?

?

邏輯回歸(又名logit, MaxEnt)分類器。
在多類情況下，如果“multi_class”選項設置為“OvR”，訓練算法使用one vs-rest (OvR)方案，如果“multi_class”選項設置為“多項”，訓練算法使用交叉熵損失。(目前，“多項”選項僅由“lbfgs”、“sag”、“saga”和“newton-cg”求解器支持。)

這個類使用“liblinear”庫、“newton-cg”、“sag”、“saga”和“lbfgs”求解器實現正則邏輯回歸。**注意正則化是在默認情況下應用的**。它可以處理稠密和稀疏輸入。使用C-ordered數組或包含64位浮點數的CSR矩陣，以獲得最佳性能;任何其他輸入格式都將被轉換(和復制)。

“newton-cg”、“sag”和“lbfgs”求解器只支持使用原始公式的L2正則化，或者不支持正則化。“liblinear”求解器支持L1和L2正則化，只有L2懲罰的對偶公式。彈性網正則化僅由“saga”求解器支持。

詳見:ref: ' User Guide <logistic_regression> '。</logistic_regression>

? .. versionadded:: 0.17
? ? Stochastic Average Gradient descent solver.
? ? .. versionadded:: 0.19
? ? SAGA solver.
? ? .. versionchanged:: 0.22
? ? The default solver changed from 'liblinear' to 'lbfgs' in 0.22.
? ??
? ? max_iter : int, default=100
? ? Maximum number of iterations taken for the solvers to converge.
? ??
? ? multi_class : {'auto', 'ovr', 'multinomial'}, default='auto'
? ? If the option chosen is 'ovr', then a binary problem is fit for each?label. For 'multinomial' the loss minimised is the multinomial loss fit? across the entire probability distribution, *even when the data is?binary*. 'multinomial' is unavailable when solver='liblinear'.? 'auto' selects 'ovr' if the data is binary, or if solver='liblinear',??and otherwise selects 'multinomial'.
? ??
? ? .. versionadded:: 0.18
? ? Stochastic Average Gradient descent solver for 'multinomial' case.
? ? .. versionchanged:: 0.22
? ? Default changed from 'ovr' to 'auto' in 0.22.
? ??
? ? verbose : int, default=0
? ? For the liblinear and lbfgs solvers set verbose to any positive? number for verbosity.
? ??
? ? warm_start : bool, default=False
? ? When set to True, reuse the solution of the previous call to fit as?initialization, otherwise, just erase the previous solution.?Useless for liblinear solver. See :term:`the Glossary <warm_start>`.
? ??
? ? .. versionadded:: 0.17
? ? *warm_start* to support *lbfgs*, *newton-cg*, *sag*, *saga* solvers.
? ??
? ? n_jobs : int, default=None
? ? Number of CPU cores used when parallelizing over classes if? multi_class='ovr'". This parameter is ignored when the ``solver`` is?set to 'liblinear' regardless of whether 'multi_class' is specified or?not. ``None`` means 1 unless in a :obj:`joblib.parallel_backend`??context. ``-1`` means using all processors.
? ? See :term:`Glossary <n_jobs>` for more details.
? ??
? ? l1_ratio : float, default=None
? ? The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only? used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent?to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent??to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination of L1 and L2.

屬性
?----------

classes_:形狀的ndarray
分類器已知的類標簽列表。

coef_:決策函數中特征的形狀(1,n_features)或(n_classes, n_features)系數的ndarray。

當給定的問題是二進制時，' coef_ '是形狀(1,n_features)。
特別是，當“multi_class=”多項“”時，“coef_”對應結果1 (True)，而“-coef_”對應結果0 (False)。

intercept_:形狀(1，)或(n_classes，)的ndarray
在決策函數中加入截距(即偏差)。

如果' fit_intercept '設置為False，則攔截設置為零。
當給定的問題是二進制時，intercept_ '的形狀是(1，)。特別是，當“multi_class=”多項“”時，“intercept_”對應結果1 (True)，而“-intercept_”對應結果0 (False)。

n_iter_:形狀(n_classes，)或(1，)的ndarray
所有類的實際迭代次數。如果是二項或多項，則只返回1個元素。對于線性求解器，只給出了所有類的最大迭代次數。

. .versionchanged:: 0.20

在SciPy <= 1.0.0中，lbfgs迭代次數可能超過' ' max_iter ' '。' ' n_iter_ ' '現在最多報告' ' max_iter ' '。

另請參閱
--------
增量訓練邏輯回歸(當給定參數' ' loss="log" ' ')。
邏輯回歸cv:內置交叉驗證的邏輯回歸。

筆記
&nbsp; &nbsp; -----
底層的C實現使用一個隨機數生成器來選擇適合模型的特性。因此，對于相同的輸入數據，結果略有不同的情況并不少見。如果出現這種情況，嘗試使用較小的tol參數。

在某些情況下，Predict輸出可能與獨立liblinear的輸出不匹配。參見:ref:“區別于liblinear <liblinear_differences>”。</liblinear_differences>

? ? def __init__(self, penalty='l2', *, dual=False, tol=1e-4, C=1.0,?
? ? ? ? fit_intercept=True, intercept_scaling=1, class_weight=None,?
? ? ? ? random_state=None, solver='lbfgs', max_iter=100,?
? ? ? ? multi_class='auto', verbose=0, warm_start=False, n_jobs=None,?
? ? ? ? l1_ratio=None):
? ? ? ? self.penalty = penalty
? ? ? ? self.dual = dual
? ? ? ? self.tol = tol
? ? ? ? self.C = C
? ? ? ? self.fit_intercept = fit_intercept
? ? ? ? self.intercept_scaling = intercept_scaling
? ? ? ? self.class_weight = class_weight
? ? ? ? self.random_state = random_state
? ? ? ? self.solver = solver
? ? ? ? self.max_iter = max_iter
? ? ? ? self.multi_class = multi_class
? ? ? ? self.verbose = verbose
? ? ? ? self.warm_start = warm_start
? ? ? ? self.n_jobs = n_jobs
? ? ? ? self.l1_ratio = l1_ratio
? ??
? ? def fit(self, X, y, sample_weight=None):
? ? ? ? """
? ? ? ? Fit the model according to the given training data.

? ? ? ? Parameters
? ? ? ? ----------
? ? ? ? X : {array-like, sparse matrix} of shape (n_samples, n_features)
? ? ? ? ? ? Training vector, where n_samples is the number of samples and
? ? ? ? ? ? n_features is the number of features.

? ? ? ? y : array-like of shape (n_samples,)
? ? ? ? ? ? Target vector relative to X.

? ? ? ? sample_weight : array-like of shape (n_samples,) default=None
? ? ? ? ? ? Array of weights that are assigned to individual samples.
? ? ? ? ? ? If not provided, then each sample is given unit weight.

? ? ? ? ? ? .. versionadded:: 0.17
? ? ? ? ? ? ? ?*sample_weight* support to LogisticRegression.

? ? ? ? Returns
? ? ? ? -------
? ? ? ? self
? ? ? ? ? ? Fitted estimator.

? ? ? ? Notes
? ? ? ? -----
? ? ? ? The SAGA solver supports both float64 and float32 bit arrays.
? ? ? ? """
? ? ? ? solver = _check_solver(self.solver, self.penalty, self.dual)
? ? ? ? if not isinstance(self.C, numbers.Number) or self.C < 0:
? ? ? ? ? ? raise ValueError(
? ? ? ? ? ? ? ? "Penalty term must be positive; got (C=%r)" % self.C)
? ? ? ? if self.penalty == 'elasticnet':
? ? ? ? ? ? if (not isinstance(self.l1_ratio, numbers.Number) or?
? ? ? ? ? ? ? ? self.l1_ratio < 0 or self.l1_ratio > 1):
? ? ? ? ? ? ? ? raise ValueError(
? ? ? ? ? ? ? ? ? ? "l1_ratio must be between 0 and 1;"
? ? ? ? ? ? ? ? ? ? " got (l1_ratio=%r)" %?
? ? ? ? ? ? ? ? ? ? self.l1_ratio)
? ? ? ? elif self.l1_ratio is not None:
? ? ? ? ? ? warnings.warn("l1_ratio parameter is only used when penalty is "
? ? ? ? ? ? ? ? "'elasticnet'. Got "
? ? ? ? ? ? ? ? "(penalty={})".
? ? ? ? ? ? ? ? format(self.penalty))
? ? ? ? if self.penalty == 'none':
? ? ? ? ? ? if self.C != 1.0: # default values
? ? ? ? ? ? ? ? warnings.warn("Setting penalty='none' will ignore the C and?
? ? ? ? ? ? ? ? ?l1_ratio "
? ? ? ? ? ? ? ? ? ? "parameters")
? ? ? ? ? ? ? ? ? ? # Note that check for l1_ratio is done right above
? ? ? ? ? ? C_ = np.inf
? ? ? ? ? ? penalty = 'l2'
? ? ? ? else:
? ? ? ? ? ? C_ = self.C
? ? ? ? ? ? penalty = self.penalty
? ? ? ? if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0:
? ? ? ? ? ? raise ValueError("Maximum number of iteration must be positive;"
? ? ? ? ? ? ? ? " got (max_iter=%r)" %?
? ? ? ? ? ? ? ? self.max_iter)
? ? ? ? if not isinstance(self.tol, numbers.Number) or self.tol < 0:
? ? ? ? ? ? raise ValueError("Tolerance for stopping criteria must be "
? ? ? ? ? ? ? ? "positive; got (tol=%r)" %?
? ? ? ? ? ? ? ? self.tol)
? ? ? ? if solver == 'lbfgs':
? ? ? ? ? ? _dtype = np.float64
? ? ? ? else:
? ? ? ? ? ? _dtype = [np.float64, np.float32]
? ? ? ? X, y = self._validate_data(X, y, accept_sparse='csr', dtype=_dtype,?
? ? ? ? ?order="C",?
? ? ? ? ? ? accept_large_sparse=solver != 'liblinear')
? ? ? ? check_classification_targets(y)
? ? ? ? self.classes_ = np.unique(y)
? ? ? ? multi_class = _check_multi_class(self.multi_class, solver,?
? ? ? ? ? ? len(self.classes_))
? ? ? ? if solver == 'liblinear':
? ? ? ? ? ? if effective_n_jobs(self.n_jobs) != 1:
? ? ? ? ? ? ? ? warnings.warn("'n_jobs' > 1 does not have any effect when"
? ? ? ? ? ? ? ? ? ? " 'solver' is set to 'liblinear'. Got 'n_jobs'"
? ? ? ? ? ? ? ? ? ? " = {}.".
? ? ? ? ? ? ? ? ? ? format(effective_n_jobs(self.n_jobs)))
? ? ? ? ? ? self.coef_, self.intercept_, n_iter_ = _fit_liblinear(X, y, self.C, self.
? ? ? ? ? ? ?fit_intercept, self.intercept_scaling, self.class_weight, self.penalty, self.
? ? ? ? ? ? ?dual, self.verbose, self.max_iter, self.tol, self.random_state,?
? ? ? ? ? ? ? ? sample_weight=sample_weight)
? ? ? ? ? ? self.n_iter_ = np.array([n_iter_])
? ? ? ? ? ? return self
? ? ? ? if solver in ['sag', 'saga']:
? ? ? ? ? ? max_squared_sum = row_norms(X, squared=True).max()
? ? ? ? else:
? ? ? ? ? ? max_squared_sum = None
? ? ? ? n_classes = len(self.classes_)
? ? ? ? classes_ = self.classes_
? ? ? ? if n_classes < 2:
? ? ? ? ? ? raise ValueError(
? ? ? ? ? ? ? ? "This solver needs samples of at least 2 classes"
? ? ? ? ? ? ? ? " in the data, but the data contains only one"
? ? ? ? ? ? ? ? " class: %r" %?
? ? ? ? ? ? ? ? classes_[0])
? ? ? ? if len(self.classes_) == 2:
? ? ? ? ? ? n_classes = 1
? ? ? ? ? ? classes_ = classes_[1:]
? ? ? ? if self.warm_start:
? ? ? ? ? ? warm_start_coef = getattr(self, 'coef_', None)
? ? ? ? else:
? ? ? ? ? ? warm_start_coef = None
? ? ? ? if warm_start_coef is not None and self.fit_intercept:
? ? ? ? ? ? warm_start_coef = np.append(warm_start_coef,?
? ? ? ? ? ? ? ? self.intercept_[:np.newaxis],?
? ? ? ? ? ? ? ? axis=1)
? ? ? ? self.coef_ = list()
? ? ? ? self.intercept_ = np.zeros(n_classes)
? ? ? ? # Hack so that we iterate only once for the multinomial case.
? ? ? ? if multi_class == 'multinomial':
? ? ? ? ? ? classes_ = [None]
? ? ? ? ? ? warm_start_coef = [warm_start_coef]
? ? ? ? if warm_start_coef is None:
? ? ? ? ? ? warm_start_coef = [None] * n_classes
? ? ? ? path_func = delayed(_logistic_regression_path)
? ? ? ? # The SAG solver releases the GIL so it's more efficient to use
? ? ? ? # threads for this solver.
? ? ? ? if solver in ['sag', 'saga']:
? ? ? ? ? ? prefer = 'threads'
? ? ? ? else:
? ? ? ? ? ? prefer = 'processes'
? ? ? ? fold_coefs_ = Parallel(n_jobs=self.n_jobs, verbose=self.verbose, **
? ? ? ? ? ? _joblib_parallel_args(prefer=prefer))(
? ? ? ? ? ? path_func(X, y, pos_class=class_, Cs=[C_],?
? ? ? ? ? ? ? ? l1_ratio=self.l1_ratio, fit_intercept=self.fit_intercept,?
? ? ? ? ? ? ? ? tol=self.tol, verbose=self.verbose, solver=solver,?
? ? ? ? ? ? ? ? multi_class=multi_class, max_iter=self.max_iter,?
? ? ? ? ? ? ? ? class_weight=self.class_weight, check_input=False,?
? ? ? ? ? ? ? ? random_state=self.random_state, coef=warm_start_coef_,?
? ? ? ? ? ? ? ? penalty=penalty, max_squared_sum=max_squared_sum,?
? ? ? ? ? ? ? ? sample_weight=sample_weight) for?
? ? ? ? ? ? (class_, warm_start_coef_) in zip(classes_, warm_start_coef))
? ? ? ? fold_coefs_, _, n_iter_ = zip(*fold_coefs_)
? ? ? ? self.n_iter_ = np.asarray(n_iter_, dtype=np.int32)[:0]
? ? ? ? n_features = X.shape[1]
? ? ? ? if multi_class == 'multinomial':
? ? ? ? ? ? self.coef_ = fold_coefs_[0][0]
? ? ? ? else:
? ? ? ? ? ? self.coef_ = np.asarray(fold_coefs_)
? ? ? ? ? ? self.coef_ = self.coef_.reshape(n_classes, n_features +?
? ? ? ? ? ? ? ? int(self.fit_intercept))
? ? ? ? if self.fit_intercept:
? ? ? ? ? ? self.intercept_ = self.coef_[:-1]
? ? ? ? ? ? self.coef_ = self.coef_[::-1]
? ? ? ? return self
? ??
? ? def predict_proba(self, X):
? ? ? ? """
? ? ? ? Probability estimates.

? ? ? ? The returned estimates for all classes are ordered by the?label of classes.??For a multi_class problem, if multi_class is set to be "multinomial"? the softmax function is used to find the predicted probability of? each class.
? ? ? ? Else use a one-vs-rest approach, i.e calculate the probability?of each class assuming it to be positive using the logistic function.? and normalize these values across all the classes.

? ? ? ? Parameters
? ? ? ? ----------
? ? ? ? X : array-like of shape (n_samples, n_features)
? ? ? ? ? ? Vector to be scored, where `n_samples` is the number of samples??and?`n_features` is the number of features.

? ? ? ? Returns
? ? ? ? -------
? ? ? ? T : array-like 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_``.
? ? ? ? """
? ? ? ? check_is_fitted(self)
? ? ? ? ovr = self.multi_class in ["ovr", "warn"] or (self.multi_class == 'auto'?
? ? ? ? ?and (self.classes_.size <= 2 or?
? ? ? ? ? ? ? ? self.solver == 'liblinear'))
? ? ? ? if ovr:
? ? ? ? ? ? return super()._predict_proba_lr(X)
? ? ? ? else:
? ? ? ? ? ? decision = self.decision_function(X)
? ? ? ? ? ? if decision.ndim == 1:
? ? ? ? ? ? ? ? # Workaround for multi_class="multinomial" and binary?
? ? ? ? ? ? ? ? ?outcomes
? ? ? ? ? ? ? ? # which requires softmax prediction with only a 1D decision.
? ? ? ? ? ? ? ? decision_2d = np.c_[-decisiondecision]
? ? ? ? ? ? else:
? ? ? ? ? ? ? ? decision_2d = decision
? ? ? ? ? ? return softmax(decision_2d, copy=False)
? ??
? ? def predict_log_proba(self, X):
? ? ? ? """
? ? ? ? Predict logarithm of probability estimates.

? ? ? ? The returned estimates for all classes are ordered by the?label of classes.

? ? ? ? Parameters
? ? ? ? ----------
? ? ? ? X : array-like of shape (n_samples, n_features)
? ? ? ? ? ? Vector to be scored, where `n_samples` is the number of samples?? and? `n_features` is the number of features.

? ? ? ? Returns
? ? ? ? -------
? ? ? ? T : array-like of 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))

概率的估計。

所有類返回的估計值都按照類的標簽排序。對于一個多類問題，將多類設為“多項式”，利用softmax函數求出每一類的預測概率。
否則使用one vs-rest方法，i。計算概率的每一類假設它是正使用logistic函數。并在所有類中規范化這些值。