Supervised learning using scikit-learn

The goal of this tutorial is to introduce you to the scikit libraries for classification. We will also cover feature selection, and evaluation.

import numpy as np
import scipy.sparse as sp_sparse

import matplotlib.pyplot as plt

import sklearn as sk
import sklearn.datasets as sk_data
import sklearn.metrics as metrics

import seaborn as sns

%matplotlib inline

Feature Selection

Feature selection is about finding the best features for your classifier. This may be important if you do not have enough training data. The idea is to find metrics that either characterize the features by themselves, or with respect to the class we want to predict, or with respect to other features.

http://scikit-learn.org/stable/modules/feature_selection.html

Variance Threshold

The VarianceThreshold selection drops features whose variance is below some threshold. If we have binary features we can estimate the treshold exactly so as to guarantee a specific ratio of 0's and 1's

from sklearn.feature_selection import VarianceThreshold
X = [[0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 1], [0, 1, 0], [0, 1, 1]]
print(np.array(X))
sel = VarianceThreshold(threshold=(.8 * (1 - .8)))
sel.fit_transform(X)

[[0 0 1]
 [0 1 0]
 [1 0 0]
 [0 1 1]
 [0 1 0]
 [0 1 1]]

array([[0, 1],
       [1, 0],
       [0, 0],
       [1, 1],
       [1, 0],
       [1, 1]])

import sklearn.datasets as sk_data
iris = sk_data.load_iris()
X = iris.data
print(X[1:10,:])
print(X.var(axis = 0))
sel = VarianceThreshold(threshold=0.2)
sel.fit_transform(X)[1:10]

[[4.9 3.  1.4 0.2]
 [4.7 3.2 1.3 0.2]
 [4.6 3.1 1.5 0.2]
 [5.  3.6 1.4 0.2]
 [5.4 3.9 1.7 0.4]
 [4.6 3.4 1.4 0.3]
 [5.  3.4 1.5 0.2]
 [4.4 2.9 1.4 0.2]
 [4.9 3.1 1.5 0.1]]
[0.68112222 0.18871289 3.09550267 0.57713289]

array([[4.9, 1.4, 0.2],
       [4.7, 1.3, 0.2],
       [4.6, 1.5, 0.2],
       [5. , 1.4, 0.2],
       [5.4, 1.7, 0.4],
       [4.6, 1.4, 0.3],
       [5. , 1.5, 0.2],
       [4.4, 1.4, 0.2],
       [4.9, 1.5, 0.1]])

Univariate Feature Selection

A more sophisticated feature selection technique uses test to determine if a feature and the class label are independent. An example of such a test is the chi-square test (there are more)

In this case we keep the features with high chi-square score and low p-value.

The features with the lowest scores and highest values are rejected.

The chi-square test is usually applied on categorical data.

from sklearn.feature_selection import SelectKBest
from sklearn.feature_selection import chi2
iris = sk_data.load_iris()
X, y = iris.data, iris.target
print(X.shape)
print('Features:')
print(X[1:10,:])
print('Labels:')
print(y[1:10])
sel = SelectKBest(chi2, k=2)
X_new = sel.fit_transform(X, y)
print('Selected Features:')
print(X_new[1:10])

(150, 4)
Features:
[[4.9 3.  1.4 0.2]
 [4.7 3.2 1.3 0.2]
 [4.6 3.1 1.5 0.2]
 [5.  3.6 1.4 0.2]
 [5.4 3.9 1.7 0.4]
 [4.6 3.4 1.4 0.3]
 [5.  3.4 1.5 0.2]
 [4.4 2.9 1.4 0.2]
 [4.9 3.1 1.5 0.1]]
Labels:
[0 0 0 0 0 0 0 0 0]
Selected Features:
[[1.4 0.2]
 [1.3 0.2]
 [1.5 0.2]
 [1.4 0.2]
 [1.7 0.4]
 [1.4 0.3]
 [1.5 0.2]
 [1.4 0.2]
 [1.5 0.1]]

The chi-square values and the p-values between features and target variable (X columns and y)

print('Chi2 values')
print(sel.scores_)
c,p = sk.feature_selection.chi2(X, y)
print('Chi2 values')
print(c) #The chi-square value between X columns and y
print('p-values')
print(p) #The p-value for the test

Chi2 values
[ 10.81782088   3.7107283  116.31261309  67.0483602 ]
Chi2 values
[ 10.81782088   3.7107283  116.31261309  67.0483602 ]
p-values
[4.47651499e-03 1.56395980e-01 5.53397228e-26 2.75824965e-15]

Supervised Learning

Python has several classes and objects for implementing different supervised learning techniques such as Regression and Classification.

Regardless of the model being implemented, the following methods are implemented:

The method fit() takes the training data and labels/values, and trains the model

The method predict() takes as input the test data and applies the model.

Preparing the data

To perform classification we first need to prepare the data into train and test datasets.

from sklearn.datasets import load_iris
import sklearn.utils as utils

iris = load_iris()
print("sample of data")
print(iris.data[:5,:])
print("the class labels vector")
print(iris.target)
print("the names of the classes:",iris.target_names)
print(iris.feature_names)

sample of data
[[5.1 3.5 1.4 0.2]
 [4.9 3.  1.4 0.2]
 [4.7 3.2 1.3 0.2]
 [4.6 3.1 1.5 0.2]
 [5.  3.6 1.4 0.2]]
the class labels vector
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
 2 2]
the names of the classes: ['setosa' 'versicolor' 'virginica']
['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']

Randomly shuffle the data. This is useful to know that the data is in random order

X, y = utils.shuffle(iris.data, iris.target, random_state=1) #shuffle the data
print(X.shape)
print(y.shape)
print(y)

(150, 4)
(150,)
[0 1 1 0 2 1 2 0 0 2 1 0 2 1 1 0 1 1 0 0 1 1 1 0 2 1 0 0 1 2 1 2 1 2 2 0 1
 0 1 2 2 0 2 2 1 2 0 0 0 1 0 0 2 2 2 2 2 1 2 1 0 2 2 0 0 2 0 2 2 1 1 2 2 0
 1 1 2 1 2 1 0 0 0 2 0 1 2 2 0 0 1 0 2 1 2 2 1 2 2 1 0 1 0 1 1 0 1 0 0 2 2
 2 0 0 1 0 2 0 2 2 0 2 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 2 0 0 2 1 2 1 2 2 1
 2 0]

Select a subset for training and a subset for testing

train_set_size = 100
X_train = X[:train_set_size]  # selects first 100 rows (examples) for train set
y_train = y[:train_set_size]
X_test = X[train_set_size:]   # selects from row 100 until the last one for test set
y_test = y[train_set_size:]
print(X_train.shape, y_train.shape)
print(X_test.shape, y_test.shape)

(100, 4) (100,)
(50, 4) (50,)

We can also use the train_test_split function of python for splitting the data into train and test sets. In this case you do not need the random shuffling (but it does not hurt).

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=0)

Classification models

http://scikit-learn.org/stable/supervised_learning.html#supervised-learning

Python has classes and objects that implement the different classification techniques that we described in class.

Decision Trees

http://scikit-learn.org/stable/modules/tree.html

Train and apply a decision tree classifier. The default score computed in the classifier object is the accuracy. Decision trees can also give us probabilities

from sklearn import tree

dtree = tree.DecisionTreeClassifier()
dtree = dtree.fit(X_train, y_train)

print("classifier accuracy:",dtree.score(X_test,y_test))

y_pred = dtree.predict(X_test)
y_prob = dtree.predict_proba(X_test)
print("classifier predictions:",y_pred[:10])
print("ground truth labels   :",y_test[:10])
print(y_prob[:10])

classifier accuracy: 0.9
classifier predictions: [0 1 0 1 1 0 1 0 0 2]
ground truth labels   : [0 1 0 1 1 0 1 0 0 2]
[[1. 0. 0.]
 [0. 1. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [0. 1. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [1. 0. 0.]
 [1. 0. 0.]
 [0. 0. 1.]]

Compute some more metrics

print("accuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))

accuracy: 0.9

Confusion matrix
[[19  0  0]
 [ 0 17  1]
 [ 0  4  9]]

Precision Score per class
[1.         0.80952381 0.9       ]

Average Precision Score
0.9054285714285715

Recall Score per class
[1.         0.94444444 0.69230769]

Average Recall Score
0.9

F1-score Score per class
[1.         0.87179487 0.7826087 ]

Average F1 Score
0.897324414715719

Visualize the decision tree.

For this you will need to install the package python-graphviz

#conda install python-graphviz
import graphviz 
print(iris.feature_names)
dot_data = tree.export_graphviz(dtree,out_file=None)
graph = graphviz.Source(dot_data)
graph

['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']

dtree2 = tree.DecisionTreeClassifier(max_depth=2)
dtree2 = dtree2.fit(X_train, y_train)
print(dtree2.score(X_test,y_test))
dot_data2 = tree.export_graphviz(dtree2,out_file=None)
graph2 = graphviz.Source(dot_data2)
graph2

0.9

k-NN Classification

https://scikit-learn.org/stable/modules/neighbors.html#classification

from sklearn.neighbors import KNeighborsClassifier

knn = KNeighborsClassifier(n_neighbors=3)
knn.fit(X_train,y_train)
print("classifier score:", knn.score(X_test,y_test))

y_pred = knn.predict(X_test)

print("\naccuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))

classifier score: 0.94

accuracy: 0.94

Confusion matrix
[[19  0  0]
 [ 0 16  2]
 [ 0  1 12]]

Precision Score per class
[1.         0.94117647 0.85714286]

Average Precision Score
0.9416806722689074

Recall Score per class
[1.         0.88888889 0.92307692]

Average Recall Score
0.94

F1-score Score per class
[1.         0.91428571 0.88888889]

Average F1 Score
0.9402539682539682

SVM Classification

http://scikit-learn.org/stable/modules/svm.html

http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC

from sklearn import svm

#svm_clf = svm.LinearSVC()
#svm_clf = svm.SVC(kernel = 'poly')
svm_clf = svm.SVC()
svm_clf.fit(X_train,y_train)
print("classifier score:",svm_clf.score(X_test,y_test))
y_pred = svm_clf.predict(X_test)
print("\naccuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))

classifier score: 0.98

accuracy: 0.98

Confusion matrix
[[19  0  0]
 [ 0 18  0]
 [ 0  1 12]]

Precision Score per class
[1.         0.94736842 1.        ]

Average Precision Score
0.9810526315789474

Recall Score per class
[1.         1.         0.92307692]

Average Recall Score
0.98

F1-score Score per class
[1.         0.97297297 0.96      ]

Average F1 Score
0.9798702702702704

Logistic Regression

http://scikit-learn.org/stable/modules/linear_model.html#logistic-regression

http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression

import sklearn.linear_model as linear_model

lr_clf = linear_model.LogisticRegression(solver='lbfgs')
lr_clf.fit(X_train, y_train)
print("classifier score:",lr_clf.score(X_test,y_test))
y_pred = lr_clf.predict(X_test)
print("\naccuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))

classifier score: 0.96

accuracy: 0.96

Confusion matrix
[[19  0  0]
 [ 0 17  1]
 [ 0  1 12]]

Precision Score per class
[1.         0.94444444 0.92307692]

Average Precision Score
0.96

Recall Score per class
[1.         0.94444444 0.92307692]

Average Recall Score
0.96

F1-score Score per class
[1.         0.94444444 0.92307692]

Average F1 Score
0.96

For Logistic Regression we can also obtain the probabilities for the different classes

probs = lr_clf.predict_proba(X_test)
print("Class Probabilities (first 10):")
print (probs[:10])
print(probs.argmax(axis = 1)[:10])
print(probs.max(axis = 1)[:10])

Class Probabilities (first 10):
[[9.83119371e-01 1.68804538e-02 1.75315569e-07]
 [4.02273980e-02 9.32025580e-01 2.77470222e-02]
 [9.41679973e-01 5.83196830e-02 3.44441536e-07]
 [4.23957279e-02 9.40670050e-01 1.69342220e-02]
 [2.44208893e-03 5.61707800e-01 4.35850111e-01]
 [9.56398788e-01 4.36006210e-02 5.90547605e-07]
 [2.74758774e-03 6.67193724e-01 3.30058688e-01]
 [9.59965982e-01 4.00331184e-02 8.99426873e-07]
 [9.27989281e-01 7.20096431e-02 1.07638094e-06]
 [4.80727038e-05 2.97373890e-02 9.70214538e-01]]
[0 1 0 1 1 0 1 0 0 2]
[0.98311937 0.93202558 0.94167997 0.94067005 0.5617078  0.95639879
 0.66719372 0.95996598 0.92798928 0.97021454]

And the coeffients of the logistic regression model

print(lr_clf.coef_)

[[-0.41315006  0.80862115 -2.20080165 -0.95080628]
 [ 0.07433106 -0.29229165 -0.03285585 -0.84578588]
 [ 0.338819   -0.5163295   2.2336575   1.79659216]]

Linear Regression

Linear Regression is implemented in the library sklearn.linear_model.LinearRegression: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html

from sklearn.linear_model import LinearRegression
X_reg = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])

# y = 1 * x_0 + 2 * x_1 + 3
y_reg = np.dot(X_reg, np.array([1, 2])) + 3

reg = LinearRegression().fit(X_reg, y_reg)

#Obtain the function coefficients
print(reg.coef_)
#and the intercept
print(reg.intercept_)

[1. 2.]
3.000000000000001

The $R^2$ score computes the "explained variance"

$R^2 = 1-\frac{\sum_i (y_i -\hat y_i)^2}{\sum_i (y_i -\bar y)^2}$

where $\hat y_i$ is the prediction for point $x_i$ and $\bar y$ is the mean value of the target variable

print(reg.score(X_reg, y_reg))

1.0

#Predict for a new point
reg.predict(np.array([[3, 5]]))

array([16.])

A more complex example with the diabetes dataset

diabetes_X, diabetes_y = sk_data.load_diabetes(return_X_y=True)

# Shuffle the data
diabetes_X, diabetes_y = utils.shuffle(diabetes_X, diabetes_y, random_state=1)

# Split the data into training/testing sets
diabetes_X_train = diabetes_X[:-20]
diabetes_X_test = diabetes_X[-20:]

# Split the targets into training/testing sets
diabetes_y_train = diabetes_y[:-20]
diabetes_y_test = diabetes_y[-20:]

# Create linear regression object
regr = linear_model.LinearRegression()

# Train the model using the training sets
regr.fit(diabetes_X_train, diabetes_y_train)

# Make predictions using the testing set
diabetes_y_pred = regr.predict(diabetes_X_test)

# The coefficients
print('Coefficients: \n', regr.coef_)
# The mean squared error
print('Mean squared error: %.2f'
      % metrics.mean_squared_error(diabetes_y_test, diabetes_y_pred))
# The coefficient of determination: 1 is perfect prediction
# Computed over the *test* data
print('Coefficient of determination: %.2f'
      % metrics.r2_score(diabetes_y_test, diabetes_y_pred))
print('Predictions:')
print(diabetes_y_pred)
print('True values:')
print(diabetes_y_test)

Coefficients: 
 [  -8.80343059 -238.68845774  515.45209151  329.26528155 -878.18276219
  530.03363161  126.03912568  213.28475276  734.46021416   67.32526032]
Mean squared error: 2304.97
Coefficient of determination: 0.68
Predictions:
[149.75303117 199.7656287  248.11294766 182.95040528  98.34540804
  96.66271486 248.59757565  64.84343648 234.52373522 209.30957394
 179.26665684  85.95716856  70.54292903 197.93453267 100.34630781
 116.81521079 134.97372936  64.08572743 178.32873088 155.32247369]
True values:
[168. 221. 310. 283.  81.  94. 277.  72. 270. 268. 174.  96.  83. 222.
  69. 153. 202.  43. 124. 276.]

More Evaluation

http://scikit-learn.org/stable/model_selection.html#model-selection

Computing Scores

p,r,f,s = metrics.precision_recall_fscore_support(y_test,y_pred)
print(p)
print(r)
print(f)
print(s)

[1.         0.94444444 0.90909091]
[1.         0.89473684 0.95238095]
[1.         0.91891892 0.93023256]
[20 19 21]

report = metrics.classification_report(y_test,y_pred)
print(report)

              precision    recall  f1-score   support

           0       1.00      1.00      1.00        20
           1       0.94      0.89      0.92        19
           2       0.91      0.95      0.93        21

    accuracy                           0.95        60
   macro avg       0.95      0.95      0.95        60
weighted avg       0.95      0.95      0.95        60

The breast cancer dataset

cancer_data = sk_data.load_breast_cancer()
X_cancer,y_cancer  = utils.shuffle(cancer_data.data, cancer_data.target, random_state=1)
X_cancer_train = X_cancer[:500]
y_cancer_train = y_cancer[:500]
X_cancer_test = X_cancer[500:]
y_cancer_test = y_cancer[500:]
lr_clf.fit(X_cancer_train, y_cancer_train)
print("classifier score:",lr_clf.score(X_cancer_test,y_cancer_test))

classifier score: 0.9565217391304348

C:\ProgramData\Anaconda3\lib\site-packages\sklearn\linear_model\_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.

Increase the number of iterations (max_iter) or scale the data as shown in:
    https://scikit-learn.org/stable/modules/preprocessing.html
Please also refer to the documentation for alternative solver options:
    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
  n_iter_i = _check_optimize_result(

y_cancer_pred = lr_clf.predict(X_cancer_test)
cancer_probs = lr_clf.predict_proba(X_cancer_test)
print("Class Probabilities (first 10):")
print (cancer_probs[:10])
y_cancer_scores = cancer_probs[:,1]
precision, recall, thresholds = metrics.precision_recall_curve(y_cancer_test,y_cancer_scores)
#plt.scatter(recall,precision)
plt.plot(recall,precision, color='darkorange',lw=2)
print(recall)
print(precision)
print(thresholds)

Class Probabilities (first 10):
[[5.83623551e-01 4.16376449e-01]
 [8.12467632e-03 9.91875324e-01]
 [9.99982549e-01 1.74507561e-05]
 [9.99865722e-01 1.34278348e-04]
 [2.34747296e-02 9.76525270e-01]
 [9.99977911e-01 2.20892708e-05]
 [4.76418230e-03 9.95235818e-01]
 [1.58051254e-03 9.98419487e-01]
 [1.92164273e-03 9.98078357e-01]
 [6.68784558e-02 9.33121544e-01]]
[1.         0.97619048 0.97619048 0.97619048 0.95238095 0.92857143
 0.9047619  0.88095238 0.85714286 0.83333333 0.80952381 0.78571429
 0.76190476 0.76190476 0.73809524 0.71428571 0.69047619 0.66666667
 0.64285714 0.61904762 0.5952381  0.57142857 0.54761905 0.52380952
 0.5        0.47619048 0.45238095 0.42857143 0.4047619  0.38095238
 0.35714286 0.33333333 0.30952381 0.28571429 0.26190476 0.23809524
 0.21428571 0.19047619 0.16666667 0.14285714 0.11904762 0.0952381
 0.07142857 0.04761905 0.02380952 0.        ]
[0.93333333 0.93181818 0.95348837 0.97619048 0.97560976 0.975
 0.97435897 0.97368421 0.97297297 0.97222222 0.97142857 0.97058824
 0.96969697 1.         1.         1.         1.         1.
 1.         1.         1.         1.         1.         1.
 1.         1.         1.         1.         1.         1.
 1.         1.         1.         1.         1.         1.
 1.         1.         1.         1.         1.         1.
 1.         1.         1.         1.        ]
[0.41637645 0.45961289 0.64904253 0.76657569 0.8447832  0.84825656
 0.85098092 0.9294684  0.93139622 0.93312154 0.93363838 0.94123622
 0.94572607 0.95397177 0.96059207 0.97652527 0.97880602 0.98474267
 0.98859163 0.98905238 0.99076026 0.99187532 0.99268795 0.99280117
 0.99284629 0.99335073 0.99495779 0.99523582 0.99535911 0.99536585
 0.996111   0.99721763 0.99738661 0.99802571 0.99807836 0.99841949
 0.99923125 0.99935453 0.99947798 0.99958699 0.99970989 0.99973228
 0.99978195 0.99979392 0.99986458]

fpr, tpr, ths = metrics.roc_curve(y_cancer_test,y_cancer_scores)
plt.plot(fpr,tpr,color='darkorange',lw=2)
print(metrics.roc_auc_score(y_cancer_test,y_cancer_scores))
plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver operating characteristic example')
plt.legend(loc="lower right")
plt.show()

No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.

0.9894179894179893

(Xtoy,y_toy)=sk_data.make_classification(n_samples=10000)
Xttrain = Xtoy[:8000,:]
Xttest = Xtoy[8000:,:]
yttrain = y_toy[:8000]
yttest = y_toy[8000:]

lr_clf.fit(Xttrain, yttrain)
#print(lr_clf.score(Xttest,yttest))
#y_tpred = lr_clf.predict(X_test)
tprobs = lr_clf.predict_proba(Xttest)
print (tprobs[:10])

y_tscores = tprobs[:,1]
precision, recall, thresholds = metrics.precision_recall_curve(yttest,y_tscores)
plt.plot(recall,precision)

[[3.20037592e-01 6.79962408e-01]
 [2.41985792e-01 7.58014208e-01]
 [5.75281926e-04 9.99424718e-01]
 [1.15252186e-01 8.84747814e-01]
 [2.67997941e-03 9.97320021e-01]
 [9.81477901e-01 1.85220986e-02]
 [9.96589111e-01 3.41088910e-03]
 [1.56750808e-02 9.84324919e-01]
 [9.13521526e-01 8.64784739e-02]
 [2.78398414e-01 7.21601586e-01]]

[<matplotlib.lines.Line2D at 0x285cad19d00>]

k-fold cross validation

In k-fold cross validation the data is split into k equal parts, the k-1 are used for training and the last one for testing. k models are trained, each time leaving a different part for testing

https://scikit-learn.org/stable/modules/cross_validation.html

There are two methods for implementing k-fold cross-validation, under the library model selection: cross_val_score, and cross validate. The latter allows multiple metrics to be considered together.

import sklearn.model_selection as model_selection

scores = model_selection.cross_val_score(#lr_clf,
                                          #svm_clf,
                                          #knn,
                                          dtree,
                                          X,
                                          y,
                                          scoring='f1_weighted',
                                          cv=5)
print (scores)
print (scores.mean())

[1.         0.93333333 0.96658312 0.96658312 0.93265993]
0.9598319029897977

scores = model_selection.cross_validate(#lr_clf,
                                          #svm_clf,
                                          #knn,
                                          dtree,
                                          X,
                                          y,
                                          scoring=['precision_weighted','recall_weighted'],
                                          cv=3)
print (scores)
print (scores['test_precision_weighted'].mean(),scores['test_recall_weighted'].mean())

{'fit_time': array([0.00199866, 0.00099945, 0.00099945]), 'score_time': array([0.00300002, 0.0039959 , 0.00399733]), 'test_precision_weighted': array([0.96      , 0.98111111, 0.88308772]), 'test_recall_weighted': array([0.96, 0.98, 0.88])}
0.9413996101364522 0.94

Creating a pipeline

If the same steps are often repeated, you can create a pipeline to perform them all at once:

https://scikit-learn.org/stable/modules/generated/sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline

Text classification Example

We will use the 20 newsgroups to do a text classification example

from sklearn.datasets import fetch_20newsgroups

categories = ['sci.space','rec.sport.baseball']
#categories = ['alt.atheism', 'rec.sport.baseball']
news_train = sk_data.fetch_20newsgroups(subset='train', 
                               remove=('headers', 'footers', 'quotes'),
                               categories=categories)
print (len(news_train.target))
X_news_train_data = news_train.data
y_news_train = news_train.target
news_test = sk_data.fetch_20newsgroups(subset='test', 
                               remove=('headers', 'footers', 'quotes'),
                               categories=categories)
print (len(news_test.target))
X_news_test_data = news_test.data
y_news_test = news_test.target

1190
791

from sklearn.linear_model import LinearRegression
import sklearn.linear_model as linear_model

import sklearn.feature_extraction.text as sk_text

vectorizer = sk_text.TfidfVectorizer(stop_words='english',
                             #max_features = 1000,
                             min_df=4, max_df=0.8)
X_news_train = vectorizer.fit_transform(X_news_train_data)

lr_clf = linear_model.LogisticRegression(solver='lbfgs')
lr_clf.fit(X_news_train, y_news_train)

LogisticRegression()

X_news_test = vectorizer.transform(X_news_test_data)
print("classifier score:",lr_clf.score(X_news_test,y_news_test))

classifier score: 0.9216182048040455

Word embeddings and Text classification

We will now see how we can train and use word embeddings. We will also see the NLTK library.

The NLTK libary allows for sohpisticated text processing. It can do stemming, create a parse tree, do PoS (Part-of-Speech) tagging, find Noun Phrases, entities,

import nltk
from nltk.tokenize import sent_tokenize, word_tokenize 

nltk.download('punkt')

[nltk_data] Downloading package punkt to
[nltk_data]     C:\Users\tsap\AppData\Roaming\nltk_data...
[nltk_data]   Package punkt is already up-to-date!

True

from nltk.corpus import stopwords
nltk.download('stopwords')

[nltk_data] Downloading package stopwords to
[nltk_data]     C:\Users\tsap\AppData\Roaming\nltk_data...
[nltk_data]   Package stopwords is already up-to-date!

True

english_stop_words = set(stopwords.words('english'))

import string as string

X_news_train_nltk = []
y_news_train_nltk = []
for x,y in zip(X_news_train_data,y_news_train):
    wt = word_tokenize(x.lower())
    doc = [w for w in wt if (w not in string.punctuation)] #keep stopwords to maintain realistic windows
    if len(doc) == 0: continue
    X_news_train_nltk.append(doc)
    y_news_train_nltk.append(y)

X_news_test_nltk = []
y_news_test_nltk = []

for x,y in zip(X_news_test_data,y_news_test):
    wt = word_tokenize(x.lower())
    doc = [w for w in wt if (w not in english_stop_words) and (w not in string.punctuation)]
    if len(doc) == 0: continue    
    X_news_test_nltk.append(doc)
    y_news_test_nltk.append(y)

The Gensim library

The Gensim library has several NLP models.

You can use existing modules to train a word2vec model: https://radimrehurek.com/gensim/models/word2vec.html

import gensim 
from gensim.models import Word2Vec

Train a CBOW embedding on the training data corpus

embedding_size = 100
cbow_model = gensim.models.Word2Vec(X_news_train_nltk, min_count = 1,size = embedding_size, window = 50) 

cbow_model.wv['space']

array([ 1.3626347e+00, -9.1802186e-01, -1.2189058e+00,  1.5490552e+00,
        1.7962173e-01, -1.8228947e-01,  7.4095041e-01, -8.6752933e-01,
        1.3819387e+00,  2.0274465e+00,  1.5030596e+00, -2.3670770e-01,
       -1.2707617e+00, -4.9571109e+00, -1.6571654e+00, -1.3996867e+00,
       -1.7083026e+00,  3.5763342e+00, -2.5275729e+00, -2.5971494e+00,
        3.9501324e-01,  1.7998517e+00,  5.9064204e-01, -1.9885430e+00,
       -8.9505285e-01, -8.8297492e-01, -5.8066773e-01,  7.0249361e-01,
       -2.8329668e+00,  2.7226403e-02,  2.1891525e+00, -3.5315511e+00,
       -3.0630670e+00, -1.1466244e+00,  3.7846091e+00,  2.0086968e+00,
        1.9489932e+00, -1.6308918e+00, -1.1899316e+00,  4.3927424e-02,
        2.0978633e-01,  1.5178644e-02, -6.9894773e-01,  1.9074910e+00,
        2.2619994e+00, -7.9161793e-01, -4.6662375e-01, -9.8577952e-01,
       -2.4329665e+00,  1.4078501e+00,  1.1600374e+00, -2.3742394e+00,
       -9.3097404e-02,  6.5130818e-01, -1.2857968e+00, -5.8206248e-01,
        3.7721002e-01, -2.0370612e+00, -1.6875947e+00,  8.9556985e-02,
       -1.2133864e+00,  1.4314138e+00,  1.0795940e+00,  2.3002479e+00,
       -5.1381910e-01, -1.7463471e+00, -1.6618823e+00,  1.0985827e+00,
        3.5473592e+00,  3.2078640e+00, -4.4867676e-01,  1.1440036e+00,
       -1.1076572e+00, -4.0362340e-01, -2.7313380e+00, -2.1890466e+00,
        1.9209883e+00,  1.2227294e+00,  4.0881285e-01,  1.1249651e+00,
        4.1052680e+00,  2.2416701e+00,  1.3895382e+00,  2.2879393e+00,
        6.7056608e-01, -2.0860527e+00,  2.4072058e-03, -6.8389457e-01,
       -2.4418426e+00, -2.1619756e+00, -4.3392124e+00, -3.3873751e+00,
        3.1392505e+00, -3.9485118e+00,  6.2412542e-01, -1.4656785e+00,
       -2.8676972e+00,  3.8035398e+00,  1.0140551e-01,  1.9707490e+00],
      dtype=float32)

Transform the train and test data

X_news_train_cbow = []
for x in X_news_train_nltk:
    vx = np.zeros(embedding_size)
    x = [w for w in x if w not in english_stop_words] # we could remove stopwords
    for w in x:   
        vx += cbow_model.wv[w]
    if len(x) >0: vx /= len(x)
    X_news_train_cbow.append(vx)

X_news_test_cbow = []
for x in X_news_test_nltk:
    vx = np.zeros(embedding_size)
    length = 0;
    for w in x: 
        if (w not in cbow_model.wv): continue
        length += 1
        vx += cbow_model.wv[w]
    if length != 0: vx /= length
    X_news_test_cbow.append(vx)

Train a classifier on the emebddings

lr_clf.fit(np.array(X_news_train_cbow), np.array(y_news_train_nltk))

LogisticRegression()

lr_clf.score(np.array(X_news_test_cbow),y_news_test_nltk)

0.8302631578947368

Train a SkipGram embedding on the training data corpus

embedding_size = 100
skipgram_model = gensim.models.Word2Vec(X_news_train_nltk, min_count = 1,size = embedding_size, window = 50, sg = 1) 

Transform the train and test data

X_news_train_skipgram = []
for x in X_news_train_nltk:
    vx = np.zeros(embedding_size)
    for w in x: 
        vx += skipgram_model.wv[w]
    vx /= len(x)
    X_news_train_skipgram.append(vx)

X_news_test_skipgram = []
for x in X_news_test_nltk:
    vx = np.zeros(embedding_size)
    length = 0
    for w in x: 
        if (w not in skipgram_model.wv): continue
        length += 1
        vx += skipgram_model.wv[w]
    if length!= 0: vx /= length
    X_news_test_skipgram.append(vx)

Train a classifier on the emebddings

lr_clf.fit(np.array(X_news_train_skipgram), np.array(y_news_train_nltk))

lr_clf.score(np.array(X_news_test_skipgram),y_news_test_nltk)

0.9355263157894737

You can also download the Google word2vec model trained over millions of documents

import gensim.downloader as api
path = api.load("word2vec-google-news-300", return_path=True)
print(path)

[==================================================] 100.0% 1662.8/1662.8MB downloaded
C:\Users\tsap/gensim-data\word2vec-google-news-300\word2vec-google-news-300.gz

#path = 'C:\\Users\\tsapa/gensim-data\word2vec-google-news-300\word2vec-google-news-300.gz'
g_model = gensim.models.KeyedVectors.load_word2vec_format(path, binary=True)  

print(len(g_model['hello']))
print(g_model['hello'])

300
[-0.05419922  0.01708984 -0.00527954  0.33203125 -0.25       -0.01397705
 -0.15039062 -0.265625    0.01647949  0.3828125  -0.03295898 -0.09716797
 -0.16308594 -0.04443359  0.00946045  0.18457031  0.03637695  0.16601562
  0.36328125 -0.25585938  0.375       0.171875    0.21386719 -0.19921875
  0.13085938 -0.07275391 -0.02819824  0.11621094  0.15332031  0.09082031
  0.06787109 -0.0300293  -0.16894531 -0.20800781 -0.03710938 -0.22753906
  0.26367188  0.012146    0.18359375  0.31054688 -0.10791016 -0.19140625
  0.21582031  0.13183594 -0.03515625  0.18554688 -0.30859375  0.04785156
 -0.10986328  0.14355469 -0.43554688 -0.0378418   0.10839844  0.140625
 -0.10595703  0.26171875 -0.17089844  0.39453125  0.12597656 -0.27734375
 -0.28125     0.14746094 -0.20996094  0.02355957  0.18457031  0.00445557
 -0.27929688 -0.03637695 -0.29296875  0.19628906  0.20703125  0.2890625
 -0.20507812  0.06787109 -0.43164062 -0.10986328 -0.2578125  -0.02331543
  0.11328125  0.23144531 -0.04418945  0.10839844 -0.2890625  -0.09521484
 -0.10351562 -0.0324707   0.07763672 -0.13378906  0.22949219  0.06298828
  0.08349609  0.02929688 -0.11474609  0.00534058 -0.12988281  0.02514648
  0.08789062  0.24511719 -0.11474609 -0.296875   -0.59375    -0.29492188
 -0.13378906  0.27734375 -0.04174805  0.11621094  0.28320312  0.00241089
  0.13867188 -0.00683594 -0.30078125  0.16210938  0.01171875 -0.13867188
  0.48828125  0.02880859  0.02416992  0.04736328  0.05859375 -0.23828125
  0.02758789  0.05981445 -0.03857422  0.06933594  0.14941406 -0.10888672
 -0.07324219  0.08789062  0.27148438  0.06591797 -0.37890625 -0.26171875
 -0.13183594  0.09570312 -0.3125      0.10205078  0.03063965  0.23632812
  0.00582886  0.27734375  0.20507812 -0.17871094 -0.31445312 -0.01586914
  0.13964844  0.13574219  0.0390625  -0.29296875  0.234375   -0.33984375
 -0.11816406  0.10644531 -0.18457031 -0.02099609  0.02563477  0.25390625
  0.07275391  0.13574219 -0.00138092 -0.2578125  -0.2890625   0.10107422
  0.19238281 -0.04882812  0.27929688 -0.3359375  -0.07373047  0.01879883
 -0.10986328 -0.04614258  0.15722656  0.06689453 -0.03417969  0.16308594
  0.08642578  0.44726562  0.02026367 -0.01977539  0.07958984  0.17773438
 -0.04370117 -0.00952148  0.16503906  0.17285156  0.23144531 -0.04272461
  0.02355957  0.18359375 -0.41601562 -0.01745605  0.16796875  0.04736328
  0.14257812  0.08496094  0.33984375  0.1484375  -0.34375    -0.14160156
 -0.06835938 -0.14648438 -0.02844238  0.07421875 -0.07666016  0.12695312
  0.05859375 -0.07568359 -0.03344727  0.23632812 -0.16308594  0.16503906
  0.1484375  -0.2421875  -0.3515625  -0.30664062  0.00491333  0.17675781
  0.46289062  0.14257812 -0.25       -0.25976562  0.04370117  0.34960938
  0.05957031  0.07617188 -0.02868652 -0.09667969 -0.01281738  0.05859375
 -0.22949219 -0.1953125  -0.12207031  0.20117188 -0.42382812  0.06005859
  0.50390625  0.20898438  0.11230469 -0.06054688  0.33203125  0.07421875
 -0.05786133  0.11083984 -0.06494141  0.05639648  0.01757812  0.08398438
  0.13769531  0.2578125   0.16796875 -0.16894531  0.01794434  0.16015625
  0.26171875  0.31640625 -0.24804688  0.05371094 -0.0859375   0.17089844
 -0.39453125 -0.00156403 -0.07324219 -0.04614258 -0.16210938 -0.15722656
  0.21289062 -0.15820312  0.04394531  0.28515625  0.01196289 -0.26953125
 -0.04370117  0.37109375  0.04663086 -0.19726562  0.3046875  -0.36523438
 -0.23632812  0.08056641 -0.04248047 -0.14648438 -0.06225586 -0.0534668
 -0.05664062  0.18945312  0.37109375 -0.22070312  0.04638672  0.02612305
 -0.11474609  0.265625   -0.02453613  0.11083984 -0.02514648 -0.12060547
  0.05297852  0.07128906  0.00063705 -0.36523438 -0.13769531 -0.12890625]

Transform the train and test data

X_news_train_gmodel = []
for x in X_news_train_nltk:
    vx = np.zeros(300)
    length = 0
    for w in x: 
        if w in g_model:
            length += 1
            vx += g_model[w]
    if length != 0: vx /= length
    X_news_train_gmodel.append(vx)

X_news_test_gmodel = []
for x in X_news_test_nltk:
    vx = np.zeros(300)
    length = 0
    for w in x: 
        if (w not in g_model): continue
        length += 1
        vx += g_model[w]
    if length != 0: vx /= length
    X_news_test_gmodel.append(vx)

Train a classifier on the emebddings

lr_clf.fit(X_news_train_gmodel, np.array(y_news_train_nltk))

LogisticRegression()

lr_clf.score(np.array(X_news_test_gmodel),y_news_test_nltk)

0.9447368421052632