# Authors: Peter Prettenhofer <peter.prettenhofer@gmail.com> (main author)
# Mathieu Blondel (partial_fit support)
#
# License: BSD 3 clause
"""Classification, regression and One-Class SVM using Stochastic Gradient
Descent (SGD).
"""
import warnings
from abc import ABCMeta, abstractmethod
from numbers import Integral, Real
import numpy as np
from ..base import (
BaseEstimator,
OutlierMixin,
RegressorMixin,
_fit_context,
clone,
is_classifier,
)
from ..exceptions import ConvergenceWarning
from ..model_selection import ShuffleSplit, StratifiedShuffleSplit
from ..utils import check_random_state, compute_class_weight, deprecated
from ..utils._param_validation import Hidden, Interval, StrOptions
from ..utils.extmath import safe_sparse_dot
from ..utils.metaestimators import available_if
from ..utils.multiclass import _check_partial_fit_first_call
from ..utils.parallel import Parallel, delayed
from ..utils.validation import _check_sample_weight, check_is_fitted
from ._base import LinearClassifierMixin, SparseCoefMixin, make_dataset
from ._sgd_fast import (
EpsilonInsensitive,
Hinge,
Huber,
Log,
ModifiedHuber,
SquaredEpsilonInsensitive,
SquaredHinge,
SquaredLoss,
_plain_sgd32,
_plain_sgd64,
)
LEARNING_RATE_TYPES = {
"constant": 1,
"optimal": 2,
"invscaling": 3,
"adaptive": 4,
"pa1": 5,
"pa2": 6,
}
PENALTY_TYPES = {"none": 0, "l2": 2, "l1": 1, "elasticnet": 3}
DEFAULT_EPSILON = 0.1
# Default value of ``epsilon`` parameter.
MAX_INT = np.iinfo(np.int32).max
class _ValidationScoreCallback:
"""Callback for early stopping based on validation score"""
def __init__(self, estimator, X_val, y_val, sample_weight_val, classes=None):
self.estimator = clone(estimator)
self.estimator.t_ = 1 # to pass check_is_fitted
if classes is not None:
self.estimator.classes_ = classes
self.X_val = X_val
self.y_val = y_val
self.sample_weight_val = sample_weight_val
def __call__(self, coef, intercept):
est = self.estimator
est.coef_ = coef.reshape(1, -1)
est.intercept_ = np.atleast_1d(intercept)
return est.score(self.X_val, self.y_val, self.sample_weight_val)
class BaseSGD(SparseCoefMixin, BaseEstimator, metaclass=ABCMeta):
"""Base class for SGD classification and regression."""
_parameter_constraints: dict = {
"fit_intercept": ["boolean"],
"max_iter": [Interval(Integral, 1, None, closed="left")],
"tol": [Interval(Real, 0, None, closed="left"), None],
"shuffle": ["boolean"],
"verbose": ["verbose"],
"random_state": ["random_state"],
"warm_start": ["boolean"],
"average": [Interval(Integral, 0, None, closed="left"), "boolean"],
}
def __init__(
self,
loss,
*,
penalty="l2",
alpha=0.0001,
C=1.0,
l1_ratio=0.15,
fit_intercept=True,
max_iter=1000,
tol=1e-3,
shuffle=True,
verbose=0,
epsilon=0.1,
random_state=None,
learning_rate="optimal",
eta0=0.0,
power_t=0.5,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=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.shuffle = shuffle
self.random_state = random_state
self.verbose = verbose
self.eta0 = eta0
self.power_t = power_t
self.early_stopping = early_stopping
self.validation_fraction = validation_fraction
self.n_iter_no_change = n_iter_no_change
self.warm_start = warm_start
self.average = average
self.max_iter = max_iter
self.tol = tol
@abstractmethod
def fit(self, X, y):
"""Fit model."""
def _more_validate_params(self, for_partial_fit=False):
"""Validate input params."""
if self.early_stopping and for_partial_fit:
raise ValueError("early_stopping should be False with partial_fit")
if (
self.learning_rate in ("constant", "invscaling", "adaptive")
and self.eta0 <= 0.0
):
raise ValueError("eta0 must be > 0")
if self.learning_rate == "optimal" and self.alpha == 0:
raise ValueError(
"alpha must be > 0 since "
"learning_rate is 'optimal'. alpha is used "
"to compute the optimal learning rate."
)
# raises ValueError if not registered
self._get_penalty_type(self.penalty)
self._get_learning_rate_type(self.learning_rate)
def _get_loss_function(self, loss):
"""Get concrete ``LossFunction`` object for str ``loss``."""
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)
def _get_learning_rate_type(self, learning_rate):
return LEARNING_RATE_TYPES[learning_rate]
def _get_penalty_type(self, penalty):
penalty = str(penalty).lower()
return PENALTY_TYPES[penalty]
def _allocate_parameter_mem(
self,
n_classes,
n_features,
input_dtype,
coef_init=None,
intercept_init=None,
one_class=0,
):
"""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, dtype=input_dtype, 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=input_dtype, order="C"
)
# allocate intercept_ for multi-class
if intercept_init is not None:
intercept_init = np.asarray(
intercept_init, order="C", dtype=input_dtype
)
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=input_dtype, order="C")
else:
# allocate coef_
if coef_init is not None:
coef_init = np.asarray(coef_init, dtype=input_dtype, 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=input_dtype, order="C")
# allocate intercept_
if intercept_init is not None:
intercept_init = np.asarray(intercept_init, dtype=input_dtype)
if intercept_init.shape != (1,) and intercept_init.shape != ():
raise ValueError("Provided intercept_init does not match dataset.")
if one_class:
self.offset_ = intercept_init.reshape(
1,
)
else:
self.intercept_ = intercept_init.reshape(
1,
)
else:
if one_class:
self.offset_ = np.zeros(1, dtype=input_dtype, order="C")
else:
self.intercept_ = np.zeros(1, dtype=input_dtype, order="C")
# initialize average parameters
if self.average > 0:
self._standard_coef = self.coef_
self._average_coef = np.zeros(
self.coef_.shape, dtype=input_dtype, order="C"
)
if one_class:
self._standard_intercept = 1 - self.offset_
else:
self._standard_intercept = self.intercept_
self._average_intercept = np.zeros(
self._standard_intercept.shape, dtype=input_dtype, order="C"
)
def _make_validation_split(self, y, sample_mask):
"""Split the dataset between training set and validation set.
Parameters
----------
y : ndarray of shape (n_samples, )
Target values.
sample_mask : ndarray of shape (n_samples, )
A boolean array indicating whether each sample should be included
for validation set.
Returns
-------
validation_mask : ndarray of shape (n_samples, )
Equal to True on the validation set, False on the training set.
"""
n_samples = y.shape[0]
validation_mask = np.zeros(n_samples, dtype=np.bool_)
if not self.early_stopping:
# use the full set for training, with an empty validation set
return validation_mask
if is_classifier(self):
splitter_type = StratifiedShuffleSplit
else:
splitter_type = ShuffleSplit
cv = splitter_type(
test_size=self.validation_fraction, random_state=self.random_state
)
idx_train, idx_val = next(cv.split(np.zeros(shape=(y.shape[0], 1)), y))
if not np.any(sample_mask[idx_val]):
raise ValueError(
"The sample weights for validation set are all zero, consider using a"
" different random state."
)
if idx_train.shape[0] == 0 or idx_val.shape[0] == 0:
raise ValueError(
"Splitting %d samples into a train set and a validation set "
"with validation_fraction=%r led to an empty set (%d and %d "
"samples). Please either change validation_fraction, increase "
"number of samples, or disable early_stopping."
% (
n_samples,
self.validation_fraction,
idx_train.shape[0],
idx_val.shape[0],
)
)
validation_mask[idx_val] = True
return validation_mask
def _make_validation_score_cb(
self, validation_mask, X, y, sample_weight, classes=None
):
if not self.early_stopping:
return None
return _ValidationScoreCallback(
self,
X[validation_mask],
y[validation_mask],
sample_weight[validation_mask],
classes=classes,
)
# TODO(1.6): Remove
# mypy error: Decorated property not supported
@deprecated( # type: ignore
"Attribute `loss_function_` was deprecated in version 1.4 and will be removed "
"in 1.6."
)
@property
def loss_function_(self):
return self._loss_function_
def _prepare_fit_binary(est, y, i, input_dtye):
"""Initialization for fit_binary.
Returns y, coef, intercept, average_coef, average_intercept.
"""
y_i = np.ones(y.shape, dtype=input_dtye, 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,
max_iter,
pos_weight,
neg_weight,
sample_weight,
validation_mask=None,
random_state=None,
):
"""Fit a single binary classifier.
The i'th class is considered the "positive" class.
Parameters
----------
est : Estimator object
The estimator to fit
i : int
Index of the positive class
X : numpy array or sparse matrix of shape [n_samples,n_features]
Training data
y : numpy array of shape [n_samples, ]
Target values
alpha : float
The regularization parameter
C : float
Maximum step size for passive aggressive
learning_rate : str
The learning rate. Accepted values are 'constant', 'optimal',
'invscaling', 'pa1' and 'pa2'.
max_iter : int
The maximum number of iterations (epochs)
pos_weight : float
The weight of the positive class
neg_weight : float
The weight of the negative class
sample_weight : numpy array of shape [n_samples, ]
The weight of each sample
validation_mask : numpy array of shape [n_samples, ], default=None
Precomputed validation mask in case _fit_binary is called in the
context of a one-vs-rest reduction.
random_state : int, RandomState instance, 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`.
"""
# 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, input_dtye=X.dtype
)
assert y_i.shape[0] == y.shape[0] == sample_weight.shape[0]
random_state = check_random_state(random_state)
dataset, intercept_decay = make_dataset(
X, y_i, sample_weight, random_state=random_state
)
penalty_type = est._get_penalty_type(est.penalty)
learning_rate_type = est._get_learning_rate_type(learning_rate)
if validation_mask is None:
validation_mask = est._make_validation_split(y_i, sample_mask=sample_weight > 0)
classes = np.array([-1, 1], dtype=y_i.dtype)
validation_score_cb = est._make_validation_score_cb(
validation_mask, X, y_i, sample_weight, classes=classes
)
# numpy mtrand expects a C long which is a signed 32 bit integer under
# Windows
seed = random_state.randint(MAX_INT)
tol = est.tol if est.tol is not None else -np.inf
_plain_sgd = _get_plain_sgd_function(input_dtype=coef.dtype)
coef, intercept, average_coef, average_intercept, n_iter_ = _plain_sgd(
coef,
intercept,
average_coef,
average_intercept,
est._loss_function_,
penalty_type,
alpha,
C,
est.l1_ratio,
dataset,
validation_mask,
est.early_stopping,
validation_score_cb,
int(est.n_iter_no_change),
max_iter,
tol,
int(est.fit_intercept),
int(est.verbose),
int(est.shuffle),
seed,
pos_weight,
neg_weight,
learning_rate_type,
est.eta0,
est.power_t,
0,
est.t_,
intercept_decay,
est.average,
)
if est.average:
if len(est.classes_) == 2:
est._average_intercept[0] = average_intercept
else:
est._average_intercept[i] = average_intercept
return coef, intercept, n_iter_
def _get_plain_sgd_function(input_dtype):
return _plain_sgd32 if input_dtype == np.float32 else _plain_sgd64
class BaseSGDClassifier(LinearClassifierMixin, BaseSGD, metaclass=ABCMeta):
loss_functions = {
"hinge": (Hinge, 1.0),
"squared_hinge": (SquaredHinge, 1.0),
"perceptron": (Hinge, 0.0),
"log_loss": (Log,),
"modified_huber": (ModifiedHuber,),
"squared_error": (SquaredLoss,),
"huber": (Huber, DEFAULT_EPSILON),
"epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
"squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON),
}
_parameter_constraints: dict = {
**BaseSGD._parameter_constraints,
"loss": [StrOptions(set(loss_functions))],
"early_stopping": ["boolean"],
"validation_fraction": [Interval(Real, 0, 1, closed="neither")],
"n_iter_no_change": [Interval(Integral, 1, None, closed="left")],
"n_jobs": [Integral, None],
"class_weight": [StrOptions({"balanced"}), dict, None],
}
@abstractmethod
def __init__(
self,
loss="hinge",
*,
penalty="l2",
alpha=0.0001,
l1_ratio=0.15,
fit_intercept=True,
max_iter=1000,
tol=1e-3,
shuffle=True,
verbose=0,
epsilon=DEFAULT_EPSILON,
n_jobs=None,
random_state=None,
learning_rate="optimal",
eta0=0.0,
power_t=0.5,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=5,
class_weight=None,
warm_start=False,
average=False,
):
super().__init__(
loss=loss,
penalty=penalty,
alpha=alpha,
l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
max_iter=max_iter,
tol=tol,
shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0,
power_t=power_t,
early_stopping=early_stopping,
validation_fraction=validation_fraction,
n_iter_no_change=n_iter_no_change,
warm_start=warm_start,
average=average,
)
self.class_weight = class_weight
self.n_jobs = n_jobs
def _partial_fit(
self,
X,
y,
alpha,
C,
loss,
learning_rate,
max_iter,
classes,
sample_weight,
coef_init,
intercept_init,
):
first_call = not hasattr(self, "classes_")
X, y = self._validate_data(
X,
y,
accept_sparse="csr",
dtype=[np.float64, np.float32],
order="C",
accept_large_sparse=False,
reset=first_call,
)
if first_call:
# TODO(1.7) remove 0 from average parameter constraint
if not isinstance(self.average, (bool, np.bool_)) and self.average == 0:
warnings.warn(
(
"Passing average=0 to disable averaging is deprecated and will"
" be removed in 1.7. Please use average=False instead."
),
FutureWarning,
)
n_samples, n_features = X.shape
_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, classes=self.classes_, y=y
)
sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
if getattr(self, "coef_", None) is None or coef_init is not None:
self._allocate_parameter_mem(
n_classes=n_classes,
n_features=n_features,
input_dtype=X.dtype,
coef_init=coef_init,
intercept_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 not hasattr(self, "t_"):
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,
max_iter=max_iter,
)
elif n_classes == 2:
self._fit_binary(
X,
y,
alpha=alpha,
C=C,
learning_rate=learning_rate,
sample_weight=sample_weight,
max_iter=max_iter,
)
else:
raise ValueError(
"The number of classes has to be greater than one; got %d class"
% n_classes
)
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_"):
# delete the attribute otherwise _partial_fit thinks it's not the first call
delattr(self, "classes_")
# TODO(1.7) remove 0 from average parameter constraint
if not isinstance(self.average, (bool, np.bool_)) and self.average == 0:
warnings.warn(
(
"Passing average=0 to disable averaging is deprecated and will be "
"removed in 1.7. Please use average=False instead."
),
FutureWarning,
)
# labels can be encoded as float, int, or string literals
# np.unique sorts in asc order; largest class id is positive class
y = self._validate_data(y=y)
classes = np.unique(y)
if self.warm_start and hasattr(self, "coef_"):
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_ = 1.0
self._partial_fit(
X,
y,
alpha,
C,
loss,
learning_rate,
self.max_iter,
classes,
sample_weight,
coef_init,
intercept_init,
)
if (
self.tol is not None
and self.tol > -np.inf
and self.n_iter_ == self.max_iter
):
warnings.warn(
(
"Maximum number of iteration reached before "
"convergence. Consider increasing max_iter to "
"improve the fit."
),
ConvergenceWarning,
)
return self
def _fit_binary(self, X, y, alpha, C, sample_weight, learning_rate, max_iter):
"""Fit a binary classifier on X and y."""
coef, intercept, n_iter_ = fit_binary(
self,
1,
X,
y,
alpha,
C,
learning_rate,
max_iter,
self._expanded_class_weight[1],
self._expanded_class_weight[0],
sample_weight,
random_state=self.random_state,
)
self.t_ += n_iter_ * X.shape[0]
self.n_iter_ = n_iter_
# 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, max_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) or OvR (One versus Rest).
"""
# Precompute the validation split using the multiclass labels
# to ensure proper balancing of the classes.
validation_mask = self._make_validation_split(y, sample_mask=sample_weight > 0)
# Use joblib to fit OvA in parallel.
# Pick the random seed for each job outside of fit_binary to avoid
# sharing the estimator random state between threads which could lead
# to non-deterministic behavior
random_state = check_random_state(self.random_state)
seeds = random_state.randint(MAX_INT, size=len(self.classes_))
result = Parallel(
n_jobs=self.n_jobs, verbose=self.verbose, require="sharedmem"
)(
delayed(fit_binary)(
self,
i,
X,
y,
alpha,
C,
learning_rate,
max_iter,
self._expanded_class_weight[i],
1.0,
sample_weight,
validation_mask=validation_mask,
random_state=seed,
)
for i, seed in enumerate(seeds)
)
# take the maximum of n_iter_ over every binary fit
n_iter_ = 0.0
for i, (_, intercept, n_iter_i) in enumerate(result):
self.intercept_[i] = intercept
n_iter_ = max(n_iter_, n_iter_i)
self.t_ += n_iter_ * X.shape[0]
self.n_iter_ = n_iter_
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(self.intercept_)
self.intercept_ = self._standard_intercept
@_fit_context(prefer_skip_nested_validation=True)
def partial_fit(self, X, y, classes=None, sample_weight=None):
"""Perform one epoch of stochastic gradient descent on given samples.
Internally, this method uses ``max_iter = 1``. Therefore, it is not
guaranteed that a minimum of the cost function is reached after calling
it once. Matters such as objective convergence, early stopping, and
learning rate adjustments should be handled by the user.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Subset of the training data.
y : ndarray of shape (n_samples,)
Subset of the target values.
classes : ndarray of shape (n_classes,), default=None
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,), default=None
Weights applied to individual samples.
If not provided, uniform weights are assumed.
Returns
-------
self : object
Returns an instance of self.
"""
if not hasattr(self, "classes_"):
self._more_validate_params(for_partial_fit=True)
if self.class_weight == "balanced":
raise ValueError(
"class_weight '{0}' is not supported for "
"partial_fit. In order to use 'balanced' weights,"
" use compute_class_weight('{0}', "
"classes=classes, y=y). "
"In place of y you can use 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.".format(self.class_weight)
)
return self._partial_fit(
X,
y,
alpha=self.alpha,
C=1.0,
loss=self.loss,
learning_rate=self.learning_rate,
max_iter=1,
classes=classes,
sample_weight=sample_weight,
coef_init=None,
intercept_init=None,
)
@_fit_context(prefer_skip_nested_validation=True)
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 : ndarray of shape (n_samples,)
Target values.
coef_init : ndarray of shape (n_classes, n_features), default=None
The initial coefficients to warm-start the optimization.
intercept_init : ndarray of shape (n_classes,), default=None
The initial intercept to warm-start the optimization.
sample_weight : array-like, shape (n_samples,), default=None
Weights applied to individual samples.
If not provided, uniform weights are assumed. These weights will
be multiplied with class_weight (passed through the
constructor) if class_weight is specified.
Returns
-------
self : object
Returns an instance of self.
"""
self._more_validate_params()
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):
"""Linear classifiers (SVM, logistic regression, etc.) 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 via the `partial_fit` method.
For best results using the default learning rate schedule, the data should
have zero mean and unit variance.
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.
Read more in the :ref:`User Guide <sgd>`.
Parameters
----------
loss : {'hinge', 'log_loss', 'modified_huber', 'squared_hinge',\
'perceptron', 'squared_error', 'huber', 'epsilon_insensitive',\
'squared_epsilon_insensitive'}, default='hinge'
The loss function to be used.
- 'hinge' gives a linear SVM.
- '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, 'squared_error', 'huber', 'epsilon_insensitive' and
'squared_epsilon_insensitive' are designed for regression but can be useful
in classification as well; see
:class:`~sklearn.linear_model.SGDRegressor` for a description.
More details about the losses formulas can be found in the
:ref:`User Guide <sgd_mathematical_formulation>`.
penalty : {'l2', 'l1', 'elasticnet', None}, default='l2'
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'. No penalty is added when set to `None`.
alpha : float, default=0.0001
Constant that multiplies the regularization term. The higher the
value, the stronger the regularization. Also used to compute the
learning rate when `learning_rate` is set to 'optimal'.
Values must be in the range `[0.0, inf)`.
l1_ratio : float, default=0.15
The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
Only used if `penalty` is 'elasticnet'.
Values must be in the range `[0.0, 1.0]`.
fit_intercept : bool, default=True
Whether the intercept should be estimated or not. If False, the
data is assumed to be already centered.
max_iter : int, default=1000
The maximum number of passes over the training data (aka epochs).
It only impacts the behavior in the ``fit`` method, and not the
:meth:`partial_fit` method.
Values must be in the range `[1, inf)`.
.. versionadded:: 0.19
tol : float or None, default=1e-3
The stopping criterion. If it is not None, training will stop
when (loss > best_loss - tol) for ``n_iter_no_change`` consecutive
epochs.
Convergence is checked against the training loss or the
validation loss depending on the `early_stopping` parameter.
Values must be in the range `[0.0, inf)`.
.. versionadded:: 0.19
shuffle : bool, default=True
Whether or not the training data should be shuffled after each epoch.
verbose : int, default=0
The verbosity level.
Values must be in the range `[0, inf)`.
epsilon : float, default=0.1
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.
Values must be in the range `[0.0, inf)`.
n_jobs : int, default=None
The number of CPUs to use to do the OVA (One Versus All, for
multi-class problems) computation.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
random_state : int, RandomState instance, default=None
Used for shuffling the data, when ``shuffle`` is set to ``True``.
Pass an int for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
Integer values must be in the range `[0, 2**32 - 1]`.
learning_rate : str, default='optimal'
The learning rate schedule:
- 'constant': `eta = eta0`
- 'optimal': `eta = 1.0 / (alpha * (t + t0))`
where `t0` is chosen by a heuristic proposed by Leon Bottou.
- 'invscaling': `eta = eta0 / pow(t, power_t)`
- 'adaptive': `eta = eta0`, as long as the training keeps decreasing.
Each time n_iter_no_change consecutive epochs fail to decrease the
training loss by tol or fail to increase validation score by tol if
`early_stopping` is `True`, the current learning rate is divided by 5.
.. versionadded:: 0.20
Added 'adaptive' option
eta0 : float, default=0.0
The initial learning rate for the 'constant', 'invscaling' or
'adaptive' schedules. The default value is 0.0 as eta0 is not used by
the default schedule 'optimal'.
Values must be in the range `[0.0, inf)`.
power_t : float, default=0.5
The exponent for inverse scaling learning rate.
Values must be in the range `(-inf, inf)`.
early_stopping : bool, default=False
Whether to use early stopping to terminate training when validation
score is not improving. If set to `True`, it will automatically set aside
a stratified fraction of training data as validation and terminate
training when validation score returned by the `score` method is not
improving by at least tol for n_iter_no_change consecutive epochs.
.. versionadded:: 0.20
Added 'early_stopping' option
validation_fraction : float, default=0.1
The proportion of training data to set aside as validation set for
early stopping. Must be between 0 and 1.
Only used if `early_stopping` is True.
Values must be in the range `(0.0, 1.0)`.
.. versionadded:: 0.20
Added 'validation_fraction' option
n_iter_no_change : int, default=5
Number of iterations with no improvement to wait before stopping
fitting.
Convergence is checked against the training loss or the
validation loss depending on the `early_stopping` parameter.
Integer values must be in the range `[1, max_iter)`.
.. versionadded:: 0.20
Added 'n_iter_no_change' option
class_weight : dict, {class_label: weight} or "balanced", default=None
Preset for the class_weight fit parameter.
Weights associated with classes. 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))``.
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.
See :term:`the Glossary <warm_start>`.
Repeatedly calling fit or partial_fit when warm_start is True can
result in a different solution than when calling fit a single time
because of the way the data is shuffled.
If a dynamic learning rate is used, the learning rate is adapted
depending on the number of samples already seen. Calling ``fit`` resets
this counter, while ``partial_fit`` will result in increasing the
existing counter.
average : bool or int, default=False
When set to `True`, computes the averaged SGD weights across all
updates 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.
Integer values must be in the range `[1, n_samples]`.
Attributes
----------
coef_ : ndarray of shape (1, n_features) if n_classes == 2 else \
(n_classes, n_features)
Weights assigned to the features.
intercept_ : ndarray of shape (1,) if n_classes == 2 else (n_classes,)
Constants in decision function.
n_iter_ : int
The actual number of iterations before reaching the stopping criterion.
For multiclass fits, it is the maximum over every binary fit.
loss_function_ : concrete ``LossFunction``
.. deprecated:: 1.4
Attribute `loss_function_` was deprecated in version 1.4 and will be
removed in 1.6.
classes_ : array of shape (n_classes,)
t_ : int
Number of weight updates performed during training.
Same as ``(n_iter_ * n_samples + 1)``.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
sklearn.svm.LinearSVC : Linear support vector classification.
LogisticRegression : Logistic regression.
Perceptron : Inherits from SGDClassifier. ``Perceptron()`` is equivalent to
``SGDClassifier(loss="perceptron", eta0=1, learning_rate="constant",
penalty=None)``.
Examples
--------
>>> import numpy as np
>>> from sklearn.linear_model import SGDClassifier
>>> from sklearn.preprocessing import StandardScaler
>>> from sklearn.pipeline import make_pipeline
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
>>> Y = np.array([1, 1, 2, 2])
>>> # Always scale the input. The most convenient way is to use a pipeline.
>>> clf = make_pipeline(StandardScaler(),
... SGDClassifier(max_iter=1000, tol=1e-3))
>>> clf.fit(X, Y)
Pipeline(steps=[('standardscaler', StandardScaler()),
('sgdclassifier', SGDClassifier())])
>>> print(clf.predict([[-0.8, -1]]))
[1]
"""
_parameter_constraints: dict = {
**BaseSGDClassifier._parameter_constraints,
"penalty": [StrOptions({"l2", "l1", "elasticnet"}), None],
"alpha": [Interval(Real, 0, None, closed="left")],
"l1_ratio": [Interval(Real, 0, 1, closed="both")],
"power_t": [Interval(Real, None, None, closed="neither")],
"epsilon": [Interval(Real, 0, None, closed="left")],
"learning_rate": [
StrOptions({"constant", "optimal", "invscaling", "adaptive"}),
Hidden(StrOptions({"pa1", "pa2"})),
],
"eta0": [Interval(Real, 0, None, closed="left")],
}
def __init__(
self,
loss="hinge",
*,
penalty="l2",
alpha=0.0001,
l1_ratio=0.15,
fit_intercept=True,
max_iter=1000,
tol=1e-3,
shuffle=True,
verbose=0,
epsilon=DEFAULT_EPSILON,
n_jobs=None,
random_state=None,
learning_rate="optimal",
eta0=0.0,
power_t=0.5,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=5,
class_weight=None,
warm_start=False,
average=False,
):
super().__init__(
loss=loss,
penalty=penalty,
alpha=alpha,
l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
max_iter=max_iter,
tol=tol,
shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
n_jobs=n_jobs,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0,
power_t=power_t,
early_stopping=early_stopping,
validation_fraction=validation_fraction,
n_iter_no_change=n_iter_no_change,
class_weight=class_weight,
warm_start=warm_start,
average=average,
)
def _check_proba(self):
if self.loss not in ("log_loss", "modified_huber"):
raise AttributeError(
"probability estimates are not available for loss=%r" % self.loss
)
return True
@available_if(_check_proba)
def predict_proba(self, X):
"""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. For other loss functions
it is necessary to perform proper probability calibration by wrapping
the classifier with
:class:`~sklearn.calibration.CalibratedClassifierCV` instead.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Input data for prediction.
Returns
-------
ndarray of 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,
https://dl.acm.org/doi/pdf/10.1145/775047.775151
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
"""
check_is_fitted(self)
if self.loss == "log_loss":
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 += 1.0
prob /= 2.0
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_loss' or loss='modified_huber' "
"(%r given)" % self.loss
)
@available_if(_check_proba)
def predict_log_proba(self, X):
"""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, sparse matrix} of shape (n_samples, n_features)
Input data for prediction.
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))
def _more_tags(self):
return {
"_xfail_checks": {
"check_sample_weights_invariance": (
"zero sample_weight is not equivalent to removing samples"
),
},
"preserves_dtype": [np.float64, np.float32],
}
class BaseSGDRegressor(RegressorMixin, BaseSGD):
loss_functions = {
"squared_error": (SquaredLoss,),
"huber": (Huber, DEFAULT_EPSILON),
"epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON),
"squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON),
}
_parameter_constraints: dict = {
**BaseSGD._parameter_constraints,
"loss": [StrOptions(set(loss_functions))],
"early_stopping": ["boolean"],
"validation_fraction": [Interval(Real, 0, 1, closed="neither")],
"n_iter_no_change": [Interval(Integral, 1, None, closed="left")],
}
@abstractmethod
def __init__(
self,
loss="squared_error",
*,
penalty="l2",
alpha=0.0001,
l1_ratio=0.15,
fit_intercept=True,
max_iter=1000,
tol=1e-3,
shuffle=True,
verbose=0,
epsilon=DEFAULT_EPSILON,
random_state=None,
learning_rate="invscaling",
eta0=0.01,
power_t=0.25,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=5,
warm_start=False,
average=False,
):
super().__init__(
loss=loss,
penalty=penalty,
alpha=alpha,
l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
max_iter=max_iter,
tol=tol,
shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0,
power_t=power_t,
early_stopping=early_stopping,
validation_fraction=validation_fraction,
n_iter_no_change=n_iter_no_change,
warm_start=warm_start,
average=average,
)
def _partial_fit(
self,
X,
y,
alpha,
C,
loss,
learning_rate,
max_iter,
sample_weight,
coef_init,
intercept_init,
):
first_call = getattr(self, "coef_", None) is None
X, y = self._validate_data(
X,
y,
accept_sparse="csr",
copy=False,
order="C",
dtype=[np.float64, np.float32],
accept_large_sparse=False,
reset=first_call,
)
y = y.astype(X.dtype, copy=False)
if first_call:
# TODO(1.7) remove 0 from average parameter constraint
if not isinstance(self.average, (bool, np.bool_)) and self.average == 0:
warnings.warn(
(
"Passing average=0 to disable averaging is deprecated and will"
" be removed in 1.7. Please use average=False instead."
),
FutureWarning,
)
n_samples, n_features = X.shape
sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
# Allocate datastructures from input arguments
if first_call:
self._allocate_parameter_mem(
n_classes=1,
n_features=n_features,
input_dtype=X.dtype,
coef_init=coef_init,
intercept_init=intercept_init,
)
if self.average > 0 and getattr(self, "_average_coef", None) is None:
self._average_coef = np.zeros(n_features, dtype=X.dtype, order="C")
self._average_intercept = np.zeros(1, dtype=X.dtype, order="C")
self._fit_regressor(
X, y, alpha, C, loss, learning_rate, sample_weight, max_iter
)
return self
@_fit_context(prefer_skip_nested_validation=True)
def partial_fit(self, X, y, sample_weight=None):
"""Perform one epoch of stochastic gradient descent on given samples.
Internally, this method uses ``max_iter = 1``. Therefore, it is not
guaranteed that a minimum of the cost function is reached after calling
it once. Matters such as objective convergence and early stopping
should be handled by the user.
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,), default=None
Weights applied to individual samples.
If not provided, uniform weights are assumed.
Returns
-------
self : object
Returns an instance of self.
"""
if not hasattr(self, "coef_"):
self._more_validate_params(for_partial_fit=True)
return self._partial_fit(
X,
y,
self.alpha,
C=1.0,
loss=self.loss,
learning_rate=self.learning_rate,
max_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,
):
# TODO(1.7) remove 0 from average parameter constraint
if not isinstance(self.average, (bool, np.bool_)) and self.average == 0:
warnings.warn(
(
"Passing average=0 to disable averaging is deprecated and will be "
"removed in 1.7. Please use average=False instead."
),
FutureWarning,
)
if self.warm_start and getattr(self, "coef_", None) 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
# Clear iteration count for multiple call to fit.
self.t_ = 1.0
self._partial_fit(
X,
y,
alpha,
C,
loss,
learning_rate,
self.max_iter,
sample_weight,
coef_init,
intercept_init,
)
if (
self.tol is not None
and self.tol > -np.inf
and self.n_iter_ == self.max_iter
):
warnings.warn(
(
"Maximum number of iteration reached before "
"convergence. Consider increasing max_iter to "
"improve the fit."
),
ConvergenceWarning,
)
return self
@_fit_context(prefer_skip_nested_validation=True)
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 : ndarray of shape (n_samples,)
Target values.
coef_init : ndarray of shape (n_features,), default=None
The initial coefficients to warm-start the optimization.
intercept_init : ndarray of shape (1,), default=None
The initial intercept to warm-start the optimization.
sample_weight : array-like, shape (n_samples,), default=None
Weights applied to individual samples (1. for unweighted).
Returns
-------
self : object
Fitted `SGDRegressor` estimator.
"""
self._more_validate_params()
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
-------
ndarray of shape (n_samples,)
Predicted target values per element in X.
"""
check_is_fitted(self)
X = self._validate_data(X, accept_sparse="csr", reset=False)
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)
Input data.
Returns
-------
ndarray of 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, max_iter
):
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 not hasattr(self, "t_"):
self.t_ = 1.0
validation_mask = self._make_validation_split(y, sample_mask=sample_weight > 0)
validation_score_cb = self._make_validation_score_cb(
validation_mask, X, y, sample_weight
)
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, MAX_INT)
dataset, intercept_decay = make_dataset(
X, y, sample_weight, random_state=random_state
)
tol = self.tol if self.tol is not None else -np.inf
if self.average:
coef = self._standard_coef
intercept = self._standard_intercept
average_coef = self._average_coef
average_intercept = self._average_intercept
else:
coef = self.coef_
intercept = self.intercept_
average_coef = None # Not used
average_intercept = [0] # Not used
_plain_sgd = _get_plain_sgd_function(input_dtype=coef.dtype)
coef, intercept, average_coef, average_intercept, self.n_iter_ = _plain_sgd(
coef,
intercept[0],
average_coef,
average_intercept[0],
loss_function,
penalty_type,
alpha,
C,
self.l1_ratio,
dataset,
validation_mask,
self.early_stopping,
validation_score_cb,
int(self.n_iter_no_change),
max_iter,
tol,
int(self.fit_intercept),
int(self.verbose),
int(self.shuffle),
seed,
1.0,
1.0,
learning_rate_type,
self.eta0,
self.power_t,
0,
self.t_,
intercept_decay,
self.average,
)
self.t_ += self.n_iter_ * X.shape[0]
if self.average > 0:
self._average_intercept = np.atleast_1d(average_intercept)
self._standard_intercept = np.atleast_1d(intercept)
if self.average <= self.t_ - 1.0:
# made enough updates for averaging to be taken into account
self.coef_ = average_coef
self.intercept_ = np.atleast_1d(average_intercept)
else:
self.coef_ = coef
self.intercept_ = np.atleast_1d(intercept)
else:
self.intercept_ = np.atleast_1d(intercept)
class SGDRegressor(BaseSGDRegressor):
"""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.
Read more in the :ref:`User Guide <sgd>`.
Parameters
----------
loss : str, default='squared_error'
The loss function to be used. The possible values are 'squared_error',
'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'
The 'squared_error' refers to the ordinary least squares fit.
'huber' modifies 'squared_error' 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.
More details about the losses formulas can be found in the
:ref:`User Guide <sgd_mathematical_formulation>`.
penalty : {'l2', 'l1', 'elasticnet', None}, default='l2'
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'. No penalty is added when set to `None`.
alpha : float, default=0.0001
Constant that multiplies the regularization term. The higher the
value, the stronger the regularization. Also used to compute the
learning rate when `learning_rate` is set to 'optimal'.
Values must be in the range `[0.0, inf)`.
l1_ratio : float, default=0.15
The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.
l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.
Only used if `penalty` is 'elasticnet'.
Values must be in the range `[0.0, 1.0]`.
fit_intercept : bool, default=True
Whether the intercept should be estimated or not. If False, the
data is assumed to be already centered.
max_iter : int, default=1000
The maximum number of passes over the training data (aka epochs).
It only impacts the behavior in the ``fit`` method, and not the
:meth:`partial_fit` method.
Values must be in the range `[1, inf)`.
.. versionadded:: 0.19
tol : float or None, default=1e-3
The stopping criterion. If it is not None, training will stop
when (loss > best_loss - tol) for ``n_iter_no_change`` consecutive
epochs.
Convergence is checked against the training loss or the
validation loss depending on the `early_stopping` parameter.
Values must be in the range `[0.0, inf)`.
.. versionadded:: 0.19
shuffle : bool, default=True
Whether or not the training data should be shuffled after each epoch.
verbose : int, default=0
The verbosity level.
Values must be in the range `[0, inf)`.
epsilon : float, default=0.1
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.
Values must be in the range `[0.0, inf)`.
random_state : int, RandomState instance, default=None
Used for shuffling the data, when ``shuffle`` is set to ``True``.
Pass an int for reproducible output across multiple function calls.
See :term:`Glossary <random_state>`.
learning_rate : str, default='invscaling'
The learning rate schedule:
- 'constant': `eta = eta0`
- 'optimal': `eta = 1.0 / (alpha * (t + t0))`
where t0 is chosen by a heuristic proposed by Leon Bottou.
- 'invscaling': `eta = eta0 / pow(t, power_t)`
- 'adaptive': eta = eta0, as long as the training keeps decreasing.
Each time n_iter_no_change consecutive epochs fail to decrease the
training loss by tol or fail to increase validation score by tol if
early_stopping is True, the current learning rate is divided by 5.
.. versionadded:: 0.20
Added 'adaptive' option
eta0 : float, default=0.01
The initial learning rate for the 'constant', 'invscaling' or
'adaptive' schedules. The default value is 0.01.
Values must be in the range `[0.0, inf)`.
power_t : float, default=0.25
The exponent for inverse scaling learning rate.
Values must be in the range `(-inf, inf)`.
early_stopping : bool, default=False
Whether to use early stopping to terminate training when validation
score is not improving. If set to True, it will automatically set aside
a fraction of training data as validation and terminate
training when validation score returned by the `score` method is not
improving by at least `tol` for `n_iter_no_change` consecutive
epochs.
.. versionadded:: 0.20
Added 'early_stopping' option
validation_fraction : float, default=0.1
The proportion of training data to set aside as validation set for
early stopping. Must be between 0 and 1.
Only used if `early_stopping` is True.
Values must be in the range `(0.0, 1.0)`.
.. versionadded:: 0.20
Added 'validation_fraction' option
n_iter_no_change : int, default=5
Number of iterations with no improvement to wait before stopping
fitting.
Convergence is checked against the training loss or the
validation loss depending on the `early_stopping` parameter.
Integer values must be in the range `[1, max_iter)`.
.. versionadded:: 0.20
Added 'n_iter_no_change' option
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.
See :term:`the Glossary <warm_start>`.
Repeatedly calling fit or partial_fit when warm_start is True can
result in a different solution than when calling fit a single time
because of the way the data is shuffled.
If a dynamic learning rate is used, the learning rate is adapted
depending on the number of samples already seen. Calling ``fit`` resets
this counter, while ``partial_fit`` will result in increasing the
existing counter.
average : bool or int, default=False
When set to True, computes the averaged SGD weights across all
updates 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_ : ndarray of shape (n_features,)
Weights assigned to the features.
intercept_ : ndarray of shape (1,)
The intercept term.
n_iter_ : int
The actual number of iterations before reaching the stopping criterion.
t_ : int
Number of weight updates performed during training.
Same as ``(n_iter_ * n_samples + 1)``.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
HuberRegressor : Linear regression model that is robust to outliers.
Lars : Least Angle Regression model.
Lasso : Linear Model trained with L1 prior as regularizer.
RANSACRegressor : RANSAC (RANdom SAmple Consensus) algorithm.
Ridge : Linear least squares with l2 regularization.
sklearn.svm.SVR : Epsilon-Support Vector Regression.
TheilSenRegressor : Theil-Sen Estimator robust multivariate regression model.
Examples
--------
>>> import numpy as np
>>> from sklearn.linear_model import SGDRegressor
>>> from sklearn.pipeline import make_pipeline
>>> from sklearn.preprocessing import StandardScaler
>>> n_samples, n_features = 10, 5
>>> rng = np.random.RandomState(0)
>>> y = rng.randn(n_samples)
>>> X = rng.randn(n_samples, n_features)
>>> # Always scale the input. The most convenient way is to use a pipeline.
>>> reg = make_pipeline(StandardScaler(),
... SGDRegressor(max_iter=1000, tol=1e-3))
>>> reg.fit(X, y)
Pipeline(steps=[('standardscaler', StandardScaler()),
('sgdregressor', SGDRegressor())])
"""
_parameter_constraints: dict = {
**BaseSGDRegressor._parameter_constraints,
"penalty": [StrOptions({"l2", "l1", "elasticnet"}), None],
"alpha": [Interval(Real, 0, None, closed="left")],
"l1_ratio": [Interval(Real, 0, 1, closed="both")],
"power_t": [Interval(Real, None, None, closed="neither")],
"learning_rate": [
StrOptions({"constant", "optimal", "invscaling", "adaptive"}),
Hidden(StrOptions({"pa1", "pa2"})),
],
"epsilon": [Interval(Real, 0, None, closed="left")],
"eta0": [Interval(Real, 0, None, closed="left")],
}
def __init__(
self,
loss="squared_error",
*,
penalty="l2",
alpha=0.0001,
l1_ratio=0.15,
fit_intercept=True,
max_iter=1000,
tol=1e-3,
shuffle=True,
verbose=0,
epsilon=DEFAULT_EPSILON,
random_state=None,
learning_rate="invscaling",
eta0=0.01,
power_t=0.25,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=5,
warm_start=False,
average=False,
):
super().__init__(
loss=loss,
penalty=penalty,
alpha=alpha,
l1_ratio=l1_ratio,
fit_intercept=fit_intercept,
max_iter=max_iter,
tol=tol,
shuffle=shuffle,
verbose=verbose,
epsilon=epsilon,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0,
power_t=power_t,
early_stopping=early_stopping,
validation_fraction=validation_fraction,
n_iter_no_change=n_iter_no_change,
warm_start=warm_start,
average=average,
)
def _more_tags(self):
return {
"_xfail_checks": {
"check_sample_weights_invariance": (
"zero sample_weight is not equivalent to removing samples"
),
},
"preserves_dtype": [np.float64, np.float32],
}
class SGDOneClassSVM(BaseSGD, OutlierMixin):
"""Solves linear One-Class SVM using Stochastic Gradient Descent.
This implementation is meant to be used with a kernel approximation
technique (e.g. `sklearn.kernel_approximation.Nystroem`) to obtain results
similar to `sklearn.svm.OneClassSVM` which uses a Gaussian kernel by
default.
Read more in the :ref:`User Guide <sgd_online_one_class_svm>`.
.. versionadded:: 1.0
Parameters
----------
nu : float, default=0.5
The nu parameter of the One Class SVM: an upper bound on the
fraction of training errors and a lower bound of the fraction of
support vectors. Should be in the interval (0, 1]. By default 0.5
will be taken.
fit_intercept : bool, default=True
Whether the intercept should be estimated or not. Defaults to True.
max_iter : int, default=1000
The maximum number of passes over the training data (aka epochs).
It only impacts the behavior in the ``fit`` method, and not the
`partial_fit`. Defaults to 1000.
Values must be in the range `[1, inf)`.
tol : float or None, default=1e-3
The stopping criterion. If it is not None, the iterations will stop
when (loss > previous_loss - tol). Defaults to 1e-3.
Values must be in the range `[0.0, inf)`.
shuffle : bool, default=True
Whether or not the training data should be shuffled after each epoch.
Defaults to True.
verbose : int, default=0
The verbosity level.
random_state : int, RandomState instance or None, 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`.
learning_rate : {'constant', 'optimal', 'invscaling', 'adaptive'}, default='optimal'
The learning rate schedule to use with `fit`. (If using `partial_fit`,
learning rate must be controlled directly).
- 'constant': `eta = eta0`
- 'optimal': `eta = 1.0 / (alpha * (t + t0))`
where t0 is chosen by a heuristic proposed by Leon Bottou.
- 'invscaling': `eta = eta0 / pow(t, power_t)`
- 'adaptive': eta = eta0, as long as the training keeps decreasing.
Each time n_iter_no_change consecutive epochs fail to decrease the
training loss by tol or fail to increase validation score by tol if
early_stopping is True, the current learning rate is divided by 5.
eta0 : float, default=0.0
The initial learning rate for the 'constant', 'invscaling' or
'adaptive' schedules. The default value is 0.0 as eta0 is not used by
the default schedule 'optimal'.
Values must be in the range `[0.0, inf)`.
power_t : float, default=0.5
The exponent for inverse scaling learning rate.
Values must be in the range `(-inf, inf)`.
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.
See :term:`the Glossary <warm_start>`.
Repeatedly calling fit or partial_fit when warm_start is True can
result in a different solution than when calling fit a single time
because of the way the data is shuffled.
If a dynamic learning rate is used, the learning rate is adapted
depending on the number of samples already seen. Calling ``fit`` resets
this counter, while ``partial_fit`` will result in increasing the
existing counter.
average : bool or int, default=False
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_ : ndarray of shape (1, n_features)
Weights assigned to the features.
offset_ : ndarray of shape (1,)
Offset used to define the decision function from the raw scores.
We have the relation: decision_function = score_samples - offset.
n_iter_ : int
The actual number of iterations to reach the stopping criterion.
t_ : int
Number of weight updates performed during training.
Same as ``(n_iter_ * n_samples + 1)``.
loss_function_ : concrete ``LossFunction``
.. deprecated:: 1.4
``loss_function_`` was deprecated in version 1.4 and will be removed in
1.6.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
sklearn.svm.OneClassSVM : Unsupervised Outlier Detection.
Notes
-----
This estimator has a linear complexity in the number of training samples
and is thus better suited than the `sklearn.svm.OneClassSVM`
implementation for datasets with a large number of training samples (say
> 10,000).
Examples
--------
>>> import numpy as np
>>> from sklearn import linear_model
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
>>> clf = linear_model.SGDOneClassSVM(random_state=42)
>>> clf.fit(X)
SGDOneClassSVM(random_state=42)
>>> print(clf.predict([[4, 4]]))
[1]
"""
loss_functions = {"hinge": (Hinge, 1.0)}
_parameter_constraints: dict = {
**BaseSGD._parameter_constraints,
"nu": [Interval(Real, 0.0, 1.0, closed="right")],
"learning_rate": [
StrOptions({"constant", "optimal", "invscaling", "adaptive"}),
Hidden(StrOptions({"pa1", "pa2"})),
],
"eta0": [Interval(Real, 0, None, closed="left")],
"power_t": [Interval(Real, None, None, closed="neither")],
}
def __init__(
self,
nu=0.5,
fit_intercept=True,
max_iter=1000,
tol=1e-3,
shuffle=True,
verbose=0,
random_state=None,
learning_rate="optimal",
eta0=0.0,
power_t=0.5,
warm_start=False,
average=False,
):
self.nu = nu
super(SGDOneClassSVM, self).__init__(
loss="hinge",
penalty="l2",
C=1.0,
l1_ratio=0,
fit_intercept=fit_intercept,
max_iter=max_iter,
tol=tol,
shuffle=shuffle,
verbose=verbose,
epsilon=DEFAULT_EPSILON,
random_state=random_state,
learning_rate=learning_rate,
eta0=eta0,
power_t=power_t,
early_stopping=False,
validation_fraction=0.1,
n_iter_no_change=5,
warm_start=warm_start,
average=average,
)
def _fit_one_class(self, X, alpha, C, sample_weight, learning_rate, max_iter):
"""Uses SGD implementation with X and y=np.ones(n_samples)."""
# The One-Class SVM uses the SGD implementation with
# y=np.ones(n_samples).
n_samples = X.shape[0]
y = np.ones(n_samples, dtype=X.dtype, order="C")
dataset, offset_decay = make_dataset(X, y, sample_weight)
penalty_type = self._get_penalty_type(self.penalty)
learning_rate_type = self._get_learning_rate_type(learning_rate)
# early stopping is set to False for the One-Class SVM. thus
# validation_mask and validation_score_cb will be set to values
# associated to early_stopping=False in _make_validation_split and
# _make_validation_score_cb respectively.
validation_mask = self._make_validation_split(y, sample_mask=sample_weight > 0)
validation_score_cb = self._make_validation_score_cb(
validation_mask, X, y, sample_weight
)
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)
tol = self.tol if self.tol is not None else -np.inf
one_class = 1
# There are no class weights for the One-Class SVM and they are
# therefore set to 1.
pos_weight = 1
neg_weight = 1
if self.average:
coef = self._standard_coef
intercept = self._standard_intercept
average_coef = self._average_coef
average_intercept = self._average_intercept
else:
coef = self.coef_
intercept = 1 - self.offset_
average_coef = None # Not used
average_intercept = [0] # Not used
_plain_sgd = _get_plain_sgd_function(input_dtype=coef.dtype)
coef, intercept, average_coef, average_intercept, self.n_iter_ = _plain_sgd(
coef,
intercept[0],
average_coef,
average_intercept[0],
self._loss_function_,
penalty_type,
alpha,
C,
self.l1_ratio,
dataset,
validation_mask,
self.early_stopping,
validation_score_cb,
int(self.n_iter_no_change),
max_iter,
tol,
int(self.fit_intercept),
int(self.verbose),
int(self.shuffle),
seed,
neg_weight,
pos_weight,
learning_rate_type,
self.eta0,
self.power_t,
one_class,
self.t_,
offset_decay,
self.average,
)
self.t_ += self.n_iter_ * n_samples
if self.average > 0:
self._average_intercept = np.atleast_1d(average_intercept)
self._standard_intercept = np.atleast_1d(intercept)
if self.average <= self.t_ - 1.0:
# made enough updates for averaging to be taken into account
self.coef_ = average_coef
self.offset_ = 1 - np.atleast_1d(average_intercept)
else:
self.coef_ = coef
self.offset_ = 1 - np.atleast_1d(intercept)
else:
self.offset_ = 1 - np.atleast_1d(intercept)
def _partial_fit(
self,
X,
alpha,
C,
loss,
learning_rate,
max_iter,
sample_weight,
coef_init,
offset_init,
):
first_call = getattr(self, "coef_", None) is None
X = self._validate_data(
X,
None,
accept_sparse="csr",
dtype=[np.float64, np.float32],
order="C",
accept_large_sparse=False,
reset=first_call,
)
if first_call:
# TODO(1.7) remove 0 from average parameter constraint
if not isinstance(self.average, (bool, np.bool_)) and self.average == 0:
warnings.warn(
(
"Passing average=0 to disable averaging is deprecated and will"
" be removed in 1.7. Please use average=False instead."
),
FutureWarning,
)
n_features = X.shape[1]
# Allocate datastructures from input arguments
sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
# We use intercept = 1 - offset where intercept is the intercept of
# the SGD implementation and offset is the offset of the One-Class SVM
# optimization problem.
if getattr(self, "coef_", None) is None or coef_init is not None:
self._allocate_parameter_mem(
n_classes=1,
n_features=n_features,
input_dtype=X.dtype,
coef_init=coef_init,
intercept_init=offset_init,
one_class=1,
)
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 and getattr(self, "_average_coef", None) is None:
self._average_coef = np.zeros(n_features, dtype=X.dtype, order="C")
self._average_intercept = np.zeros(1, dtype=X.dtype, order="C")
self._loss_function_ = self._get_loss_function(loss)
if not hasattr(self, "t_"):
self.t_ = 1.0
# delegate to concrete training procedure
self._fit_one_class(
X,
alpha=alpha,
C=C,
learning_rate=learning_rate,
sample_weight=sample_weight,
max_iter=max_iter,
)
return self
@_fit_context(prefer_skip_nested_validation=True)
def partial_fit(self, X, y=None, sample_weight=None):
"""Fit linear One-Class SVM with Stochastic Gradient Descent.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Subset of the training data.
y : Ignored
Not used, present for API consistency by convention.
sample_weight : array-like, shape (n_samples,), optional
Weights applied to individual samples.
If not provided, uniform weights are assumed.
Returns
-------
self : object
Returns a fitted instance of self.
"""
if not hasattr(self, "coef_"):
self._more_validate_params(for_partial_fit=True)
alpha = self.nu / 2
return self._partial_fit(
X,
alpha,
C=1.0,
loss=self.loss,
learning_rate=self.learning_rate,
max_iter=1,
sample_weight=sample_weight,
coef_init=None,
offset_init=None,
)
def _fit(
self,
X,
alpha,
C,
loss,
learning_rate,
coef_init=None,
offset_init=None,
sample_weight=None,
):
# TODO(1.7) remove 0 from average parameter constraint
if not isinstance(self.average, (bool, np.bool_)) and self.average == 0:
warnings.warn(
(
"Passing average=0 to disable averaging is deprecated and will be "
"removed in 1.7. Please use average=False instead."
),
FutureWarning,
)
if self.warm_start and hasattr(self, "coef_"):
if coef_init is None:
coef_init = self.coef_
if offset_init is None:
offset_init = self.offset_
else:
self.coef_ = None
self.offset_ = None
# Clear iteration count for multiple call to fit.
self.t_ = 1.0
self._partial_fit(
X,
alpha,
C,
loss,
learning_rate,
self.max_iter,
sample_weight,
coef_init,
offset_init,
)
if (
self.tol is not None
and self.tol > -np.inf
and self.n_iter_ == self.max_iter
):
warnings.warn(
(
"Maximum number of iteration reached before "
"convergence. Consider increasing max_iter to "
"improve the fit."
),
ConvergenceWarning,
)
return self
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y=None, coef_init=None, offset_init=None, sample_weight=None):
"""Fit linear One-Class SVM with Stochastic Gradient Descent.
This solves an equivalent optimization problem of the
One-Class SVM primal optimization problem and returns a weight vector
w and an offset rho such that the decision function is given by
<w, x> - rho.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
y : Ignored
Not used, present for API consistency by convention.
coef_init : array, shape (n_classes, n_features)
The initial coefficients to warm-start the optimization.
offset_init : array, shape (n_classes,)
The initial offset 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. These weights will
be multiplied with class_weight (passed through the
constructor) if class_weight is specified.
Returns
-------
self : object
Returns a fitted instance of self.
"""
self._more_validate_params()
alpha = self.nu / 2
self._fit(
X,
alpha=alpha,
C=1.0,
loss=self.loss,
learning_rate=self.learning_rate,
coef_init=coef_init,
offset_init=offset_init,
sample_weight=sample_weight,
)
return self
def decision_function(self, X):
"""Signed distance to the separating hyperplane.
Signed distance is positive for an inlier and negative for an
outlier.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Testing data.
Returns
-------
dec : array-like, shape (n_samples,)
Decision function values of the samples.
"""
check_is_fitted(self, "coef_")
X = self._validate_data(X, accept_sparse="csr", reset=False)
decisions = safe_sparse_dot(X, self.coef_.T, dense_output=True) - self.offset_
return decisions.ravel()
def score_samples(self, X):
"""Raw scoring function of the samples.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Testing data.
Returns
-------
score_samples : array-like, shape (n_samples,)
Unshiffted scoring function values of the samples.
"""
score_samples = self.decision_function(X) + self.offset_
return score_samples
def predict(self, X):
"""Return labels (1 inlier, -1 outlier) of the samples.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Testing data.
Returns
-------
y : array, shape (n_samples,)
Labels of the samples.
"""
y = (self.decision_function(X) >= 0).astype(np.int32)
y[y == 0] = -1 # for consistency with outlier detectors
return y
def _more_tags(self):
return {
"_xfail_checks": {
"check_sample_weights_invariance": (
"zero sample_weight is not equivalent to removing samples"
)
},
"preserves_dtype": [np.float64, np.float32],
}