"""
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>
# Arthur Mensch <arthur.mensch@m4x.org
import numbers
import warnings
import numpy as np
from scipy import optimize, sparse
from scipy.special import expit
from .base import LinearClassifierMixin, SparseCoefMixin, BaseEstimator
from .sag import sag_solver
from ..preprocessing import LabelEncoder, LabelBinarizer
from ..svm.base import _fit_liblinear
from ..utils import check_array, check_consistent_length, compute_class_weight
from ..utils import check_random_state
from ..utils.extmath import (log_logistic, safe_sparse_dot, softmax,
squared_norm)
from ..utils.extmath import row_norms
from ..utils.fixes import logsumexp
from ..utils.optimize import newton_cg
from ..utils.validation import check_X_y
from ..exceptions import NotFittedError
from ..utils.multiclass import check_classification_targets
from ..externals.joblib import Parallel, delayed
from ..model_selection 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.
Returns
-------
w : ndarray, shape (n_features,)
Coefficient vector without the intercept weight (w[-1]) if the
intercept should be fit. Unchanged otherwise.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data. Unchanged.
yz : float
y * np.dot(X, w).
"""
c = 0.
if w.size == X.shape[1] + 1:
c = w[-1]
w = w[:-1]
z = safe_sparse_dot(X, w) + c
yz = y * z
return w, c, yz
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 : array-like, 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_samples, 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(n_samples)
# 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 : array-like, 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_grad_hess(w, X, y, alpha, sample_weight=None):
"""Computes the gradient and the Hessian, in the case of a 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 : array-like, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
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])
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 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 : array-like, 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.
Reference
---------
Bishop, C. M. (2006). Pattern recognition and machine learning.
Springer. (Chapter 4.3.4)
"""
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 : array-like, 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
Reference
---------
Bishop, C. M. (2006). Pattern recognition and machine learning.
Springer. (Chapter 4.3.4)
"""
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)),
dtype=X.dtype)
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_grad_hess(w, X, Y, alpha, sample_weight):
"""
Computes the gradient and the Hessian, in the case of a multinomial loss.
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 : array-like, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
Returns
-------
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` is unused. Refactoring to avoid computing it does not
# significantly speed up the computation and decreases readability
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 grad, hessp
def _check_solver_option(solver, multi_class, penalty, dual):
if solver not in ['liblinear', 'newton-cg', 'lbfgs', 'sag', 'saga']:
raise ValueError("Logistic Regression supports only liblinear, "
"newton-cg, lbfgs, sag and saga solvers, got %s"
% solver)
if multi_class not in ['multinomial', 'ovr']:
raise ValueError("multi_class should be either multinomial or "
"ovr, got %s" % multi_class)
if multi_class == 'multinomial' and solver == 'liblinear':
raise ValueError("Solver %s does not support "
"a multinomial backend." % solver)
if solver not in ['liblinear', 'saga']:
if penalty != 'l2':
raise ValueError("Solver %s supports only l2 penalties, "
"got %s penalty." % (solver, penalty))
if solver != 'liblinear':
if dual:
raise ValueError("Solver %s supports only "
"dual=False, got dual=%s" % (solver, dual))
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,
class_weight=None, dual=False, penalty='l2',
intercept_scaling=1., multi_class='ovr',
random_state=None, check_input=True,
max_squared_sum=None, sample_weight=None):
"""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.
Note that there will be no speedup with liblinear solver, since it does
not handle warm-starting.
Read more in the :ref:`User Guide <logistic_regression>`.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
Input data.
y : array-like, shape (n_samples,)
Input data, target values.
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 : 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.
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', 'sag', 'saga'}
Numerical solver to use.
coef : array-like, shape (n_features,), default None
Initialization value for coefficients of logistic regression.
Useless for liblinear solver.
class_weight : dict or 'balanced', optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
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',
'sag' and 'lbfgs' solvers support only l2 penalties.
intercept_scaling : float, default 1.
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 equal 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' and
'newton-cg' solvers.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`. Used when ``solver`` == 'sag' or
'liblinear'.
check_input : bool, default True
If False, the input arrays X and y will not be checked.
max_squared_sum : float, default None
Maximum squared sum of X over samples. Used only in SAG solver.
If None, it will be computed, going through all the samples.
The value should be precomputed to speed up cross validation.
sample_weight : array-like, shape(n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
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.
n_iter : array, shape (n_cs,)
Actual number of iteration for each Cs.
Notes
-----
You might get slightly different results with the solver liblinear than
with the others since this uses LIBLINEAR which penalizes the intercept.
.. versionchanged:: 0.19
The "copy" parameter was removed.
"""
if isinstance(Cs, numbers.Integral):
Cs = np.logspace(-4, 4, Cs)
_check_solver_option(solver, multi_class, penalty, dual)
# Preprocessing.
if check_input:
X = check_array(X, accept_sparse='csr', dtype=np.float64)
y = check_array(y, ensure_2d=False, dtype=None)
check_consistent_length(X, y)
_, n_features = X.shape
classes = np.unique(y)
random_state = check_random_state(random_state)
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 sample weights exist, convert them to array (support for lists)
# and check length
# Otherwise set them to 1 for all examples
if sample_weight is not None:
sample_weight = np.array(sample_weight, dtype=X.dtype, order='C')
check_consistent_length(y, sample_weight)
else:
sample_weight = np.ones(X.shape[0], dtype=X.dtype)
# If class_weights is a dict (provided by the user), the weights
# are assigned to the original labels. If it is "balanced", then
# the class_weights are assigned after masking the labels with a OvR.
le = LabelEncoder()
if isinstance(class_weight, dict) or multi_class == 'multinomial':
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), dtype=X.dtype)
mask_classes = np.array([-1, 1])
mask = (y == pos_class)
y_bin = np.ones(y.shape, dtype=X.dtype)
y_bin[~mask] = -1.
# for compute_class_weight
if class_weight == "balanced":
class_weight_ = compute_class_weight(class_weight, mask_classes,
y_bin)
sample_weight *= class_weight_[le.fit_transform(y_bin)]
else:
if solver not in ['sag', 'saga']:
lbin = LabelBinarizer()
Y_multi = lbin.fit_transform(y)
if Y_multi.shape[1] == 1:
Y_multi = np.hstack([1 - Y_multi, Y_multi])
else:
# SAG multinomial solver needs LabelEncoder, not LabelBinarizer
le = LabelEncoder()
Y_multi = le.fit_transform(y).astype(X.dtype, copy=False)
w0 = np.zeros((classes.size, n_features + int(fit_intercept)),
order='F', dtype=X.dtype)
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_classes = classes.size
if n_classes == 2:
n_classes = 1
if (coef.shape[0] != n_classes 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.
if solver in ['lbfgs', 'newton-cg']:
w0 = w0.ravel()
target = Y_multi
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_grad_hess
warm_start_sag = {'coef': w0.T}
else:
target = y_bin
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_grad_hess
warm_start_sag = {'coef': np.expand_dims(w0, axis=1)}
coefs = list()
n_iter = np.zeros(len(Cs), dtype=np.int32)
for i, C in enumerate(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.")
try:
n_iter_i = info['nit'] - 1
except:
n_iter_i = info['funcalls'] - 1
elif solver == 'newton-cg':
args = (X, target, 1. / C, sample_weight)
w0, n_iter_i = newton_cg(hess, func, grad, w0, args=args,
maxiter=max_iter, tol=tol)
elif solver == 'liblinear':
coef_, intercept_, n_iter_i, = _fit_liblinear(
X, target, C, fit_intercept, intercept_scaling, None,
penalty, dual, verbose, max_iter, tol, random_state,
sample_weight=sample_weight)
if fit_intercept:
w0 = np.concatenate([coef_.ravel(), intercept_])
else:
w0 = coef_.ravel()
elif solver in ['sag', 'saga']:
if multi_class == 'multinomial':
target = target.astype(np.float64)
loss = 'multinomial'
else:
loss = 'log'
if penalty == 'l1':
alpha = 0.
beta = 1. / C
else:
alpha = 1. / C
beta = 0.
w0, n_iter_i, warm_start_sag = sag_solver(
X, target, sample_weight, loss, alpha,
beta, max_iter, tol,
verbose, random_state, False, max_squared_sum, warm_start_sag,
is_saga=(solver == 'saga'))
else:
raise ValueError("solver must be one of {'liblinear', 'lbfgs', "
"'newton-cg', 'sag'}, 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.copy())
n_iter[i] = n_iter_i
return coefs, np.array(Cs), n_iter
# 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, intercept_scaling=1.,
multi_class='ovr', random_state=None,
max_squared_sum=None, sample_weight=None):
"""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 or None, optional, default: None
A string (see model evaluation documentation) or
a scorer callable object / function with signature
``scorer(estimator, X, y)``. 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 or 'balanced', optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
verbose : int
For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.
solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}
Decides which solver to use.
penalty : str, 'l1' or 'l2'
Used to specify the norm used in the penalization. The 'newton-cg',
'sag' 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.
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. Does not work for
liblinear solver.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`. Used when ``solver`` == 'sag' and
'liblinear'.
max_squared_sum : float, default None
Maximum squared sum of X over samples. Used only in SAG solver.
If None, it will be computed, going through all the samples.
The value should be precomputed to speed up cross validation.
sample_weight : array-like, shape(n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
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.
n_iter : array, shape(n_cs,)
Actual number of iteration for each Cs.
"""
_check_solver_option(solver, multi_class, penalty, dual)
X_train = X[train]
X_test = X[test]
y_train = y[train]
y_test = y[test]
if sample_weight is not None:
sample_weight = check_array(sample_weight, ensure_2d=False)
check_consistent_length(y, sample_weight)
sample_weight = sample_weight[train]
coefs, Cs, n_iter = logistic_regression_path(
X_train, y_train, Cs=Cs, fit_intercept=fit_intercept,
solver=solver, max_iter=max_iter, class_weight=class_weight,
pos_class=pos_class, multi_class=multi_class,
tol=tol, verbose=verbose, dual=dual, penalty=penalty,
intercept_scaling=intercept_scaling, random_state=random_state,
check_input=False, max_squared_sum=max_squared_sum,
sample_weight=sample_weight)
log_reg = LogisticRegression(fit_intercept=fit_intercept)
# 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 = np.ones(y_test.shape, dtype=np.float64)
y_test[~mask] = -1.
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), n_iter
class LogisticRegression(BaseEstimator, LinearClassifierMixin,
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',
'sag' and 'newton-cg' solvers.)
This class implements regularized logistic regression using the
'liblinear' library, 'newton-cg', 'sag' 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', 'sag', 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.
Read more in the :ref:`User Guide <logistic_regression>`.
Parameters
----------
penalty : str, 'l1' or 'l2', default: 'l2'
Used to specify the norm used in the penalization. The 'newton-cg',
'sag' and 'lbfgs' solvers support only l2 penalties.
.. versionadded:: 0.19
l1 penalty with SAGA solver (allowing 'multinomial' + L1)
dual : bool, default: False
Dual or primal formulation. Dual formulation is only implemented for
l2 penalty with liblinear solver. Prefer dual=False when
n_samples > n_features.
tol : float, default: 1e-4
Tolerance for stopping criteria.
C : float, 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 to the decision function.
intercept_scaling : float, default 1.
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 equal 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 or 'balanced', default: None
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
.. versionadded:: 0.17
*class_weight='balanced'*
random_state : int, RandomState instance or None, optional, default: None
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`. Used when ``solver`` == 'sag' or
'liblinear'.
solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'},
default: 'liblinear'
Algorithm to use in the optimization problem.
- For small datasets, 'liblinear' is a good choice, whereas 'sag' and
'saga' are faster for large ones.
- For multiclass problems, only 'newton-cg', 'sag', 'saga' and 'lbfgs'
handle multinomial loss; 'liblinear' is limited to one-versus-rest
schemes.
- 'newton-cg', 'lbfgs' and 'sag' only handle L2 penalty, whereas
'liblinear' and 'saga' handle L1 penalty.
Note that 'sag' and 'saga' fast convergence is only guaranteed on
features with approximately the same scale. You can
preprocess the data with a scaler from sklearn.preprocessing.
.. versionadded:: 0.17
Stochastic Average Gradient descent solver.
.. versionadded:: 0.19
SAGA solver.
max_iter : int, default: 100
Useful only for the newton-cg, sag and lbfgs solvers.
Maximum number of iterations taken for the solvers to converge.
multi_class : str, {'ovr', 'multinomial'}, default: 'ovr'
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. Does not work for liblinear
solver.
.. versionadded:: 0.18
Stochastic Average Gradient descent solver for 'multinomial' case.
verbose : int, default: 0
For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.
warm_start : bool, default: False
When set to True, reuse the solution of the previous call to fit as
initialization, otherwise, just erase the previous solution.
Useless for liblinear solver.
.. versionadded:: 0.17
*warm_start* to support *lbfgs*, *newton-cg*, *sag*, *saga* solvers.
n_jobs : int, default: 1
Number of CPU cores used when parallelizing over classes if
multi_class='ovr'". This parameter is ignored when the ``solver``is set
to 'liblinear' regardless of whether 'multi_class' is specified or
not. If given a value of -1, all cores are used.
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.
intercept_ : array, shape (1,) or (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.
`intercept_` is of shape(1,) when the problem is binary.
n_iter_ : array, shape (n_classes,) or (1, )
Actual number of iterations for all classes. If binary or multinomial,
it returns only 1 element. For liblinear solver, only the maximum
number of iteration across all classes is given.
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/
SAG -- Mark Schmidt, Nicolas Le Roux, and Francis Bach
Minimizing Finite Sums with the Stochastic Average Gradient
https://hal.inria.fr/hal-00860051/document
SAGA -- Defazio, A., Bach F. & Lacoste-Julien S. (2014).
SAGA: A Fast Incremental Gradient Method With Support
for Non-Strongly Convex Composite Objectives
https://arxiv.org/abs/1407.0202
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
"""
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, warm_start=False, n_jobs=1):
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
self.warm_start = warm_start
self.n_jobs = n_jobs
[docs] def fit(self, X, y, sample_weight=None):
"""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 is the number of samples and
n_features is the number of features.
y : array-like, shape (n_samples,)
Target vector relative to X.
sample_weight : array-like, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
.. versionadded:: 0.17
*sample_weight* support to LogisticRegression.
Returns
-------
self : object
Returns self.
"""
if not isinstance(self.C, numbers.Number) or self.C < 0:
raise ValueError("Penalty term must be positive; got (C=%r)"
% self.C)
if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0:
raise ValueError("Maximum number of iteration must be positive;"
" got (max_iter=%r)" % self.max_iter)
if not isinstance(self.tol, numbers.Number) or self.tol < 0:
raise ValueError("Tolerance for stopping criteria must be "
"positive; got (tol=%r)" % self.tol)
if self.solver in ['newton-cg']:
_dtype = [np.float64, np.float32]
else:
_dtype = np.float64
X, y = check_X_y(X, y, accept_sparse='csr', dtype=_dtype,
order="C")
check_classification_targets(y)
self.classes_ = np.unique(y)
n_samples, n_features = X.shape
_check_solver_option(self.solver, self.multi_class, self.penalty,
self.dual)
if self.solver == 'liblinear':
if self.n_jobs != 1:
warnings.warn("'n_jobs' > 1 does not have any effect when"
" 'solver' is set to 'liblinear'. Got 'n_jobs'"
" = {}.".format(self.n_jobs))
self.coef_, self.intercept_, 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, self.random_state,
sample_weight=sample_weight)
self.n_iter_ = np.array([n_iter_])
return self
if self.solver in ['sag', 'saga']:
max_squared_sum = row_norms(X, squared=True).max()
else:
max_squared_sum = None
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:]
if self.warm_start:
warm_start_coef = getattr(self, 'coef_', None)
else:
warm_start_coef = None
if warm_start_coef is not None and self.fit_intercept:
warm_start_coef = np.append(warm_start_coef,
self.intercept_[:, np.newaxis],
axis=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]
warm_start_coef = [warm_start_coef]
if warm_start_coef is None:
warm_start_coef = [None] * n_classes
path_func = delayed(logistic_regression_path)
# The SAG solver releases the GIL so it's more efficient to use
# threads for this solver.
if self.solver in ['sag', 'saga']:
backend = 'threading'
else:
backend = 'multiprocessing'
fold_coefs_ = Parallel(n_jobs=self.n_jobs, verbose=self.verbose,
backend=backend)(
path_func(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, check_input=False,
random_state=self.random_state, coef=warm_start_coef_,
penalty=self.penalty,
max_squared_sum=max_squared_sum,
sample_weight=sample_weight)
for class_, warm_start_coef_ in zip(classes_, warm_start_coef))
fold_coefs_, _, n_iter_ = zip(*fold_coefs_)
self.n_iter_ = np.asarray(n_iter_, dtype=np.int32)[:, 0]
if self.multi_class == 'multinomial':
self.coef_ = fold_coefs_[0][0]
else:
self.coef_ = np.asarray(fold_coefs_)
self.coef_ = self.coef_.reshape(n_classes, n_features +
int(self.fit_intercept))
if self.fit_intercept:
self.intercept_ = self.coef_[:, -1]
self.coef_ = self.coef_[:, :-1]
return self
[docs] def predict_proba(self, X):
"""Probability estimates.
The returned estimates for all classes are ordered by the
label of classes.
For a multi_class problem, if multi_class is set to be "multinomial"
the softmax function is used to find the predicted probability of
each class.
Else use a one-vs-rest approach, i.e calculate the probability
of each class assuming it to be positive using the logistic function.
and normalize these values across all the 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_``.
"""
if not hasattr(self, "coef_"):
raise NotFittedError("Call fit before prediction")
calculate_ovr = self.coef_.shape[0] == 1 or self.multi_class == "ovr"
if calculate_ovr:
return super(LogisticRegression, self)._predict_proba_lr(X)
else:
return softmax(self.decision_function(X), copy=False)
[docs] 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):
"""Logistic Regression CV (aka logit, MaxEnt) classifier.
This class implements logistic regression using liblinear, newton-cg, sag
of lbfgs optimizer. The newton-cg, sag 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 it is supposed to be faster for high-dimensional dense data.
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.
Read more in the :ref:`User Guide <logistic_regression>`.
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 to the decision function.
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.model_selection` module for the
list of possible cross-validation objects.
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',
'sag' and 'lbfgs' solvers support only l2 penalties.
scoring : string, callable, or None
A string (see model evaluation documentation) or
a scorer callable object / function with signature
``scorer(estimator, X, y)``. For a list of scoring functions
that can be used, look at :mod:`sklearn.metrics`. The
default scoring option used is 'accuracy'.
solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'},
default: 'lbfgs'
Algorithm to use in the optimization problem.
- For small datasets, 'liblinear' is a good choice, whereas 'sag' and
'saga' are faster for large ones.
- For multiclass problems, only 'newton-cg', 'sag', 'saga' and 'lbfgs'
handle multinomial loss; 'liblinear' is limited to one-versus-rest
schemes.
- 'newton-cg', 'lbfgs' and 'sag' only handle L2 penalty, whereas
'liblinear' and 'saga' handle L1 penalty.
- 'liblinear' might be slower in LogisticRegressionCV because it does
not handle warm-starting.
Note that 'sag' and 'saga' fast convergence is only guaranteed on
features with approximately the same scale. You can preprocess the data
with a scaler from sklearn.preprocessing.
.. versionadded:: 0.17
Stochastic Average Gradient descent solver.
.. versionadded:: 0.19
SAGA solver.
tol : float, optional
Tolerance for stopping criteria.
max_iter : int, optional
Maximum number of iterations of the optimization algorithm.
class_weight : dict or 'balanced', optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
.. versionadded:: 0.17
class_weight == 'balanced'
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', 'sag' 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.
intercept_scaling : float, default 1.
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 equal 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 'newton-cg',
'sag', 'saga' and 'lbfgs' solver.
.. versionadded:: 0.18
Stochastic Average Gradient descent solver for 'multinomial' case.
random_state : int, RandomState instance or None, optional, default None
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
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.
intercept_ : array, shape (1,) or (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.
`intercept_` 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.
`C_` is of shape(n_classes,) when the problem is binary.
n_iter_ : array, shape (n_classes, n_folds, n_cs) or (1, n_folds, n_cs)
Actual number of iterations for all classes, folds and Cs.
In the binary or multinomial cases, the first dimension is equal to 1.
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',
random_state=None):
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
self.random_state = random_state
[docs] def fit(self, X, y, sample_weight=None):
"""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 is the number of samples and
n_features is the number of features.
y : array-like, shape (n_samples,)
Target vector relative to X.
sample_weight : array-like, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
self : object
Returns self.
"""
_check_solver_option(self.solver, self.multi_class, self.penalty,
self.dual)
if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0:
raise ValueError("Maximum number of iteration must be positive;"
" got (max_iter=%r)" % self.max_iter)
if not isinstance(self.tol, numbers.Number) or self.tol < 0:
raise ValueError("Tolerance for stopping criteria must be "
"positive; got (tol=%r)" % self.tol)
X, y = check_X_y(X, y, accept_sparse='csr', dtype=np.float64,
order="C")
check_classification_targets(y)
class_weight = self.class_weight
# Encode for string labels
label_encoder = LabelEncoder().fit(y)
y = label_encoder.transform(y)
if isinstance(class_weight, dict):
class_weight = dict((label_encoder.transform([cls])[0], v)
for cls, v in class_weight.items())
# The original class labels
classes = self.classes_ = label_encoder.classes_
encoded_labels = label_encoder.transform(label_encoder.classes_)
if self.solver in ['sag', 'saga']:
max_squared_sum = row_norms(X, squared=True).max()
else:
max_squared_sum = None
# init cross-validation generator
cv = check_cv(self.cv, y, classifier=True)
folds = list(cv.split(X, y))
# Use the label encoded classes
n_classes = len(encoded_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" % classes[0])
if n_classes == 2:
# OvR in case of binary problems is as good as fitting
# the higher label
n_classes = 1
encoded_labels = encoded_labels[1:]
classes = classes[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.
if self.multi_class == 'multinomial':
iter_encoded_labels = iter_classes = [None]
else:
iter_encoded_labels = encoded_labels
iter_classes = classes
# compute the class weights for the entire dataset y
if class_weight == "balanced":
class_weight = compute_class_weight(class_weight,
np.arange(len(self.classes_)),
y)
class_weight = dict(enumerate(class_weight))
path_func = delayed(_log_reg_scoring_path)
# The SAG solver releases the GIL so it's more efficient to use
# threads for this solver.
if self.solver in ['sag', 'saga']:
backend = 'threading'
else:
backend = 'multiprocessing'
fold_coefs_ = Parallel(n_jobs=self.n_jobs, verbose=self.verbose,
backend=backend)(
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=class_weight, scoring=self.scoring,
multi_class=self.multi_class,
intercept_scaling=self.intercept_scaling,
random_state=self.random_state,
max_squared_sum=max_squared_sum,
sample_weight=sample_weight
)
for label in iter_encoded_labels
for train, test in folds)
if self.multi_class == 'multinomial':
multi_coefs_paths, Cs, multi_scores, n_iter_ = 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]
self.n_iter_ = np.reshape(n_iter_, (1, len(folds),
len(self.Cs_)))
else:
coefs_paths, Cs, scores, n_iter_ = zip(*fold_coefs_)
self.Cs_ = Cs[0]
coefs_paths = np.reshape(coefs_paths, (n_classes, len(folds),
len(self.Cs_), -1))
self.n_iter_ = np.reshape(n_iter_, (n_classes, len(folds),
len(self.Cs_)))
self.coefs_paths_ = dict(zip(classes, coefs_paths))
scores = np.reshape(scores, (n_classes, len(folds), -1))
self.scores_ = dict(zip(classes, 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, (cls, encoded_label) in enumerate(
zip(iter_classes, iter_encoded_labels)):
if self.multi_class == 'ovr':
# The scores_ / coefs_paths_ dict have unencoded class
# labels as their keys
scores = self.scores_[cls]
coefs_paths = self.coefs_paths_[cls]
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)
# Note that y is label encoded and hence pos_class must be
# the encoded label / None (for 'multinomial')
w, _, _ = logistic_regression_path(
X, y, pos_class=encoded_label, Cs=[C_], solver=self.solver,
fit_intercept=self.fit_intercept, coef=coef_init,
max_iter=self.max_iter, tol=self.tol,
penalty=self.penalty,
class_weight=class_weight,
multi_class=self.multi_class,
verbose=max(0, self.verbose - 1),
random_state=self.random_state,
check_input=False, max_squared_sum=max_squared_sum,
sample_weight=sample_weight)
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
