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# Authors: Peter Prettenhofer <peter.prettenhofer@gmail.com> (main author)
# Mathieu Blondel (partial_fit support)
#
# License: BSD 3 clause
"""Classification and regression using Stochastic Gradient Descent (SGD)."""
import numpy as np
import scipy.sparse as sp
from abc import ABCMeta, abstractmethod
from ..externals.joblib import Parallel, delayed
from .base import LinearClassifierMixin, SparseCoefMixin
from ..base import BaseEstimator, RegressorMixin
from ..feature_selection.from_model import _LearntSelectorMixin
from ..utils import (check_array, check_random_state, check_X_y)
from ..utils.extmath import safe_sparse_dot
from ..utils.multiclass import _check_partial_fit_first_call
from ..externals import six
from .sgd_fast import plain_sgd, average_sgd
from ..utils.seq_dataset import ArrayDataset, CSRDataset
from ..utils import compute_class_weight
from .sgd_fast import Hinge
from .sgd_fast import SquaredHinge
from .sgd_fast import Log
from .sgd_fast import ModifiedHuber
from .sgd_fast import SquaredLoss
from .sgd_fast import Huber
from .sgd_fast import EpsilonInsensitive
from .sgd_fast import SquaredEpsilonInsensitive
LEARNING_RATE_TYPES = {"constant": 1, "optimal": 2, "invscaling": 3,
"pa1": 4, "pa2": 5}
PENALTY_TYPES = {"none": 0, "l2": 2, "l1": 1, "elasticnet": 3}
SPARSE_INTERCEPT_DECAY = 0.01
"""For sparse data intercept updates are scaled by this decay factor to avoid
intercept oscillation."""
DEFAULT_EPSILON = 0.1
"""Default value of ``epsilon`` parameter. """
class BaseSGD(six.with_metaclass(ABCMeta, BaseEstimator, SparseCoefMixin)):
"""Base class for SGD classification and regression."""
def __init__(self, loss, penalty='l2', alpha=0.0001, C=1.0,
l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=False,
verbose=0, epsilon=0.1, random_state=None,
learning_rate="optimal", eta0=0.0, power_t=0.5,
warm_start=False, average=False):
self.loss = loss
self.penalty = penalty
self.learning_rate = learning_rate
self.epsilon = epsilon
self.alpha = alpha
self.C = C
self.l1_ratio = l1_ratio
self.fit_intercept = fit_intercept
self.n_iter = n_iter
self.shuffle = shuffle
self.random_state = random_state
self.verbose = verbose
self.eta0 = eta0
self.power_t = power_t
self.warm_start = warm_start
self.average = average
self._validate_params()
self.coef_ = None
if self.average > 0:
self.standard_coef_ = None
self.average_coef_ = None
# iteration count for learning rate schedule
# must not be int (e.g. if ``learning_rate=='optimal'``)
self.t_ = None
def set_params(self, *args, **kwargs):
super(BaseSGD, self).set_params(*args, **kwargs)
self._validate_params()
return self
@abstractmethod
def fit(self, X, y):
"""Fit model."""
def _validate_params(self):
"""Validate input params. """
if not isinstance(self.shuffle, bool):
raise ValueError("shuffle must be either True or False")
if self.n_iter <= 0:
raise ValueError("n_iter must be > zero")
if not (0.0 <= self.l1_ratio <= 1.0):
raise ValueError("l1_ratio must be in [0, 1]")
if self.alpha < 0.0:
raise ValueError("alpha must be >= 0")
if self.learning_rate in ("constant", "invscaling"):
if self.eta0 <= 0.0:
raise ValueError("eta0 must be > 0")
# raises ValueError if not registered
self._get_penalty_type(self.penalty)
self._get_learning_rate_type(self.learning_rate)
if self.loss not in self.loss_functions:
raise ValueError("The loss %s is not supported. " % self.loss)
def _get_loss_function(self, loss):
"""Get concrete ``LossFunction`` object for str ``loss``. """
try:
loss_ = self.loss_functions[loss]
loss_class, args = loss_[0], loss_[1:]
if loss in ('huber', 'epsilon_insensitive',
'squared_epsilon_insensitive'):
args = (self.epsilon, )
return loss_class(*args)
except KeyError:
raise ValueError("The loss %s is not supported. " % loss)
def _get_learning_rate_type(self, learning_rate):
try:
return LEARNING_RATE_TYPES[learning_rate]
except KeyError:
raise ValueError("learning rate %s "
"is not supported. " % learning_rate)
def _get_penalty_type(self, penalty):
penalty = str(penalty).lower()
try:
return PENALTY_TYPES[penalty]
except KeyError:
raise ValueError("Penalty %s is not supported. " % penalty)
def _validate_sample_weight(self, sample_weight, n_samples):
"""Set the sample weight array."""
if sample_weight is None:
# uniform sample weights
sample_weight = np.ones(n_samples, dtype=np.float64, order='C')
else:
# user-provided array
sample_weight = np.asarray(sample_weight, dtype=np.float64,
order="C")
if sample_weight.shape[0] != n_samples:
raise ValueError("Shapes of X and sample_weight do not match.")
return sample_weight
def _allocate_parameter_mem(self, n_classes, n_features, coef_init=None,
intercept_init=None):
"""Allocate mem for parameters; initialize if provided."""
if n_classes > 2:
# allocate coef_ for multi-class
if coef_init is not None:
coef_init = np.asarray(coef_init, order="C")
if coef_init.shape != (n_classes, n_features):
raise ValueError("Provided coef_ does not match dataset. ")
self.coef_ = coef_init
else:
self.coef_ = np.zeros((n_classes, n_features),
dtype=np.float64, order="C")
# allocate intercept_ for multi-class
if intercept_init is not None:
intercept_init = np.asarray(intercept_init, order="C")
if intercept_init.shape != (n_classes, ):
raise ValueError("Provided intercept_init "
"does not match dataset.")
self.intercept_ = intercept_init
else:
self.intercept_ = np.zeros(n_classes, dtype=np.float64,
order="C")
else:
# allocate coef_ for binary problem
if coef_init is not None:
coef_init = np.asarray(coef_init, dtype=np.float64,
order="C")
coef_init = coef_init.ravel()
if coef_init.shape != (n_features,):
raise ValueError("Provided coef_init does not "
"match dataset.")
self.coef_ = coef_init
else:
self.coef_ = np.zeros(n_features,
dtype=np.float64,
order="C")
# allocate intercept_ for binary problem
if intercept_init is not None:
intercept_init = np.asarray(intercept_init, dtype=np.float64)
if intercept_init.shape != (1,) and intercept_init.shape != ():
raise ValueError("Provided intercept_init "
"does not match dataset.")
self.intercept_ = intercept_init.reshape(1,)
else:
self.intercept_ = np.zeros(1, dtype=np.float64, order="C")
# initialize average parameters
if self.average > 0:
self.standard_coef_ = self.coef_
self.standard_intercept_ = self.intercept_
self.average_coef_ = np.zeros(self.coef_.shape,
dtype=np.float64,
order="C")
self.average_intercept_ = np.zeros(self.standard_intercept_.shape,
dtype=np.float64,
order="C")
def _make_dataset(X, y_i, sample_weight):
"""Create ``Dataset`` abstraction for sparse and dense inputs.
This also returns the ``intercept_decay`` which is different
for sparse datasets.
"""
if sp.issparse(X):
dataset = CSRDataset(X.data, X.indptr, X.indices, y_i, sample_weight)
intercept_decay = SPARSE_INTERCEPT_DECAY
else:
dataset = ArrayDataset(X, y_i, sample_weight)
intercept_decay = 1.0
return dataset, intercept_decay
def _prepare_fit_binary(est, y, i):
"""Initialization for fit_binary.
Returns y, coef, intercept.
"""
y_i = np.ones(y.shape, dtype=np.float64, order="C")
y_i[y != est.classes_[i]] = -1.0
average_intercept = 0
average_coef = None
if len(est.classes_) == 2:
if not est.average:
coef = est.coef_.ravel()
intercept = est.intercept_[0]
else:
coef = est.standard_coef_.ravel()
intercept = est.standard_intercept_[0]
average_coef = est.average_coef_.ravel()
average_intercept = est.average_intercept_[0]
else:
if not est.average:
coef = est.coef_[i]
intercept = est.intercept_[i]
else:
coef = est.standard_coef_[i]
intercept = est.standard_intercept_[i]
average_coef = est.average_coef_[i]
average_intercept = est.average_intercept_[i]
return y_i, coef, intercept, average_coef, average_intercept
def fit_binary(est, i, X, y, alpha, C, learning_rate, n_iter,
pos_weight, neg_weight, sample_weight):
"""Fit a single binary classifier.
The i'th class is considered the "positive" class.
"""
# if average is not true, average_coef, and average_intercept will be
# unused
y_i, coef, intercept, average_coef, average_intercept = \
_prepare_fit_binary(est, y, i)
assert y_i.shape[0] == y.shape[0] == sample_weight.shape[0]
dataset, intercept_decay = _make_dataset(X, y_i, sample_weight)
penalty_type = est._get_penalty_type(est.penalty)
learning_rate_type = est._get_learning_rate_type(learning_rate)
# XXX should have random_state_!
random_state = check_random_state(est.random_state)
# numpy mtrand expects a C long which is a signed 32 bit integer under
# Windows
seed = random_state.randint(0, np.iinfo(np.int32).max)
if not est.average:
return plain_sgd(coef, intercept, est.loss_function,
penalty_type, alpha, C, est.l1_ratio,
dataset, n_iter, int(est.fit_intercept),
int(est.verbose), int(est.shuffle), seed,
pos_weight, neg_weight,
learning_rate_type, est.eta0,
est.power_t, est.t_, intercept_decay)
else:
standard_coef, standard_intercept, average_coef, \
average_intercept = average_sgd(coef, intercept, average_coef,
average_intercept,
est.loss_function, penalty_type,
alpha, C, est.l1_ratio, dataset,
n_iter, int(est.fit_intercept),
int(est.verbose), int(est.shuffle),
seed, pos_weight, neg_weight,
learning_rate_type, est.eta0,
est.power_t, est.t_,
intercept_decay,
est.average)
if len(est.classes_) == 2:
est.average_intercept_[0] = average_intercept
else:
est.average_intercept_[i] = average_intercept
return standard_coef, standard_intercept
class BaseSGDClassifier(six.with_metaclass(ABCMeta, BaseSGD,
LinearClassifierMixin)):
loss_functions = {
"hinge": (Hinge, 1.0),
"squared_hinge": (SquaredHinge, 1.0),
"perceptron": (Hinge, 0.0),
"log": (Log, ),
"modified_huber": (ModifiedHuber, ),
"squared_loss": (SquaredLoss, ),
"huber": (Huber, DEFAULT_EPSILON),
"epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
"squared_epsilon_insensitive": (SquaredEpsilonInsensitive,
DEFAULT_EPSILON),
}
@abstractmethod
def __init__(self, loss="hinge", penalty='l2', alpha=0.0001, l1_ratio=0.15,
fit_intercept=True, n_iter=5, shuffle=False, verbose=0,
epsilon=DEFAULT_EPSILON, n_jobs=1, random_state=None,
learning_rate="optimal", eta0=0.0, power_t=0.5,
class_weight=None, warm_start=False, average=False):
super(BaseSGDClassifier, self).__init__(loss=loss, penalty=penalty,
alpha=alpha, l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
n_iter=n_iter, shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0, power_t=power_t,
warm_start=warm_start,
average=average)
self.class_weight = class_weight
self.classes_ = None
self.n_jobs = int(n_jobs)
def _partial_fit(self, X, y, alpha, C,
loss, learning_rate, n_iter,
classes, sample_weight,
coef_init, intercept_init):
X, y = check_X_y(X, y, 'csr', dtype=np.float64, order="C")
n_samples, n_features = X.shape
self._validate_params()
_check_partial_fit_first_call(self, classes)
n_classes = self.classes_.shape[0]
# Allocate datastructures from input arguments
self._expanded_class_weight = compute_class_weight(self.class_weight,
self.classes_, y)
sample_weight = self._validate_sample_weight(sample_weight, n_samples)
if self.coef_ is None or coef_init is not None:
self._allocate_parameter_mem(n_classes, n_features,
coef_init, intercept_init)
elif n_features != self.coef_.shape[-1]:
raise ValueError("Number of features %d does not match previous data %d."
% (n_features, self.coef_.shape[-1]))
self.loss_function = self._get_loss_function(loss)
if self.t_ is None:
self.t_ = 1.0
# delegate to concrete training procedure
if n_classes > 2:
self._fit_multiclass(X, y, alpha=alpha, C=C,
learning_rate=learning_rate,
sample_weight=sample_weight, n_iter=n_iter)
elif n_classes == 2:
self._fit_binary(X, y, alpha=alpha, C=C,
learning_rate=learning_rate,
sample_weight=sample_weight, n_iter=n_iter)
else:
raise ValueError("The number of class labels must be "
"greater than one.")
return self
def _fit(self, X, y, alpha, C, loss, learning_rate, coef_init=None,
intercept_init=None, sample_weight=None):
if hasattr(self, "classes_"):
self.classes_ = None
X, y = check_X_y(X, y, 'csr', dtype=np.float64, order="C")
n_samples, n_features = X.shape
# labels can be encoded as float, int, or string literals
# np.unique sorts in asc order; largest class id is positive class
classes = np.unique(y)
if self.warm_start and self.coef_ is not None:
if coef_init is None:
coef_init = self.coef_
if intercept_init is None:
intercept_init = self.intercept_
else:
self.coef_ = None
self.intercept_ = None
if self.average > 0:
self.standard_coef_ = self.coef_
self.standard_intercept_ = self.intercept_
self.average_coef_ = None
self.average_intercept_ = None
# Clear iteration count for multiple call to fit.
self.t_ = None
self._partial_fit(X, y, alpha, C, loss, learning_rate, self.n_iter,
classes, sample_weight, coef_init, intercept_init)
return self
def _fit_binary(self, X, y, alpha, C, sample_weight,
learning_rate, n_iter):
"""Fit a binary classifier on X and y. """
coef, intercept = fit_binary(self, 1, X, y, alpha, C,
learning_rate, n_iter,
self._expanded_class_weight[1],
self._expanded_class_weight[0],
sample_weight)
self.t_ += n_iter * X.shape[0]
# need to be 2d
if self.average > 0:
if self.average <= self.t_ - 1:
self.coef_ = self.average_coef_.reshape(1, -1)
self.intercept_ = self.average_intercept_
else:
self.coef_ = self.standard_coef_.reshape(1, -1)
self.standard_intercept_ = np.atleast_1d(intercept)
self.intercept_ = self.standard_intercept_
else:
self.coef_ = coef.reshape(1, -1)
# intercept is a float, need to convert it to an array of length 1
self.intercept_ = np.atleast_1d(intercept)
def _fit_multiclass(self, X, y, alpha, C, learning_rate,
sample_weight, n_iter):
"""Fit a multi-class classifier by combining binary classifiers
Each binary classifier predicts one class versus all others. This
strategy is called OVA: One Versus All.
"""
# Use joblib to fit OvA in parallel.
result = Parallel(n_jobs=self.n_jobs, backend="threading",
verbose=self.verbose)(
delayed(fit_binary)(self, i, X, y, alpha, C, learning_rate,
n_iter, self._expanded_class_weight[i], 1.,
sample_weight)
for i in range(len(self.classes_)))
for i, (_, intercept) in enumerate(result):
self.intercept_[i] = intercept
self.t_ += n_iter * X.shape[0]
if self.average > 0:
if self.average <= self.t_ - 1.0:
self.coef_ = self.average_coef_
self.intercept_ = self.average_intercept_
else:
self.coef_ = self.standard_coef_
self.standard_intercept_ = np.atleast_1d(intercept)
self.intercept_ = self.standard_intercept_
def partial_fit(self, X, y, classes=None, sample_weight=None):
"""Fit linear model with Stochastic Gradient Descent.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Subset of the training data
y : numpy array, shape (n_samples,)
Subset of the target values
classes : array, shape (n_classes,)
Classes across all calls to partial_fit.
Can be obtained by via `np.unique(y_all)`, where y_all is the
target vector of the entire dataset.
This argument is required for the first call to partial_fit
and can be omitted in the subsequent calls.
Note that y doesn't need to contain all labels in `classes`.
sample_weight : array-like, shape (n_samples,), optional
Weights applied to individual samples.
If not provided, uniform weights are assumed.
Returns
-------
self : returns an instance of self.
"""
if self.class_weight == 'auto':
raise ValueError("class_weight 'auto' is not supported for "
"partial_fit. In order to use 'auto' weights, "
"use compute_class_weight('auto', classes, y). "
"In place of y you can us a large enough sample "
"of the full training set target to properly "
"estimate the class frequency distributions. "
"Pass the resulting weights as the class_weight "
"parameter.")
return self._partial_fit(X, y, alpha=self.alpha, C=1.0, loss=self.loss,
learning_rate=self.learning_rate, n_iter=1,
classes=classes, sample_weight=sample_weight,
coef_init=None, intercept_init=None)
def fit(self, X, y, coef_init=None, intercept_init=None,
class_weight=None, sample_weight=None):
"""Fit linear model with Stochastic Gradient Descent.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data
y : numpy array, shape (n_samples,)
Target values
coef_init : array, shape (n_classes, n_features)
The initial coefficients to warm-start the optimization.
intercept_init : array, shape (n_classes,)
The initial intercept to warm-start the optimization.
sample_weight : array-like, shape (n_samples,), optional
Weights applied to individual samples.
If not provided, uniform weights are assumed.
Returns
-------
self : returns an instance of self.
"""
return self._fit(X, y, alpha=self.alpha, C=1.0,
loss=self.loss, learning_rate=self.learning_rate,
coef_init=coef_init, intercept_init=intercept_init,
sample_weight=sample_weight)
class SGDClassifier(BaseSGDClassifier, _LearntSelectorMixin):
"""Linear classifiers (SVM, logistic regression, a.o.) with SGD training.
This estimator implements regularized linear models with stochastic
gradient descent (SGD) learning: the gradient of the loss is estimated
each sample at a time and the model is updated along the way with a
decreasing strength schedule (aka learning rate). SGD allows minibatch
(online/out-of-core) learning, see the partial_fit method.
This implementation works with data represented as dense or sparse arrays
of floating point values for the features. The model it fits can be
controlled with the loss parameter; by default, it fits a linear support
vector machine (SVM).
The regularizer is a penalty added to the loss function that shrinks model
parameters towards the zero vector using either the squared euclidean norm
L2 or the absolute norm L1 or a combination of both (Elastic Net). If the
parameter update crosses the 0.0 value because of the regularizer, the
update is truncated to 0.0 to allow for learning sparse models and achieve
online feature selection.
Parameters
----------
loss : str, 'hinge', 'log', 'modified_huber', 'squared_hinge',\
'perceptron', or a regression loss: 'squared_loss', 'huber',\
'epsilon_insensitive', or 'squared_epsilon_insensitive'
The loss function to be used. Defaults to 'hinge', which gives a
linear SVM.
The 'log' loss gives logistic regression, a probabilistic classifier.
'modified_huber' is another smooth loss that brings tolerance to
outliers as well as probability estimates.
'squared_hinge' is like hinge but is quadratically penalized.
'perceptron' is the linear loss used by the perceptron algorithm.
The other losses are designed for regression but can be useful in
classification as well; see SGDRegressor for a description.
penalty : str, 'l2' or 'l1' or 'elasticnet'
The penalty (aka regularization term) to be used. Defaults to 'l2'
which is the standard regularizer for linear SVM models. 'l1' and
'elasticnet' might bring sparsity to the model (feature selection)
not achievable with 'l2'.
alpha : float
Constant that multiplies the regularization term. Defaults to 0.0001
l1_ratio : float
The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
Defaults to 0.15.
fit_intercept : bool
Whether the intercept should be estimated or not. If False, the
data is assumed to be already centered. Defaults to True.
n_iter : int, optional
The number of passes over the training data (aka epochs). The number
of iterations is set to 1 if using partial_fit.
Defaults to 5.
shuffle : bool, optional
Whether or not the training data should be shuffled after each epoch.
Defaults to False.
random_state : int seed, RandomState instance, or None (default)
The seed of the pseudo random number generator to use when
shuffling the data.
verbose : integer, optional
The verbosity level
epsilon : float
Epsilon in the epsilon-insensitive loss functions; only if `loss` is
'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
For 'huber', determines the threshold at which it becomes less
important to get the prediction exactly right.
For epsilon-insensitive, any differences between the current prediction
and the correct label are ignored if they are less than this threshold.
n_jobs : integer, optional
The number of CPUs to use to do the OVA (One Versus All, for
multi-class problems) computation. -1 means 'all CPUs'. Defaults
to 1.
learning_rate : string, optional
The learning rate:
constant: eta = eta0
optimal: eta = 1.0 / (t + t0) [default]
invscaling: eta = eta0 / pow(t, power_t)
eta0 : double
The initial learning rate for the 'constant' or 'invscaling'
schedules. The default value is 0.0 as eta0 is not used by the
default schedule 'optimal'.
power_t : double
The exponent for inverse scaling learning rate [default 0.5].
class_weight : dict, {class_label: weight} or "auto" or None, optional
Preset for the class_weight fit parameter.
Weights associated with classes. If not given, all classes
are supposed to have weight one.
The "auto" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies.
warm_start : bool, optional
When set to True, reuse the solution of the previous call to fit as
initialization, otherwise, just erase the previous solution.
average : bool or int, optional
When set to True, computes the averaged SGD weights and stores the
result in the coef_ attribute. If set to an int greater than 1,
averaging will begin once the total number of samples seen reaches
average. So average=10 will begin averaging after seeing 10 samples.
Attributes
----------
coef_ : array, shape (1, n_features) if n_classes == 2 else (n_classes,\
n_features)
Weights assigned to the features.
intercept_ : array, shape (1,) if n_classes == 2 else (n_classes,)
Constants in decision function.
Examples
--------
>>> import numpy as np
>>> from sklearn import linear_model
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
>>> Y = np.array([1, 1, 2, 2])
>>> clf = linear_model.SGDClassifier()
>>> clf.fit(X, Y)
... #doctest: +NORMALIZE_WHITESPACE
SGDClassifier(alpha=0.0001, average=False, class_weight=None, epsilon=0.1,
eta0=0.0, fit_intercept=True, l1_ratio=0.15,
learning_rate='optimal', loss='hinge', n_iter=5, n_jobs=1,
penalty='l2', power_t=0.5, random_state=None, shuffle=False,
verbose=0, warm_start=False)
>>> print(clf.predict([[-0.8, -1]]))
[1]
See also
--------
LinearSVC, LogisticRegression, Perceptron
"""
def __init__(self, loss="hinge", penalty='l2', alpha=0.0001, l1_ratio=0.15,
fit_intercept=True, n_iter=5, shuffle=False, verbose=0,
epsilon=DEFAULT_EPSILON, n_jobs=1, random_state=None,
learning_rate="optimal", eta0=0.0, power_t=0.5,
class_weight=None, warm_start=False, average=False):
super(SGDClassifier, self).__init__(
loss=loss, penalty=penalty, alpha=alpha, l1_ratio=l1_ratio,
fit_intercept=fit_intercept, n_iter=n_iter, shuffle=shuffle,
verbose=verbose, epsilon=epsilon, n_jobs=n_jobs,
random_state=random_state, learning_rate=learning_rate, eta0=eta0,
power_t=power_t, class_weight=class_weight, warm_start=warm_start,
average=average)
def _check_proba(self):
if self.loss not in ("log", "modified_huber"):
raise AttributeError("probability estimates are not available for"
" loss=%r" % self.loss)
@property
def predict_proba(self):
"""Probability estimates.
This method is only available for log loss and modified Huber loss.
Multiclass probability estimates are derived from binary (one-vs.-rest)
estimates by simple normalization, as recommended by Zadrozny and
Elkan.
Binary probability estimates for loss="modified_huber" are given by
(clip(decision_function(X), -1, 1) + 1) / 2.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Returns
-------
array, 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_`.
References
----------
Zadrozny and Elkan, "Transforming classifier scores into multiclass
probability estimates", SIGKDD'02,
http://www.research.ibm.com/people/z/zadrozny/kdd2002-Transf.pdf
The justification for the formula in the loss="modified_huber"
case is in the appendix B in:
http://jmlr.csail.mit.edu/papers/volume2/zhang02c/zhang02c.pdf
"""
self._check_proba()
return self._predict_proba
def _predict_proba(self, X):
if self.loss == "log":
return self._predict_proba_lr(X)
elif self.loss == "modified_huber":
binary = (len(self.classes_) == 2)
scores = self.decision_function(X)
if binary:
prob2 = np.ones((scores.shape[0], 2))
prob = prob2[:, 1]
else:
prob = scores
np.clip(scores, -1, 1, prob)
prob += 1.
prob /= 2.
if binary:
prob2[:, 0] -= prob
prob = prob2
else:
# the above might assign zero to all classes, which doesn't
# normalize neatly; work around this to produce uniform
# probabilities
prob_sum = prob.sum(axis=1)
all_zero = (prob_sum == 0)
if np.any(all_zero):
prob[all_zero, :] = 1
prob_sum[all_zero] = len(self.classes_)
# normalize
prob /= prob_sum.reshape((prob.shape[0], -1))
return prob
else:
raise NotImplementedError("predict_(log_)proba only supported when"
" loss='log' or loss='modified_huber' "
"(%r given)" % self.loss)
@property
def predict_log_proba(self):
"""Log of probability estimates.
This method is only available for log loss and modified Huber loss.
When loss="modified_huber", probability estimates may be hard zeros
and ones, so taking the logarithm is not possible.
See ``predict_proba`` for details.
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_`.
"""
self._check_proba()
return self._predict_log_proba
def _predict_log_proba(self, X):
return np.log(self.predict_proba(X))
class BaseSGDRegressor(BaseSGD, RegressorMixin):
loss_functions = {
"squared_loss": (SquaredLoss, ),
"huber": (Huber, DEFAULT_EPSILON),
"epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
"squared_epsilon_insensitive": (SquaredEpsilonInsensitive,
DEFAULT_EPSILON),
}
@abstractmethod
def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001,
l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=False,
verbose=0, epsilon=DEFAULT_EPSILON, random_state=None,
learning_rate="invscaling", eta0=0.01, power_t=0.25,
warm_start=False, average=False):
super(BaseSGDRegressor, self).__init__(loss=loss, penalty=penalty,
alpha=alpha, l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
n_iter=n_iter, shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0, power_t=power_t,
warm_start=warm_start,
average=average)
def _partial_fit(self, X, y, alpha, C, loss, learning_rate,
n_iter, sample_weight,
coef_init, intercept_init):
X, y = check_X_y(X, y, "csr", copy=False, order='C', dtype=np.float64)
y = y.astype(np.float64)
n_samples, n_features = X.shape
self._validate_params()
# Allocate datastructures from input arguments
sample_weight = self._validate_sample_weight(sample_weight, n_samples)
if self.coef_ is None:
self._allocate_parameter_mem(1, n_features,
coef_init, intercept_init)
elif n_features != self.coef_.shape[-1]:
raise ValueError("Number of features %d does not match previous data %d."
% (n_features, self.coef_.shape[-1]))
if self.average > 0 and self.average_coef_ is None:
self.average_coef_ = np.zeros(n_features,
dtype=np.float64,
order="C")
self.average_intercept_ = np.zeros(1,
dtype=np.float64,
order="C")
self._fit_regressor(X, y, alpha, C, loss, learning_rate,
sample_weight, n_iter)
return self
def partial_fit(self, X, y, sample_weight=None):
"""Fit linear model with Stochastic Gradient Descent.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Subset of training data
y : numpy array of shape (n_samples,)
Subset of target values
sample_weight : array-like, shape (n_samples,), optional
Weights applied to individual samples.
If not provided, uniform weights are assumed.
Returns
-------
self : returns an instance of self.
"""
return self._partial_fit(X, y, self.alpha, C=1.0,
loss=self.loss,
learning_rate=self.learning_rate, n_iter=1,
sample_weight=sample_weight,
coef_init=None, intercept_init=None)
def _fit(self, X, y, alpha, C, loss, learning_rate, coef_init=None,
intercept_init=None, sample_weight=None):
if self.warm_start and self.coef_ is not None:
if coef_init is None:
coef_init = self.coef_
if intercept_init is None:
intercept_init = self.intercept_
else:
self.coef_ = None
self.intercept_ = None
if self.average > 0:
self.standard_intercept_ = self.intercept_
self.standard_coef_ = self.coef_
self.average_coef_ = None
self.average_intercept_ = None
# Clear iteration count for multiple call to fit.
self.t_ = None
return self._partial_fit(X, y, alpha, C, loss, learning_rate,
self.n_iter, sample_weight,
coef_init, intercept_init)
def fit(self, X, y, coef_init=None, intercept_init=None,
sample_weight=None):
"""Fit linear model with Stochastic Gradient Descent.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data
y : numpy array, shape (n_samples,)
Target values
coef_init : array, shape (n_features,)
The initial coefficients to warm-start the optimization.
intercept_init : array, shape (1,)
The initial intercept to warm-start the optimization.
sample_weight : array-like, shape (n_samples,), optional
Weights applied to individual samples (1. for unweighted).
Returns
-------
self : returns an instance of self.
"""
return self._fit(X, y, alpha=self.alpha, C=1.0,
loss=self.loss, learning_rate=self.learning_rate,
coef_init=coef_init,
intercept_init=intercept_init,
sample_weight=sample_weight)
def decision_function(self, X):
"""Predict using the linear model
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Returns
-------
array, shape (n_samples,)
Predicted target values per element in X.
"""
X = check_array(X, accept_sparse='csr')
scores = safe_sparse_dot(X, self.coef_.T,
dense_output=True) + self.intercept_
return scores.ravel()
def predict(self, X):
"""Predict using the linear model
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Returns
-------
array, shape (n_samples,)
Predicted target values per element in X.
"""
return self.decision_function(X)
def _fit_regressor(self, X, y, alpha, C, loss, learning_rate,
sample_weight, n_iter):
dataset, intercept_decay = _make_dataset(X, y, sample_weight)
loss_function = self._get_loss_function(loss)
penalty_type = self._get_penalty_type(self.penalty)
learning_rate_type = self._get_learning_rate_type(learning_rate)
if self.t_ is None:
self.t_ = 1.0
random_state = check_random_state(self.random_state)
# numpy mtrand expects a C long which is a signed 32 bit integer under
# Windows
seed = random_state.randint(0, np.iinfo(np.int32).max)
if self.average > 0:
self.standard_coef_, self.standard_intercept_, \
self.average_coef_, self.average_intercept_ =\
average_sgd(self.standard_coef_,
self.standard_intercept_[0],
self.average_coef_,
self.average_intercept_[0],
loss_function,
penalty_type,
alpha, C,
self.l1_ratio,
dataset,
n_iter,
int(self.fit_intercept),
int(self.verbose),
int(self.shuffle),
seed,
1.0, 1.0,
learning_rate_type,
self.eta0, self.power_t, self.t_,
intercept_decay, self.average)
self.average_intercept_ = np.atleast_1d(self.average_intercept_)
self.standard_intercept_ = np.atleast_1d(self.standard_intercept_)
self.t_ += n_iter * X.shape[0]
if self.average <= self.t_ - 1.0:
self.coef_ = self.average_coef_
self.intercept_ = self.average_intercept_
else:
self.coef_ = self.standard_coef_
self.intercept_ = self.standard_intercept_
else:
self.coef_, self.intercept_ = \
plain_sgd(self.coef_,
self.intercept_[0],
loss_function,
penalty_type,
alpha, C,
self.l1_ratio,
dataset,
n_iter,
int(self.fit_intercept),
int(self.verbose),
int(self.shuffle),
seed,
1.0, 1.0,
learning_rate_type,
self.eta0, self.power_t, self.t_,
intercept_decay)
self.t_ += n_iter * X.shape[0]
self.intercept_ = np.atleast_1d(self.intercept_)
class SGDRegressor(BaseSGDRegressor, _LearntSelectorMixin):
"""Linear model fitted by minimizing a regularized empirical loss with SGD
SGD stands for Stochastic Gradient Descent: the gradient of the loss is
estimated each sample at a time and the model is updated along the way with
a decreasing strength schedule (aka learning rate).
The regularizer is a penalty added to the loss function that shrinks model
parameters towards the zero vector using either the squared euclidean norm
L2 or the absolute norm L1 or a combination of both (Elastic Net). If the
parameter update crosses the 0.0 value because of the regularizer, the
update is truncated to 0.0 to allow for learning sparse models and achieve
online feature selection.
This implementation works with data represented as dense numpy arrays of
floating point values for the features.
Parameters
----------
loss : str, 'squared_loss', 'huber', 'epsilon_insensitive', \
or 'squared_epsilon_insensitive'
The loss function to be used. Defaults to 'squared_loss' which refers
to the ordinary least squares fit. 'huber' modifies 'squared_loss' to
focus less on getting outliers correct by switching from squared to
linear loss past a distance of epsilon. 'epsilon_insensitive' ignores
errors less than epsilon and is linear past that; this is the loss
function used in SVR. 'squared_epsilon_insensitive' is the same but
becomes squared loss past a tolerance of epsilon.
penalty : str, 'l2' or 'l1' or 'elasticnet'
The penalty (aka regularization term) to be used. Defaults to 'l2'
which is the standard regularizer for linear SVM models. 'l1' and
'elasticnet' might bring sparsity to the model (feature selection)
not achievable with 'l2'.
alpha : float
Constant that multiplies the regularization term. Defaults to 0.0001
l1_ratio : float
The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
Defaults to 0.15.
fit_intercept : bool
Whether the intercept should be estimated or not. If False, the
data is assumed to be already centered. Defaults to True.
n_iter : int, optional
The number of passes over the training data (aka epochs). The number
of iterations is set to 1 if using partial_fit.
Defaults to 5.
shuffle : bool, optional
Whether or not the training data should be shuffled after each epoch.
Defaults to False.
random_state : int seed, RandomState instance, or None (default)
The seed of the pseudo random number generator to use when
shuffling the data.
verbose : integer, optional
The verbosity level.
epsilon : float
Epsilon in the epsilon-insensitive loss functions; only if `loss` is
'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.
For 'huber', determines the threshold at which it becomes less
important to get the prediction exactly right.
For epsilon-insensitive, any differences between the current prediction
and the correct label are ignored if they are less than this threshold.
learning_rate : string, optional
The learning rate:
constant: eta = eta0
optimal: eta = 1.0/(alpha * t)
invscaling: eta = eta0 / pow(t, power_t) [default]
eta0 : double, optional
The initial learning rate [default 0.01].
power_t : double, optional
The exponent for inverse scaling learning rate [default 0.25].
warm_start : bool, optional
When set to True, reuse the solution of the previous call to fit as
initialization, otherwise, just erase the previous solution.
average : bool or int, optional
When set to True, computes the averaged SGD weights and stores the
result in the coef_ attribute. If set to an int greater than 1,
averaging will begin once the total number of samples seen reaches
average. So average=10 will begin averaging after seeing 10 samples.
Attributes
----------
coef_ : array, shape (n_features,)
Weights asigned to the features.
intercept_ : array, shape (1,)
The intercept term.
`average_coef_` : array, shape (n_features,)
Averaged weights assigned to the features.
`average_intercept_` : array, shape (1,)
The averaged intercept term.
Examples
--------
>>> import numpy as np
>>> from sklearn import linear_model
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = linear_model.SGDRegressor()
>>> clf.fit(X, y)
... #doctest: +NORMALIZE_WHITESPACE
SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.01,
fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',
loss='squared_loss', n_iter=5, penalty='l2', power_t=0.25,
random_state=None, shuffle=False, verbose=0, warm_start=False)
See also
--------
Ridge, ElasticNet, Lasso, SVR
"""
def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001,
l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=False,
verbose=0, epsilon=DEFAULT_EPSILON, random_state=None,
learning_rate="invscaling", eta0=0.01, power_t=0.25,
warm_start=False, average=False):
super(SGDRegressor, self).__init__(loss=loss, penalty=penalty,
alpha=alpha, l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
n_iter=n_iter, shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0, power_t=power_t,
warm_start=warm_start,
average=average)