %d, expected shape '
|
|
'%d or %d' % (coef.size, n_features, w0.size)
|
|
)
|
|
w0[:coef.size] = coef
|
|
else:
|
|
# For binary problems coef.shape[0] should be 1, otherwise it
|
|
# should be classes.size.
|
|
n_vectors = classes.size
|
|
if n_vectors == 2:
|
|
n_vectors = 1
|
|
|
|
if (coef.shape[0] != n_vectors or
|
|
coef.shape[1] not in (n_features, n_features + 1)):
|
|
raise ValueError(
|
|
'Initialization coef is of shape (%d, %d), expected '
|
|
'shape (%d, %d) or (%d, %d)' % (
|
|
coef.shape[0], coef.shape[1], classes.size,
|
|
n_features, classes.size, n_features + 1
|
|
)
|
|
)
|
|
w0[:, :coef.shape[1]] = coef
|
|
|
|
if multi_class == 'multinomial':
|
|
# fmin_l_bfgs_b and newton-cg accepts only ravelled parameters.
|
|
w0 = w0.ravel()
|
|
target = Y_bin
|
|
if solver == 'lbfgs':
|
|
func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2]
|
|
elif solver == 'newton-cg':
|
|
func = lambda x, *args: _multinomial_loss(x, *args)[0]
|
|
grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1]
|
|
hess = _multinomial_loss_grad_hess
|
|
else:
|
|
target = y
|
|
if solver == 'lbfgs':
|
|
func = _logistic_loss_and_grad
|
|
elif solver == 'newton-cg':
|
|
func = _logistic_loss
|
|
grad = lambda x, *args: _logistic_loss_and_grad(x, *args)[1]
|
|
hess = _logistic_loss_grad_hess
|
|
|
|
coefs = list()
|
|
|
|
for C in Cs:
|
|
if solver == 'lbfgs':
|
|
try:
|
|
w0, loss, info = optimize.fmin_l_bfgs_b(
|
|
func, w0, fprime=None,
|
|
args=(X, target, 1. / C, sample_weight),
|
|
iprint=(verbose > 0) - 1, pgtol=tol, maxiter=max_iter
|
|
)
|
|
except TypeError:
|
|
# old scipy doesn't have maxiter
|
|
w0, loss, info = optimize.fmin_l_bfgs_b(
|
|
func, w0, fprime=None,
|
|
args=(X, target, 1. / C, sample_weight),
|
|
iprint=(verbose > 0) - 1, pgtol=tol
|
|
)
|
|
if info["warnflag"] == 1 and verbose > 0:
|
|
warnings.warn("lbfgs failed to converge. Increase the number "
|
|
"of iterations.")
|
|
elif solver == 'newton-cg':
|
|
args = (X, target, 1. / C, sample_weight)
|
|
w0 = newton_cg(hess, func, grad, w0, args=args, maxiter=max_iter,
|
|
tol=tol)
|
|
elif solver == 'liblinear':
|
|
coef_, intercept_, _, = _fit_liblinear(
|
|
X, y, C, fit_intercept, intercept_scaling, class_weight,
|
|
penalty, dual, verbose, max_iter, tol,
|
|
)
|
|
if fit_intercept:
|
|
w0 = np.concatenate([coef_.ravel(), intercept_])
|
|
else:
|
|
w0 = coef_.ravel()
|
|
else:
|
|
raise ValueError("solver must be one of {'liblinear', 'lbfgs', "
|
|
"'newton-cg'}, got '%s' instead" % solver)
|
|
|
|
if multi_class == 'multinomial':
|
|
multi_w0 = np.reshape(w0, (classes.size, -1))
|
|
if classes.size == 2:
|
|
multi_w0 = multi_w0[1][np.newaxis, :]
|
|
coefs.append(multi_w0)
|
|
else:
|
|
coefs.append(w0)
|
|
return coefs, np.array(Cs)
|
|
|
|
|
|
# helper function for LogisticCV
|
|
def _log_reg_scoring_path(X, y, train, test, pos_class=None, Cs=10,
|
|
scoring=None, fit_intercept=False,
|
|
max_iter=100, tol=1e-4, class_weight=None,
|
|
verbose=0, solver='lbfgs', penalty='l2',
|
|
dual=False, copy=True, intercept_scaling=1.,
|
|
multi_class='ovr'):
|
|
"""Computes scores across logistic_regression_path
|
|
|
|
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 labels.
|
|
|
|
train : list of indices
|
|
The indices of the train set.
|
|
|
|
test : list of indices
|
|
The indices of the test set.
|
|
|
|
pos_class : int, None
|
|
The class with respect to which we perform a one-vs-all fit.
|
|
If None, then it is assumed that the given problem is binary.
|
|
|
|
Cs : list of floats | int
|
|
Each of the values in Cs describes the inverse of
|
|
regularization strength. If Cs is as an int, then a grid of Cs
|
|
values are chosen in a logarithmic scale between 1e-4 and 1e4.
|
|
If not provided, then a fixed set of values for Cs are used.
|
|
|
|
scoring : callable
|
|
For a list of scoring functions that can be used, look at
|
|
:mod:`sklearn.metrics`. The default scoring option used is
|
|
accuracy_score.
|
|
|
|
fit_intercept : bool
|
|
If False, then the bias term is set to zero. Else the last
|
|
term of each coef_ gives us the intercept.
|
|
|
|
max_iter : int
|
|
Maximum number of iterations for the solver.
|
|
|
|
tol : float
|
|
Tolerance for stopping criteria.
|
|
|
|
class_weight : {dict, 'auto'}, optional
|
|
Over-/undersamples the samples of each class according to the given
|
|
weights. If not given, all classes are supposed to have weight one.
|
|
The 'auto' mode selects weights inversely proportional to class
|
|
frequencies in the training set.
|
|
|
|
verbose : int
|
|
For the liblinear and lbfgs solvers set verbose to any positive
|
|
number for verbosity.
|
|
|
|
solver : {'lbfgs', 'newton-cg', 'liblinear'}
|
|
Decides which solver to use.
|
|
|
|
penalty : str, 'l1' or 'l2'
|
|
Used to specify the norm used in the penalization. The newton-cg and
|
|
lbfgs solvers support only l2 penalties.
|
|
|
|
dual : bool
|
|
Dual or primal formulation. Dual formulation is only implemented for
|
|
l2 penalty with liblinear solver. Prefer dual=False when
|
|
n_samples > n_features.
|
|
|
|
intercept_scaling : float, default 1.
|
|
This parameter is useful only when the solver 'liblinear' is used
|
|
and self.fit_intercept is set to True. In this case, x becomes
|
|
[x, self.intercept_scaling],
|
|
i.e. a "synthetic" feature with constant value equals to
|
|
intercept_scaling is appended to the instance vector.
|
|
The intercept becomes intercept_scaling * synthetic feature weight
|
|
Note! the synthetic feature weight is subject to l1/l2 regularization
|
|
as all other features.
|
|
To lessen the effect of regularization on synthetic feature weight
|
|
(and therefore on the intercept) intercept_scaling has to be increased.
|
|
|
|
multi_class : str, {'ovr', 'multinomial'}
|
|
Multiclass option can be either 'ovr' or 'multinomial'. If the option
|
|
chosen is 'ovr', then a binary problem is fit for each label. Else
|
|
the loss minimised is the multinomial loss fit across
|
|
the entire probability distribution. Works only for the 'lbfgs'
|
|
solver.
|
|
|
|
Returns
|
|
-------
|
|
coefs : ndarray, shape (n_cs, n_features) or (n_cs, n_features + 1)
|
|
List of coefficients for the Logistic Regression model. If
|
|
fit_intercept is set to True then the second dimension will be
|
|
n_features + 1, where the last item represents the intercept.
|
|
|
|
Cs : ndarray
|
|
Grid of Cs used for cross-validation.
|
|
|
|
scores : ndarray, shape (n_cs,)
|
|
Scores obtained for each Cs.
|
|
"""
|
|
|
|
log_reg = LogisticRegression(fit_intercept=fit_intercept)
|
|
|
|
X_train = X[train]
|
|
X_test = X[test]
|
|
y_train = y[train]
|
|
y_test = y[test]
|
|
|
|
# The score method of Logistic Regression has a classes_ attribute.
|
|
if multi_class == 'ovr':
|
|
log_reg.classes_ = np.array([-1, 1])
|
|
elif multi_class == 'multinomial':
|
|
log_reg.classes_ = np.unique(y_train)
|
|
else:
|
|
raise ValueError("multi_class should be either multinomial or ovr, "
|
|
"got %d" % multi_class)
|
|
|
|
if pos_class is not None:
|
|
mask = (y_test == pos_class)
|
|
y_test[mask] = 1
|
|
y_test[~mask] = -1
|
|
|
|
# To deal with object dtypes, we need to convert into an array of floats.
|
|
y_test = as_float_array(y_test, copy=False)
|
|
|
|
coefs, Cs = logistic_regression_path(X_train, y_train, Cs=Cs,
|
|
fit_intercept=fit_intercept,
|
|
solver=solver,
|
|
max_iter=max_iter,
|
|
class_weight=class_weight,
|
|
copy=copy, pos_class=pos_class,
|
|
multi_class=multi_class,
|
|
tol=tol, verbose=verbose,
|
|
dual=dual, penalty=penalty,
|
|
intercept_scaling=intercept_scaling)
|
|
|
|
scores = list()
|
|
|
|
if isinstance(scoring, six.string_types):
|
|
scoring = SCORERS[scoring]
|
|
for w in coefs:
|
|
if multi_class == 'ovr':
|
|
w = w[np.newaxis, :]
|
|
if fit_intercept:
|
|
log_reg.coef_ = w[:, :-1]
|
|
log_reg.intercept_ = w[:, -1]
|
|
else:
|
|
log_reg.coef_ = w
|
|
log_reg.intercept_ = 0.
|
|
|
|
if scoring is None:
|
|
scores.append(log_reg.score(X_test, y_test))
|
|
else:
|
|
scores.append(scoring(log_reg, X_test, y_test))
|
|
return coefs, Cs, np.array(scores)
|
|
|
|
|
|
class LogisticRegression(BaseEstimator, LinearClassifierMixin,
|
|
_LearntSelectorMixin, SparseCoefMixin):
|
|
"""Logistic Regression (aka logit, MaxEnt) classifier.
|
|
|
|
In the multiclass case, the training algorithm uses the one-vs-rest (OvR)
|
|
scheme if the 'multi_class' option is set to 'ovr' and uses the
|
|
cross-entropy loss, if the 'multi_class' option is set to 'multinomial'.
|
|
(Currently the 'multinomial' option is supported only by the 'lbfgs' and
|
|
'newton-cg' solvers.)
|
|
|
|
This class implements regularized logistic regression using the
|
|
`liblinear` library, newton-cg and lbfgs solvers. It can handle both
|
|
dense and sparse input. Use C-ordered arrays or CSR matrices containing
|
|
64-bit floats for optimal performance; any other input format will be
|
|
converted (and copied).
|
|
|
|
The newton-cg and lbfgs solvers support only L2 regularization with primal
|
|
formulation. The liblinear solver supports both L1 and L2 regularization,
|
|
with a dual formulation only for the L2 penalty.
|
|
|
|
Parameters
|
|
----------
|
|
penalty : str, 'l1' or 'l2'
|
|
Used to specify the norm used in the penalization. The newton-cg and
|
|
lbfgs solvers support only l2 penalties.
|
|
|
|
dual : bool
|
|
Dual or primal formulation. Dual formulation is only implemented for
|
|
l2 penalty with liblinear solver. Prefer dual=False when
|
|
n_samples > n_features.
|
|
|
|
C : float, optional (default=1.0)
|
|
Inverse of regularization strength; must be a positive float.
|
|
Like in support vector machines, smaller values specify stronger
|
|
regularization.
|
|
|
|
fit_intercept : bool, default: True
|
|
Specifies if a constant (a.k.a. bias or intercept) should be
|
|
added the decision function.
|
|
|
|
intercept_scaling : float, default: 1
|
|
Useful only if solver is liblinear.
|
|
when self.fit_intercept is True, instance vector x becomes
|
|
[x, self.intercept_scaling],
|
|
i.e. a "synthetic" feature with constant value equals to
|
|
intercept_scaling is appended to the instance vector.
|
|
The intercept becomes intercept_scaling * synthetic feature weight
|
|
Note! the synthetic feature weight is subject to l1/l2 regularization
|
|
as all other features.
|
|
To lessen the effect of regularization on synthetic feature weight
|
|
(and therefore on the intercept) intercept_scaling has to be increased.
|
|
|
|
class_weight : {dict, 'auto'}, optional
|
|
Over-/undersamples the samples of each class according to the given
|
|
weights. If not given, all classes are supposed to have weight one.
|
|
The 'auto' mode selects weights inversely proportional to class
|
|
frequencies in the training set.
|
|
|
|
max_iter : int
|
|
Useful only for the newton-cg and lbfgs solvers. Maximum number of
|
|
iterations taken for the solvers to converge.
|
|
|
|
random_state : int seed, RandomState instance, or None (default)
|
|
The seed of the pseudo random number generator to use when
|
|
shuffling the data.
|
|
|
|
solver : {'newton-cg', 'lbfgs', 'liblinear'}
|
|
Algorithm to use in the optimization problem.
|
|
|
|
tol : float, optional
|
|
Tolerance for stopping criteria.
|
|
|
|
multi_class : str, {'ovr', 'multinomial'}
|
|
Multiclass option can be either 'ovr' or 'multinomial'. If the option
|
|
chosen is 'ovr', then a binary problem is fit for each label. Else
|
|
the loss minimised is the multinomial loss fit across
|
|
the entire probability distribution. Works only for the 'lbfgs'
|
|
solver.
|
|
|
|
verbose : int
|
|
For the liblinear and lbfgs solvers set verbose to any positive
|
|
number for verbosity.
|
|
|
|
Attributes
|
|
----------
|
|
coef_ : array, shape (n_classes, n_features)
|
|
Coefficient of the features in the decision function.
|
|
|
|
intercept_ : array, shape (n_classes,)
|
|
Intercept (a.k.a. bias) added to the decision function.
|
|
If `fit_intercept` is set to False, the intercept is set to zero.
|
|
|
|
n_iter_ : int
|
|
Maximum of the actual number of iterations across all classes.
|
|
Valid only for the liblinear solver.
|
|
|
|
See also
|
|
--------
|
|
SGDClassifier : incrementally trained logistic regression (when given
|
|
the parameter ``loss="log"``).
|
|
sklearn.svm.LinearSVC : learns SVM models using the same algorithm.
|
|
|
|
Notes
|
|
-----
|
|
The underlying C implementation uses a random number generator to
|
|
select features when fitting the model. It is thus not uncommon,
|
|
to have slightly different results for the same input data. If
|
|
that happens, try with a smaller tol parameter.
|
|
|
|
Predict output may not match that of standalone liblinear in certain
|
|
cases. See :ref:`differences from liblinear <liblinear_differences>`
|
|
in the narrative documentation.
|
|
|
|
References
|
|
----------
|
|
|
|
LIBLINEAR -- A Library for Large Linear Classification
|
|
http://www.csie.ntu.edu.tw/~cjlin/liblinear/
|
|
|
|
Hsiang-Fu Yu, Fang-Lan Huang, Chih-Jen Lin (2011). Dual coordinate descent
|
|
methods for logistic regression and maximum entropy models.
|
|
Machine Learning 85(1-2):41-75.
|
|
http://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf
|
|
|
|
|
|
See also
|
|
--------
|
|
sklearn.linear_model.SGDClassifier
|
|
"""
|
|
|
|
def __init__(self, penalty='l2', dual=False, tol=1e-4, C=1.0,
|
|
fit_intercept=True, intercept_scaling=1, class_weight=None,
|
|
random_state=None, solver='liblinear', max_iter=100,
|
|
multi_class='ovr', verbose=0):
|
|
|
|
self.penalty = penalty
|
|
self.dual = dual
|
|
self.tol = tol
|
|
self.C = C
|
|
self.fit_intercept = fit_intercept
|
|
self.intercept_scaling = intercept_scaling
|
|
self.class_weight = class_weight
|
|
self.random_state = random_state
|
|
self.solver = solver
|
|
self.max_iter = max_iter
|
|
self.multi_class = multi_class
|
|
self.verbose = verbose
|
|
|
|
def fit(self, X, y):
|
|
"""Fit the model according to the given training data.
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix}, shape (n_samples, n_features)
|
|
Training vector, where n_samples in the number of samples and
|
|
n_features is the number of features.
|
|
|
|
y : array-like, shape (n_samples,)
|
|
Target vector relative to X.
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
if self.C < 0:
|
|
raise ValueError("Penalty term must be positive; got (C=%r)"
|
|
% self.C)
|
|
|
|
X, y = check_X_y(X, y, accept_sparse='csr', dtype=np.float64, order="C")
|
|
self.classes_ = np.unique(y)
|
|
if self.solver not in ['liblinear', 'newton-cg', 'lbfgs']:
|
|
raise ValueError(
|
|
"Logistic Regression supports only liblinear, newton-cg and "
|
|
"lbfgs solvers, Got solver=%s" % self.solver
|
|
)
|
|
|
|
if self.solver == 'liblinear' and self.multi_class == 'multinomial':
|
|
raise ValueError("Solver %s does not support a multinomial "
|
|
"backend." % self.solver)
|
|
if self.multi_class not in ['ovr', 'multinomial']:
|
|
raise ValueError("multi_class should be either ovr or multinomial "
|
|
"got %s" % self.multi_class)
|
|
|
|
if self.solver == 'liblinear':
|
|
self.coef_, self.intercept_, self.n_iter_ = _fit_liblinear(
|
|
X, y, self.C, self.fit_intercept, self.intercept_scaling,
|
|
self.class_weight, self.penalty, self.dual, self.verbose,
|
|
self.max_iter, self.tol
|
|
)
|
|
return self
|
|
|
|
n_classes = len(self.classes_)
|
|
classes_ = self.classes_
|
|
if n_classes < 2:
|
|
raise ValueError("This solver needs samples of at least 2 classes"
|
|
" in the data, but the data contains only one"
|
|
" class: %r" % classes_[0])
|
|
|
|
if len(self.classes_) == 2:
|
|
n_classes = 1
|
|
classes_ = classes_[1:]
|
|
|
|
self.coef_ = list()
|
|
self.intercept_ = np.zeros(n_classes)
|
|
|
|
# Hack so that we iterate only once for the multinomial case.
|
|
if self.multi_class == 'multinomial':
|
|
classes_ = [None]
|
|
|
|
for ind, class_ in enumerate(classes_):
|
|
coef_, _ = logistic_regression_path(
|
|
X, y, pos_class=class_, Cs=[self.C],
|
|
fit_intercept=self.fit_intercept, tol=self.tol,
|
|
verbose=self.verbose, solver=self.solver,
|
|
multi_class=self.multi_class, max_iter=self.max_iter,
|
|
class_weight=self.class_weight)
|
|
self.coef_.append(coef_[0])
|
|
|
|
self.coef_ = np.squeeze(self.coef_)
|
|
# For the binary case, this get squeezed to a 1-D array.
|
|
if self.coef_.ndim == 1:
|
|
self.coef_ = self.coef_[np.newaxis, :]
|
|
|
|
self.coef_ = np.asarray(self.coef_)
|
|
if self.fit_intercept:
|
|
self.intercept_ = self.coef_[:, -1]
|
|
self.coef_ = self.coef_[:, :-1]
|
|
|
|
return self
|
|
|
|
def predict_proba(self, X):
|
|
"""Probability estimates.
|
|
|
|
The returned estimates for all classes are ordered by the
|
|
label of classes.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape = [n_samples, n_features]
|
|
|
|
Returns
|
|
-------
|
|
T : array-like, shape = [n_samples, n_classes]
|
|
Returns the probability of the sample for each class in the model,
|
|
where classes are ordered as they are in ``self.classes_``.
|
|
"""
|
|
return self._predict_proba_lr(X)
|
|
|
|
def predict_log_proba(self, X):
|
|
"""Log of probability estimates.
|
|
|
|
The returned estimates for all classes are ordered by the
|
|
label of classes.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape = [n_samples, n_features]
|
|
|
|
Returns
|
|
-------
|
|
T : array-like, shape = [n_samples, n_classes]
|
|
Returns the log-probability of the sample for each class in the
|
|
model, where classes are ordered as they are in ``self.classes_``.
|
|
"""
|
|
return np.log(self.predict_proba(X))
|
|
|
|
|
|
class LogisticRegressionCV(LogisticRegression, BaseEstimator,
|
|
LinearClassifierMixin, _LearntSelectorMixin):
|
|
"""Logistic Regression CV (aka logit, MaxEnt) classifier.
|
|
|
|
This class implements logistic regression using liblinear, newton-cg or
|
|
LBFGS optimizer. The newton-cg and lbfgs solvers support only L2
|
|
regularization with primal formulation. The liblinear solver supports both
|
|
L1 and L2 regularization, with a dual formulation only for the L2 penalty.
|
|
|
|
For the grid of Cs values (that are set by default to be ten values in
|
|
a logarithmic scale between 1e-4 and 1e4), the best hyperparameter is
|
|
selected by the cross-validator StratifiedKFold, but it can be changed
|
|
using the cv parameter. In the case of newton-cg and lbfgs solvers,
|
|
we warm start along the path i.e guess the initial coefficients of the
|
|
present fit to be the coefficients got after convergence in the previous
|
|
fit, so in general it is supposed to be faster.
|
|
|
|
For a multiclass problem, the hyperparameters for each class are computed
|
|
using the best scores got by doing a one-vs-rest in parallel across all
|
|
folds and classes. Hence this is not the true multinomial loss.
|
|
|
|
Parameters
|
|
----------
|
|
Cs : list of floats | int
|
|
Each of the values in Cs describes the inverse of regularization
|
|
strength. If Cs is as an int, then a grid of Cs values are chosen
|
|
in a logarithmic scale between 1e-4 and 1e4.
|
|
Like in support vector machines, smaller values specify stronger
|
|
regularization.
|
|
|
|
fit_intercept : bool, default: True
|
|
Specifies if a constant (a.k.a. bias or intercept) should be
|
|
added the decision function.
|
|
|
|
class_weight : {dict, 'auto'}, optional
|
|
Over-/undersamples the samples of each class according to the given
|
|
weights. If not given, all classes are supposed to have weight one.
|
|
The 'auto' mode selects weights inversely proportional to class
|
|
frequencies in the training set.
|
|
|
|
cv : integer or cross-validation generator
|
|
The default cross-validation generator used is Stratified K-Folds.
|
|
If an integer is provided, then it is the number of folds used.
|
|
See the module :mod:`sklearn.cross_validation` module for the
|
|
list of possible cross-validation objects.
|
|
|
|
penalty : str, 'l1' or 'l2'
|
|
Used to specify the norm used in the penalization. The newton-cg and
|
|
lbfgs solvers support only l2 penalties.
|
|
|
|
dual : bool
|
|
Dual or primal formulation. Dual formulation is only implemented for
|
|
l2 penalty with liblinear solver. Prefer dual=False when
|
|
n_samples > n_features.
|
|
|
|
scoring : callabale
|
|
Scoring function to use as cross-validation criteria. For a list of
|
|
scoring functions that can be used, look at :mod:`sklearn.metrics`.
|
|
The default scoring option used is accuracy_score.
|
|
|
|
solver : {'newton-cg', 'lbfgs', 'liblinear'}
|
|
Algorithm to use in the optimization problem.
|
|
|
|
tol : float, optional
|
|
Tolerance for stopping criteria.
|
|
|
|
max_iter : int, optional
|
|
Maximum number of iterations of the optimization algorithm.
|
|
|
|
class_weight : {dict, 'auto'}, optional
|
|
Over-/undersamples the samples of each class according to the given
|
|
weights. If not given, all classes are supposed to have weight one.
|
|
The 'auto' mode selects weights inversely proportional to class
|
|
frequencies in the training set.
|
|
|
|
n_jobs : int, optional
|
|
Number of CPU cores used during the cross-validation loop. If given
|
|
a value of -1, all cores are used.
|
|
|
|
verbose : int
|
|
For the liblinear and lbfgs solvers set verbose to any positive
|
|
number for verbosity.
|
|
|
|
refit : bool
|
|
If set to True, the scores are averaged across all folds, and the
|
|
coefs and the C that corresponds to the best score is taken, and a
|
|
final refit is done using these parameters.
|
|
Otherwise the coefs, intercepts and C that correspond to the
|
|
best scores across folds are averaged.
|
|
|
|
multi_class : str, {'ovr', 'multinomial'}
|
|
Multiclass option can be either 'ovr' or 'multinomial'. If the option
|
|
chosen is 'ovr', then a binary problem is fit for each label. Else
|
|
the loss minimised is the multinomial loss fit across
|
|
the entire probability distribution. Works only for the 'lbfgs'
|
|
solver.
|
|
|
|
intercept_scaling : float, default 1.
|
|
Useful only if solver is liblinear.
|
|
This parameter is useful only when the solver 'liblinear' is used
|
|
and self.fit_intercept is set to True. In this case, x becomes
|
|
[x, self.intercept_scaling],
|
|
i.e. a "synthetic" feature with constant value equals to
|
|
intercept_scaling is appended to the instance vector.
|
|
The intercept becomes intercept_scaling * synthetic feature weight
|
|
Note! the synthetic feature weight is subject to l1/l2 regularization
|
|
as all other features.
|
|
To lessen the effect of regularization on synthetic feature weight
|
|
(and therefore on the intercept) intercept_scaling has to be increased.
|
|
|
|
Attributes
|
|
----------
|
|
coef_ : array, shape (1, n_features) or (n_classes, n_features)
|
|
Coefficient of the features in the decision function.
|
|
|
|
`coef_` is of shape (1, n_features) when the given problem
|
|
is binary.
|
|
`coef_` is readonly property derived from `raw_coef_` that
|
|
follows the internal memory layout of liblinear.
|
|
|
|
intercept_ : array, shape (1,) or (n_classes,)
|
|
Intercept (a.k.a. bias) added to the decision function.
|
|
It is available only when parameter intercept is set to True
|
|
and is of shape(1,) when the problem is binary.
|
|
|
|
Cs_ : array
|
|
Array of C i.e. inverse of regularization parameter values used
|
|
for cross-validation.
|
|
|
|
coefs_paths_ : array, shape (n_folds, len(Cs_), n_features) or
|
|
(n_folds, len(Cs_), n_features + 1)
|
|
dict with classes as the keys, and the path of coefficients obtained
|
|
during cross-validating across each fold and then across each Cs
|
|
after doing an OvR for the corresponding class as values.
|
|
If the 'multi_class' option is set to 'multinomial', then
|
|
the coefs_paths are the coefficients corresponding to each class.
|
|
Each dict value has shape (n_folds, len(Cs_), n_features) or
|
|
(n_folds, len(Cs_), n_features + 1) depending on whether the
|
|
intercept is fit or not.
|
|
|
|
scores_ : dict
|
|
dict with classes as the keys, and the values as the
|
|
grid of scores obtained during cross-validating each fold, after doing
|
|
an OvR for the corresponding class. If the 'multi_class' option
|
|
given is 'multinomial' then the same scores are repeated across
|
|
all classes, since this is the multinomial class.
|
|
Each dict value has shape (n_folds, len(Cs))
|
|
|
|
C_ : array, shape (n_classes,) or (n_classes - 1,)
|
|
Array of C that maps to the best scores across every class. If refit is
|
|
set to False, then for each class, the best C is the average of the
|
|
C's that correspond to the best scores for each fold.
|
|
|
|
See also
|
|
--------
|
|
LogisticRegression
|
|
|
|
"""
|
|
|
|
def __init__(self, Cs=10, fit_intercept=True, cv=None, dual=False,
|
|
penalty='l2', scoring=None, solver='lbfgs', tol=1e-4,
|
|
max_iter=100, class_weight=None, n_jobs=1, verbose=0,
|
|
refit=True, intercept_scaling=1., multi_class='ovr'):
|
|
self.Cs = Cs
|
|
self.fit_intercept = fit_intercept
|
|
self.cv = cv
|
|
self.dual = dual
|
|
self.penalty = penalty
|
|
self.scoring = scoring
|
|
self.tol = tol
|
|
self.max_iter = max_iter
|
|
self.class_weight = class_weight
|
|
self.n_jobs = n_jobs
|
|
self.verbose = verbose
|
|
self.solver = solver
|
|
self.refit = refit
|
|
self.intercept_scaling = intercept_scaling
|
|
self.multi_class = multi_class
|
|
|
|
def fit(self, X, y):
|
|
"""Fit the model according to the given training data.
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix}, shape (n_samples, n_features)
|
|
Training vector, where n_samples in the number of samples and
|
|
n_features is the number of features.
|
|
|
|
y : array-like, shape (n_samples,)
|
|
Target vector relative to X.
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
if self.solver != 'liblinear':
|
|
if self.penalty != 'l2':
|
|
raise ValueError("newton-cg and lbfgs solvers support only "
|
|
"l2 penalties.")
|
|
if self.dual:
|
|
raise ValueError("newton-cg and lbfgs solvers support only "
|
|
"the primal form.")
|
|
|
|
X = check_array(X, accept_sparse='csr', dtype=np.float64)
|
|
y = check_array(y, ensure_2d=False)
|
|
|
|
if self.multi_class not in ['ovr', 'multinomial']:
|
|
raise ValueError("multi_class backend should be either "
|
|
"'ovr' or 'multinomial'"
|
|
" got %s" % self.multi_class)
|
|
|
|
if y.ndim == 2 and y.shape[1] == 1:
|
|
warnings.warn(
|
|
"A column-vector y was passed when a 1d array was"
|
|
" expected. Please change the shape of y to "
|
|
"(n_samples, ), for example using ravel().",
|
|
DataConversionWarning
|
|
)
|
|
y = np.ravel(y)
|
|
|
|
check_consistent_length(X, y)
|
|
|
|
# init cross-validation generator
|
|
cv = _check_cv(self.cv, X, y, classifier=True)
|
|
folds = list(cv)
|
|
|
|
self._enc = LabelEncoder()
|
|
self._enc.fit(y)
|
|
|
|
labels = self.classes_ = np.unique(y)
|
|
n_classes = len(labels)
|
|
|
|
if n_classes < 2:
|
|
raise ValueError("This solver needs samples of at least 2 classes"
|
|
" in the data, but the data contains only one"
|
|
" class: %r" % self.classes_[0])
|
|
if n_classes == 2:
|
|
# OvR in case of binary problems is as good as fitting
|
|
# the higher label
|
|
n_classes = 1
|
|
labels = labels[1:]
|
|
|
|
# We need this hack to iterate only once over labels, in the case of
|
|
# multi_class = multinomial, without changing the value of the labels.
|
|
iter_labels = labels
|
|
if self.multi_class == 'multinomial':
|
|
iter_labels = [None]
|
|
|
|
if self.class_weight and not(isinstance(self.class_weight, dict) or
|
|
self.class_weight == 'auto'):
|
|
raise ValueError("class_weight provided should be a "
|
|
"dict or 'auto'")
|
|
|
|
path_func = delayed(_log_reg_scoring_path)
|
|
|
|
fold_coefs_ = Parallel(n_jobs=self.n_jobs, verbose=self.verbose)(
|
|
path_func(X, y, train, test, pos_class=label, Cs=self.Cs,
|
|
fit_intercept=self.fit_intercept, penalty=self.penalty,
|
|
dual=self.dual, solver=self.solver, tol=self.tol,
|
|
max_iter=self.max_iter, verbose=self.verbose,
|
|
class_weight=self.class_weight, scoring=self.scoring,
|
|
multi_class=self.multi_class,
|
|
intercept_scaling=self.intercept_scaling
|
|
)
|
|
for label in iter_labels
|
|
for train, test in folds)
|
|
|
|
if self.multi_class == 'multinomial':
|
|
multi_coefs_paths, Cs, multi_scores = zip(*fold_coefs_)
|
|
multi_coefs_paths = np.asarray(multi_coefs_paths)
|
|
multi_scores = np.asarray(multi_scores)
|
|
|
|
# This is just to maintain API similarity between the ovr and
|
|
# multinomial option.
|
|
# Coefs_paths in now n_folds X len(Cs) X n_classes X n_features
|
|
# we need it to be n_classes X len(Cs) X n_folds X n_features
|
|
# to be similar to "ovr".
|
|
coefs_paths = np.rollaxis(multi_coefs_paths, 2, 0)
|
|
|
|
# Multinomial has a true score across all labels. Hence the
|
|
# shape is n_folds X len(Cs). We need to repeat this score
|
|
# across all labels for API similarity.
|
|
scores = np.tile(multi_scores, (n_classes, 1, 1))
|
|
self.Cs_ = Cs[0]
|
|
|
|
else:
|
|
coefs_paths, Cs, scores = zip(*fold_coefs_)
|
|
self.Cs_ = Cs[0]
|
|
coefs_paths = np.reshape(coefs_paths, (n_classes, len(folds),
|
|
len(self.Cs_), -1))
|
|
|
|
self.coefs_paths_ = dict(zip(labels, coefs_paths))
|
|
scores = np.reshape(scores, (n_classes, len(folds), -1))
|
|
self.scores_ = dict(zip(labels, scores))
|
|
|
|
self.C_ = list()
|
|
self.coef_ = np.empty((n_classes, X.shape[1]))
|
|
self.intercept_ = np.zeros(n_classes)
|
|
|
|
# hack to iterate only once for multinomial case.
|
|
if self.multi_class == 'multinomial':
|
|
scores = multi_scores
|
|
coefs_paths = multi_coefs_paths
|
|
|
|
for index, label in enumerate(iter_labels):
|
|
if self.multi_class == 'ovr':
|
|
scores = self.scores_[label]
|
|
coefs_paths = self.coefs_paths_[label]
|
|
|
|
if self.refit:
|
|
best_index = scores.sum(axis=0).argmax()
|
|
|
|
C_ = self.Cs_[best_index]
|
|
self.C_.append(C_)
|
|
if self.multi_class == 'multinomial':
|
|
coef_init = np.mean(coefs_paths[:, best_index, :, :],
|
|
axis=0)
|
|
else:
|
|
coef_init = np.mean(coefs_paths[:, best_index, :], axis=0)
|
|
w, _ = logistic_regression_path(
|
|
X, y, pos_class=label, Cs=[C_], solver=self.solver,
|
|
fit_intercept=self.fit_intercept, coef=coef_init,
|
|
max_iter=self.max_iter, tol=self.tol,
|
|
class_weight=self.class_weight,
|
|
multi_class=self.multi_class,
|
|
verbose=max(0, self.verbose - 1))
|
|
w = w[0]
|
|
|
|
else:
|
|
# Take the best scores across every fold and the average of all
|
|
# coefficients corresponding to the best scores.
|
|
best_indices = np.argmax(scores, axis=1)
|
|
w = np.mean([
|
|
coefs_paths[i][best_indices[i]]
|
|
for i in range(len(folds))
|
|
], axis=0)
|
|
self.C_.append(np.mean(self.Cs_[best_indices]))
|
|
|
|
if self.multi_class == 'multinomial':
|
|
self.C_ = np.tile(self.C_, n_classes)
|
|
self.coef_ = w[:, :X.shape[1]]
|
|
if self.fit_intercept:
|
|
self.intercept_ = w[:, -1]
|
|
else:
|
|
self.coef_[index] = w[: X.shape[1]]
|
|
if self.fit_intercept:
|
|
self.intercept_[index] = w[-1]
|
|
|
|
self.C_ = np.asarray(self.C_)
|
|
return self
|