# Logistic Regression¶

Logistic regression of a categorical dependent variable

*Configuration*:

penaltyUsed 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)

dualDual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.

CInverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization.

fit_interceptSpecifies if a constant (a.k.a. bias or intercept) should be added to the decision function.

intercept_scalingUseful 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_weightWeights 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’

tolTolerance for stopping criteria.

multi_classIf 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.

max_iterUseful only for the newton-cg, sag and lbfgs solvers. Maximum number of iterations taken for the solvers to converge.

solverAlgorithm to use in the optimization problem.

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

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.

n_jobsNumber of CPU cores used when parallelizing over classes if multi_class=”ovr”. Ignored when the solver is set to “liblinear” regardless of multi_class. If given -1 then all cores are used

random_stateThe 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’.

warm_startWhen 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 warm_start.

New in version 0.17:

warm_startto supportlbfgs,newton-cg,sag,sagasolvers.

*Attributes*:

n_iter_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.

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`

.

coef_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_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).

*Input ports*:

*Output ports*:**model**: model- Model

**penalty**(penalty)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**(dual)- Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
**C**(C)- Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization.
**fit_intercept**(fit_intercept)- Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.
**intercept_scaling**(intercept_scaling)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**(class_weight)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’***tol**(tol)- Tolerance for stopping criteria.
**multi_class**(multi_class)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.

**max_iter**(max_iter)- Useful only for the newton-cg, sag and lbfgs solvers. Maximum number of iterations taken for the solvers to converge.
**solver**(solver)Algorithm to use in the optimization problem.

- For small datasets, ‘liblinear’ is a good choice, whereas ‘sag’ and ‘saga’ are faster for large ones.
- For multiclass problems, only ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ handle multinomial loss; ‘liblinear’ is limited to one-versus-rest schemes.
- ‘newton-cg’, ‘lbfgs’ and ‘sag’ only handle L2 penalty, whereas ‘liblinear’ and ‘saga’ handle L1 penalty.

Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

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.

**n_jobs**(n_jobs)- Number of CPU cores used when parallelizing over classes if multi_class=”ovr”. Ignored when the solver is set to “liblinear” regardless of multi_class. If given -1 then all cores are used
**random_state**(random_state)- 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’. **warm_start**(warm_start)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 warm_start.

New in version 0.17:

*warm_start*to support*lbfgs*,*newton-cg*,*sag*,*saga*solvers.

Some of the docstrings for this module have been automatically extracted from the scikit-learn library and are covered by their respective licenses.