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logistic.py
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/
logistic.py
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"""
Logistic Regression
"""
# Author: Gael Varoquaux <gael.varoquaux@normalesup.org>
# Fabian Pedregosa <f@bianp.net>
# Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
# Manoj Kumar <manojkumarsivaraj334@gmail.com>
# Lars Buitinck
# Simon Wu <s8wu@uwaterloo.ca>
import numbers
import warnings
import numpy as np
from scipy import optimize, sparse
from .base import LinearClassifierMixin, SparseCoefMixin, BaseEstimator
from ..feature_selection.from_model import _LearntSelectorMixin
from ..preprocessing import LabelEncoder, LabelBinarizer
from ..svm.base import _fit_liblinear
from ..utils import check_array, check_consistent_length, compute_class_weight
from ..utils.extmath import (logsumexp, log_logistic, safe_sparse_dot,
squared_norm)
from ..utils.optimize import newton_cg
from ..utils.validation import (as_float_array, DataConversionWarning,
check_X_y)
from ..utils.fixes import expit
from ..externals.joblib import Parallel, delayed
from ..cross_validation import _check_cv
from ..externals import six
from ..metrics import SCORERS
# .. some helper functions for logistic_regression_path ..
def _intercept_dot(w, X, y):
"""Computes y * np.dot(X, w).
It takes into consideration if the intercept should be fit or not.
Parameters
----------
w : ndarray, shape (n_features,) or (n_features + 1,)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
y : ndarray, shape (n_samples,)
Array of labels.
"""
c = 0.
if w.size == X.shape[1] + 1:
c = w[-1]
w = w[:-1]
z = safe_sparse_dot(X, w) + c
return w, c, y * z
def _logistic_loss_and_grad(w, X, y, alpha, sample_weight=None):
"""Computes the logistic loss and gradient.
Parameters
----------
w : ndarray, shape (n_features,) or (n_features + 1,)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
y : ndarray, shape (n_samples,)
Array of labels.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
out : float
Logistic loss.
grad : ndarray, shape (n_features,) or (n_features + 1,)
Logistic gradient.
"""
_, n_features = X.shape
grad = np.empty_like(w)
w, c, yz = _intercept_dot(w, X, y)
if sample_weight is None:
sample_weight = np.ones(y.shape[0])
# Logistic loss is the negative of the log of the logistic function.
out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w)
z = expit(yz)
z0 = sample_weight * (z - 1) * y
grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w
# Case where we fit the intercept.
if grad.shape[0] > n_features:
grad[-1] = z0.sum()
return out, grad
def _logistic_loss(w, X, y, alpha, sample_weight=None):
"""Computes the logistic loss.
Parameters
----------
w : ndarray, shape (n_features,) or (n_features + 1,)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
y : ndarray, shape (n_samples,)
Array of labels.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
out : float
Logistic loss.
"""
w, c, yz = _intercept_dot(w, X, y)
if sample_weight is None:
sample_weight = np.ones(y.shape[0])
# Logistic loss is the negative of the log of the logistic function.
out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w)
return out
def _logistic_loss_grad_hess(w, X, y, alpha, sample_weight=None):
"""Computes the logistic loss, gradient and the Hessian.
Parameters
----------
w : ndarray, shape (n_features,) or (n_features + 1,)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
y : ndarray, shape (n_samples,)
Array of labels.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
out : float
Logistic loss.
grad : ndarray, shape (n_features,) or (n_features + 1,)
Logistic gradient.
Hs : callable
Function that takes the gradient as a parameter and returns the
matrix product of the Hessian and gradient.
"""
n_samples, n_features = X.shape
grad = np.empty_like(w)
fit_intercept = grad.shape[0] > n_features
w, c, yz = _intercept_dot(w, X, y)
if sample_weight is None:
sample_weight = np.ones(y.shape[0])
# Logistic loss is the negative of the log of the logistic function.
out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w)
z = expit(yz)
z0 = sample_weight * (z - 1) * y
grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w
# Case where we fit the intercept.
if fit_intercept:
grad[-1] = z0.sum()
# The mat-vec product of the Hessian
d = sample_weight * z * (1 - z)
if sparse.issparse(X):
dX = safe_sparse_dot(sparse.dia_matrix((d, 0),
shape=(n_samples, n_samples)), X)
else:
# Precompute as much as possible
dX = d[:, np.newaxis] * X
if fit_intercept:
# Calculate the double derivative with respect to intercept
# In the case of sparse matrices this returns a matrix object.
dd_intercept = np.squeeze(np.array(dX.sum(axis=0)))
def Hs(s):
ret = np.empty_like(s)
ret[:n_features] = X.T.dot(dX.dot(s[:n_features]))
ret[:n_features] += alpha * s[:n_features]
# For the fit intercept case.
if fit_intercept:
ret[:n_features] += s[-1] * dd_intercept
ret[-1] = dd_intercept.dot(s[:n_features])
ret[-1] += d.sum() * s[-1]
return ret
return out, grad, Hs
def _multinomial_loss(w, X, Y, alpha, sample_weight):
"""Computes multinomial loss and class probabilities.
Parameters
----------
w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features + 1),)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Y : ndarray, shape (n_samples, n_classes)
Transformed labels according to the output of LabelBinarizer.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
loss : float
Multinomial loss.
p : ndarray, shape (n_samples, n_classes)
Estimated class probabilities.
w : ndarray, shape (n_classes, n_features)
Reshaped param vector excluding intercept terms.
"""
n_classes = Y.shape[1]
n_features = X.shape[1]
fit_intercept = w.size == (n_classes * (n_features + 1))
w = w.reshape(n_classes, -1)
sample_weight = sample_weight[:, np.newaxis]
if fit_intercept:
intercept = w[:, -1]
w = w[:, :-1]
else:
intercept = 0
p = safe_sparse_dot(X, w.T)
p += intercept
p -= logsumexp(p, axis=1)[:, np.newaxis]
loss = -(sample_weight * Y * p).sum()
loss += 0.5 * alpha * squared_norm(w)
p = np.exp(p, p)
return loss, p, w
def _multinomial_loss_grad(w, X, Y, alpha, sample_weight):
"""Computes the multinomial loss, gradient and class probabilities.
Parameters
----------
w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features + 1),)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Y : ndarray, shape (n_samples, n_classes)
Transformed labels according to the output of LabelBinarizer.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
Returns
-------
loss : float
Multinomial loss.
grad : ndarray, shape (n_classes * n_features,) or
(n_classes * (n_features + 1),)
Ravelled gradient of the multinomial loss.
p : ndarray, shape (n_samples, n_classes)
Estimated class probabilities
"""
n_classes = Y.shape[1]
n_features = X.shape[1]
fit_intercept = (w.size == n_classes * (n_features + 1))
grad = np.zeros((n_classes, n_features + bool(fit_intercept)))
loss, p, w = _multinomial_loss(w, X, Y, alpha, sample_weight)
sample_weight = sample_weight[:, np.newaxis]
diff = sample_weight * (p - Y)
grad[:, :n_features] = safe_sparse_dot(diff.T, X)
grad[:, :n_features] += alpha * w
if fit_intercept:
grad[:, -1] = diff.sum(axis=0)
return loss, grad.ravel(), p
def _multinomial_loss_grad_hess(w, X, Y, alpha, sample_weight):
"""
Provides multinomial loss, gradient, and a function for computing hessian
vector product.
Parameters
----------
w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features + 1),)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Y : ndarray, shape (n_samples, n_classes)
Transformed labels according to the output of LabelBinarizer.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
Returns
-------
loss : float
Multinomial loss.
grad : array, shape (n_classes * n_features,) or
(n_classes * (n_features + 1),)
Ravelled gradient of the multinomial loss.
hessp : callable
Function that takes in a vector input of shape (n_classes * n_features)
or (n_classes * (n_features + 1)) and returns matrix-vector product
with hessian.
References
----------
Barak A. Pearlmutter (1993). Fast Exact Multiplication by the Hessian.
http://www.bcl.hamilton.ie/~barak/papers/nc-hessian.pdf
"""
n_features = X.shape[1]
n_classes = Y.shape[1]
fit_intercept = w.size == (n_classes * (n_features + 1))
loss, grad, p = _multinomial_loss_grad(w, X, Y, alpha, sample_weight)
sample_weight = sample_weight[:, np.newaxis]
# Hessian-vector product derived by applying the R-operator on the gradient
# of the multinomial loss function.
def hessp(v):
v = v.reshape(n_classes, -1)
if fit_intercept:
inter_terms = v[:, -1]
v = v[:, :-1]
else:
inter_terms = 0
# r_yhat holds the result of applying the R-operator on the multinomial
# estimator.
r_yhat = safe_sparse_dot(X, v.T)
r_yhat += inter_terms
r_yhat += (-p * r_yhat).sum(axis=1)[:, np.newaxis]
r_yhat *= p
r_yhat *= sample_weight
hessProd = np.zeros((n_classes, n_features + bool(fit_intercept)))
hessProd[:, :n_features] = safe_sparse_dot(r_yhat.T, X)
hessProd[:, :n_features] += v * alpha
if fit_intercept:
hessProd[:, -1] = r_yhat.sum(axis=0)
return hessProd.ravel()
return loss, grad, hessp
def logistic_regression_path(X, y, pos_class=None, Cs=10, fit_intercept=True,
max_iter=100, tol=1e-4, verbose=0,
solver='lbfgs', coef=None, copy=True,
class_weight=None, dual=False, penalty='l2',
intercept_scaling=1., multi_class='ovr'):
"""Compute a Logistic Regression model for a list of regularization
parameters.
This is an implementation that uses the result of the previous model
to speed up computations along the set of solutions, making it faster
than sequentially calling LogisticRegression for the different parameters.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
Input data.
y : array-like, shape (n_samples,)
Input data, target values.
Cs : int | array-like, shape (n_cs,)
List of values for the regularization parameter or integer specifying
the number of regularization parameters that should be used. In this
case, the parameters will be chosen in a logarithmic scale between
1e-4 and 1e4.
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.
fit_intercept : bool
Whether to fit an intercept for the model. In this case the shape of
the returned array is (n_cs, n_features + 1).
max_iter : int
Maximum number of iterations for the solver.
tol : float
Stopping criterion. For the newton-cg and lbfgs solvers, the iteration
will stop when ``max{|g_i | i = 1, ..., n} <= tol``
where ``g_i`` is the i-th component of the gradient.
verbose : int
For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.
solver : {'lbfgs', 'newton-cg', 'liblinear'}
Numerical solver to use.
coef : array-like, shape (n_features,), default None
Initialization value for coefficients of logistic regression.
copy : bool, default True
Whether or not to produce a copy of the data. Setting this to
True will be useful in cases, when logistic_regression_path
is called repeatedly with the same data, as y is modified
along the path.
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.
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.
penalty : str, 'l1' or 'l2'
Used to specify the norm used in the penalization. The newton-cg and
lbfgs solvers support only l2 penalties.
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.
Notes
-----
You might get slighly different results with the solver liblinear than
with the others since this uses LIBLINEAR which penalizes the intercept.
"""
if isinstance(Cs, numbers.Integral):
Cs = np.logspace(-4, 4, Cs)
if multi_class not in ['multinomial', 'ovr']:
raise ValueError("multi_class can be either 'multinomial' or 'ovr'"
"got %s" % multi_class)
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, dtype=None)
_, 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 coef.size not 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.
copy : bool, default True
Whether or not to produce a copy of the data. Setting this to
True will be useful in cases, when ``_log_reg_scoring_path`` is called
repeatedly with the same data, as y is modified along the path.
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
----------