Regresión Logística¶
Documentación en sklearn del método de regresión logística
In [1]:
import numpy as np
import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn import datasets
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
warnings.filterwarnings('ignore')
In [2]:
import mlutils
Ejemplo basado en este link.
Vamos a usar la base de datos de Iris para ver la regresión logística:
In [3]:
# import some data to play with
iris = datasets.load_iris()
In [4]:
dir(iris)
Out[4]:
['DESCR', 'data', 'data_module', 'feature_names', 'filename', 'frame', 'target', 'target_names']
In [5]:
print(iris.DESCR)
.. _iris_dataset:
Iris plants dataset
--------------------
**Data Set Characteristics:**
:Number of Instances: 150 (50 in each of three classes)
:Number of Attributes: 4 numeric, predictive attributes and the class
:Attribute Information:
- sepal length in cm
- sepal width in cm
- petal length in cm
- petal width in cm
- class:
- Iris-Setosa
- Iris-Versicolour
- Iris-Virginica
:Summary Statistics:
============== ==== ==== ======= ===== ====================
Min Max Mean SD Class Correlation
============== ==== ==== ======= ===== ====================
sepal length: 4.3 7.9 5.84 0.83 0.7826
sepal width: 2.0 4.4 3.05 0.43 -0.4194
petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)
petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)
============== ==== ==== ======= ===== ====================
:Missing Attribute Values: None
:Class Distribution: 33.3% for each of 3 classes.
:Creator: R.A. Fisher
:Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
:Date: July, 1988
The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken
from Fisher's paper. Note that it's the same as in R, but not as in the UCI
Machine Learning Repository, which has two wrong data points.
This is perhaps the best known database to be found in the
pattern recognition literature. Fisher's paper is a classic in the field and
is referenced frequently to this day. (See Duda & Hart, for example.) The
data set contains 3 classes of 50 instances each, where each class refers to a
type of iris plant. One class is linearly separable from the other 2; the
latter are NOT linearly separable from each other.
.. topic:: References
- Fisher, R.A. "The use of multiple measurements in taxonomic problems"
Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to
Mathematical Statistics" (John Wiley, NY, 1950).
- Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.
(Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.
- Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
Structure and Classification Rule for Recognition in Partially Exposed
Environments". IEEE Transactions on Pattern Analysis and Machine
Intelligence, Vol. PAMI-2, No. 1, 67-71.
- Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule". IEEE Transactions
on Information Theory, May 1972, 431-433.
- See also: 1988 MLC Proceedings, 54-64. Cheeseman et al"s AUTOCLASS II
conceptual clustering system finds 3 classes in the data.
- Many, many more ...
In [6]:
df = pd.DataFrame(iris.data,columns=iris.feature_names)
df['target'] = iris.target
sns.pairplot(df,hue='target')
plt.show()
Reduzcamos la base de datos para facilitar la comprensión de lo que estamos haciendo
In [7]:
X = iris.data[:, :2] # we only take the first two features.
# sepal length, sepal width
y = iris.target
X = X[y<2] # we only take two classes
y = y[y<2] # we only take two classes
# setosa y versicolor
In [8]:
def plot_decision_boundary(X, y, regression):
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
h = .02 # step size in the mesh
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
Z = regression.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure(1, figsize=(4, 3))
plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='k', cmap=plt.cm.Paired)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.show()
Probemos diferentes argumentos del método LogisticRegression para ver qué pasa...
In [9]:
LogisticRegression?
Init signature: LogisticRegression( penalty='l2', *, dual=False, tol=0.0001, 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, ) Docstring: 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', 'saga' and 'newton-cg' solvers.) This class implements regularized logistic regression using the 'liblinear' library, 'newton-cg', 'sag', 'saga' and 'lbfgs' solvers. **Note that regularization is applied by default**. 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, or no regularization. The 'liblinear' solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. The Elastic-Net regularization is only supported by the 'saga' solver. Read more in the :ref:`User Guide <logistic_regression>`. Parameters ---------- penalty : {'l1', 'l2', 'elasticnet', 'none'}, default='l2' Specify the norm of the penalty: - `'none'`: no penalty is added; - `'l2'`: add a L2 penalty term and it is the default choice; - `'l1'`: add a L1 penalty term; - `'elasticnet'`: both L1 and L2 penalty terms are added. .. warning:: Some penalties may not work with some solvers. See the parameter `solver` below, to know the compatibility between the penalty and solver. .. versionadded:: 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. .. versionadded:: 0.17 *class_weight='balanced'* random_state : int, RandomState instance, default=None Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the data. See :term:`Glossary <random_state>` for details. solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'}, default='lbfgs' Algorithm to use in the optimization problem. Default is 'lbfgs'. To choose a solver, you might want to consider the following aspects: - 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. .. warning:: The choice of the algorithm depends on the penalty chosen: Supported penalties by solver: - 'newton-cg' - ['l2', 'none'] - 'lbfgs' - ['l2', 'none'] - 'liblinear' - ['l1', 'l2'] - 'sag' - ['l2', 'none'] - 'saga' - ['elasticnet', 'l1', 'l2', 'none'] .. note:: 'sag' and 'saga' fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from :mod:`sklearn.preprocessing`. .. seealso:: Refer to the User Guide for more information regarding :class:`LogisticRegression` and more specifically the `Table <https://scikit-learn.org/dev/modules/linear_model.html#logistic-regression>`_ summarazing solver/penalty supports. .. 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. Attributes ---------- classes_ : ndarray of shape (n_classes, ) A list of class labels known to the classifier. coef_ : ndarray of 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_ : ndarray of 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_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 n_iter_ : ndarray of 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. .. versionchanged:: 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``. 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 :ref:`differences from liblinear <liblinear_differences>` in the narrative documentation. References ---------- L-BFGS-B -- Software for Large-scale Bound-constrained Optimization Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales. http://users.iems.northwestern.edu/~nocedal/lbfgsb.html LIBLINEAR -- A Library for Large Linear Classification https://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). :arxiv:`"SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives" <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. https://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf Examples -------- >>> from sklearn.datasets import load_iris >>> from sklearn.linear_model import LogisticRegression >>> X, y = load_iris(return_X_y=True) >>> clf = LogisticRegression(random_state=0).fit(X, y) >>> clf.predict(X[:2, :]) array([0, 0]) >>> clf.predict_proba(X[:2, :]) 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... File: c:\anaconda3\envs\diplodatos\lib\site-packages\sklearn\linear_model\_logistic.py Type: type Subclasses: LogisticRegressionCV
In [10]:
# create an instance of Logistic Regression Classifier
logreg = LogisticRegression(C=1e+3, solver='liblinear', max_iter=2).fit(X, y)
plot_decision_boundary(X, y, logreg)
Algo de información acerca de los solvers o métodos de optimización que utiliza scikit-learn para encontrar un mínimo.
In [11]:
# update the number of iterations
logreg = LogisticRegression(C=1e+3, solver='liblinear', max_iter=20).fit(X, y)
plot_decision_boundary(X, y, logreg)
In [12]:
# update the number of iterations
logreg = LogisticRegression(C=1e+3, solver='liblinear', max_iter=20, penalty='l1').fit(X, y)
plot_decision_boundary(X, y, logreg)
In [13]:
logreg = LogisticRegression(C=1e+8, solver='saga', max_iter=20, penalty='elasticnet',l1_ratio=0.7).fit(X, y)
plot_decision_boundary(X, y, logreg)
