linear_model.LogisticRegression¶

class pai4sk.linear_model.LogisticRegression(penalty='l2', dual=False, tol=0.0001, C=1.0, fit_intercept=True, intercept_scaling=1, class_weight=None, random_state=None, solver='warn', max_iter=100, multi_class='warn', verbose=0, warm_start=False, n_jobs=None, use_gpu=True, device_ids=[], return_training_history=None, privacy=False, eta=0.3, batch_size=100, privacy_epsilon=10, grad_clip=1, num_threads=1)¶

Logistic Regression (aka logit, MaxEnt) classifier.

In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross- entropy loss if the ‘multi_class’ option is set to ‘multinomial’. (Currently the ‘multinomial’ option is supported only by the ‘lbfgs’, ‘sag’ and ‘newton-cg’ solvers.)

This class implements regularized logistic regression using the ‘liblinear’ library, ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied).

The ‘newton-cg’, ‘sag’, and ‘lbfgs’ solvers support only L2 regularization with primal formulation. The ‘liblinear’ solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty.

Read more in the User Guide.

For SnapML solver this supports both local and distributed(MPI) method of execution.

Parameters:

penalty (str, 'l1' or 'l2', default: 'l2') –
Used to specify the norm used in the penalization. The ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers support only l2 penalties.

New in version 0.19: l1 penalty with SAGA solver (allowing ‘multinomial’ + L1)
dual (bool, default: False) – Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
tol (float, default: 1e-4) – Tolerance for stopping criteria.
C (float, default: 1.0) – Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization.
fit_intercept (bool, default: True) – Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.
intercept_scaling (float, default 1.) –
Useful only when the solver ‘liblinear’ is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic_feature_weight.

Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.
class_weight (dict or 'balanced', default: None) –
Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

New in version 0.17: class_weight=’balanced’
random_state (int, RandomState instance or None, optional, default: None) – The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when solver == ‘sag’ or ‘liblinear’.
solver (str, {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga', 'snapml'}, default: 'snapml', if 'snap_ml' library is in PYTHONPATH, else,) –
default: ‘liblinear’.

Algorithm to use in the optimization problem.
- For small datasets, ‘liblinear’ is a good choice, whereas ‘sag’ and ‘saga’ are faster for large ones.
- For multiclass problems, only ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ handle multinomial loss; ‘liblinear’ is limited to one-versus-rest schemes.
- ’newton-cg’, ‘lbfgs’ and ‘sag’ only handle L2 penalty, whereas ‘liblinear’ and ‘saga’ handle L1 penalty.
Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from pai4sk.preprocessing.

New in version 0.17: Stochastic Average Gradient descent solver.

New in version 0.19: SAGA solver.

Changed in version 0.20: Default will change from ‘liblinear’ to ‘lbfgs’ in 0.22.
max_iter (int, default: 100) – Useful only for the newton-cg, sag and lbfgs solvers. Maximum number of iterations taken for the solvers to converge.
multi_class (str, {'ovr', 'multinomial', 'auto'}, default: 'ovr') –
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’.

New in version 0.18: Stochastic Average Gradient descent solver for ‘multinomial’ case.

Changed in version 0.20: Default will change 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 the Glossary.

New in version 0.17: warm_start to support lbfgs, newton-cg, sag, saga solvers.
n_jobs (int or None, optional (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 joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
use_gpu (bool, default : True) – Flag for indicating the hardware platform used for training. If True, the training is performed using the GPU. If False, the training is performed using the CPU. The value of this parameter is subjected to changed based on the training data unless set explicitly. Applicable only for snapml solver
device_ids (array-like of int, default : []) – If use_gpu is True, it indicates the IDs of the GPUs used for training. For single-GPU training, set device_ids to the GPU ID to be used for training, e.g., [0]. For multi-GPU training, set device_ids to a list of GPU IDs to be used for training, e.g., [0, 1]. Applicable only for snapml solver
num_threads (int, default : 1) – The number of threads used for running the training. The value of this parameter should be a multiple of 32 if the training is performed on GPU (use_gpu=True) (default value for GPU is 256). Applicable only for snapml solver
return_training_history (str or None, default : None) – How much information about the training should be collected and returned by the fit function. By default no information is returned (None), but this parameter can be set to “summary”, to obtain summary statistics at the end of training, or “full” to obtain a complete set of statistics for the entire training procedure. Note, enabling either option will result in slower training. Applicable only for snapml solver
privacy (bool, default : False) – Train the model using a differentially private algorithm.
eta (float, default : 0.3) – Learning rate for the differentially private training algorithm.
batch_size (int, default : 100) – Mini-batch size for the differentially private training algorithm.
privacy_epsilon (float, default : 10.0) – Target privacy gaurantee. Learned model will be (privacy_epsilon, 0.01)-private.
grad_clip (float, default: 1.0) – Gradient clipping parameter for the differentially private training algorithm

Variables:

coef (array, shape (1, n_features) or (n_classes, n_features)) –
Coefficient of the features in the decision function.

coef_ is of shape (1, n_features) when the given problem is binary. In particular, when multi_class=’multinomial’, coef_ corresponds to outcome 1 (True) and -coef_ corresponds to outcome 0 (False).
intercept (array, shape (1,) or (n_classes,)) –
Intercept (a.k.a. bias) added to the decision function.

If fit_intercept is set to False, the intercept is set to zero. intercept_ is of shape (1,) when the given problem is binary. In particular, when multi_class=’multinomial’, intercept_ corresponds to outcome 1 (True) and -intercept_ corresponds to outcome 0 (False).
n_iter (array, shape (n_classes,) or (1, )) – Actual number of iterations for all classes. If binary or multinomial, it returns only 1 element. For liblinear solver, only the maximum number of iteration across all classes is given.
training_history (dict) – It returns a dictionary with the following keys : ‘epochs’, ‘t_elap_sec’, ‘train_obj’. If ‘return_training_history’ is set to “summary”, ‘epochs’ contains the total number of epochs performed, ‘t_elap_sec’ contains the total time for completing all of those epochs. If ‘return_training_history’ is set to “full”, ‘epochs’ indicates the number of epochs that have elapsed so far, and ‘t_elap_sec’ contains the time to do those epochs. ‘train_obj’ is the training loss. Applicable only for snapml solver.
support (array-like) – Indices of the features that contribute to the decision. (only available for L1)
model_sparsity (float) –
Fraction of non-zeros in the model parameters. (only available for L1)

Changed in version 0.20: In SciPy <= 1.0.0 the number of lbfgs iterations may exceed max_iter. n_iter_ will now report at most max_iter.

Examples

>>> from pai4sk.datasets import load_iris
>>> from pai4sk.linear_model import LogisticRegression
>>> X, y = load_iris(return_X_y=True)
>>> clf = LogisticRegression(random_state=0, solver='lbfgs',
...                          multi_class='multinomial').fit(X, y)
>>> clf.predict(X[:2, :])
array([0, 0])
>>> clf.predict_proba(X[:2, :]) # doctest: +ELLIPSIS
array([[9.8...e-01, 1.8...e-02, 1.4...e-08],
       [9.7...e-01, 2.8...e-02, ...e-08]])
>>> clf.score(X, y)
0.97...

See also

SGDClassifier: incrementally trained logistic regression (when given the parameter loss="log").
LogisticRegressionCV: Logistic regression with built-in cross validation

Notes

The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon, to have slightly different results for the same input data. If that happens, try with a smaller tol parameter.

Predict output may not match that of standalone liblinear in certain cases. See differences from liblinear in the narrative documentation.

References

LIBLINEAR – A Library for Large Linear Classification: http://www.csie.ntu.edu.tw/~cjlin/liblinear/
SAG – Mark Schmidt, Nicolas Le Roux, and Francis Bach: Minimizing Finite Sums with the Stochastic Average Gradient https://hal.inria.fr/hal-00860051/document
SAGA – Defazio, A., Bach F. & Lacoste-Julien S. (2014).: SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives https://arxiv.org/abs/1407.0202
Hsiang-Fu Yu, Fang-Lan Huang, Chih-Jen Lin (2011). Dual coordinate descent: methods for logistic regression and maximum entropy models. Machine Learning 85(1-2):41-75. http://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf

fit(X, y, sample_weight=None)¶

Fit the model according to the given training data. :param X: Training vector, where n_samples is the number of samples and

n_features is the number of features. For SnapML solver it also supports input of types SnapML data partition and DeviceNDArray.

Parameters:	y (array-like, shape (n_samples,) or (n_samples, n_targets)) – Target vector relative to X. sample_weight (array-like, shape (n_samples,) optional) – Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. .. versionadded:: 0.17 sample_weight support to LogisticRegression.
Returns:	self
Return type:	object

predict(X, num_threads=0)¶

Class predictions The returned class estimates. :param X: Dataset used for predicting class estimates.

For SnapML solver it also supports input of type SnapML data partition.

Parameters:	num_threads (int, default : 0) – Number of threads used to run inference. By default inference runs with maximum number of available threads.
Returns:	proba – Returns the predicted class of the sample.
Return type:	array-like, shape = (n_samples,)

predict_log_proba(X)¶

Log of probability estimates. The returned estimates for all classes are ordered by the label of classes. :param X: For SnapML solver it also supports input of type SnapML data partition. :type X: array-like, shape = [n_samples, n_features]

Returns:	T – Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in `self.classes_`.
Return type:	array-like, shape = [n_samples, n_classes]

predict_proba(X, num_threads=0)¶

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. :param X: For SnapML solver it also supports input of type SnapML data partition. :type X: array-like, shape = [n_samples, n_features] :param num_threads: Number of threads used to run inference.

By default inference runs with maximum number of available threads.

Returns:	T – Returns the probability of the sample for each class in the model, where classes are ordered as they are in `self.classes_`.
Return type:	array-like, shape = [n_samples, n_classes]