Comparing classifiers (including Bayesian networks) with scikit-learn
In this notebook, we use the skbn module to insert bayesian networks into some examples from the scikit-learn documentation (that we refer).
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In [1]:
import pyAgrum as gum
import pyAgrum.lib.notebook as gnb
from pyAgrum.skbn import BNClassifier
Binary classifiers
In [2]:
# From https://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html)
# Code source: Gael Varoquaux
# Andreas Muller
# Modified for documentation by Jaques Grobler
# License: BSD 3 clause
In [3]:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patheffects as pe
from matplotlib.colors import ListedColormap
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import make_moons, make_circles, make_classification
from sklearn.neural_network import MLPClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier, AdaBoostClassifier
from sklearn.naive_bayes import GaussianNB
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
In [4]:
# the data
X, y = make_classification(n_features=2, n_redundant=0, n_informative=2,
random_state=1, n_clusters_per_class=1)
rng = np.random.RandomState(2)
X += 2 * rng.uniform(size=X.shape)
linearly_separable = (X, y)
datasets = [make_moons(noise=0.3, random_state=0),
make_circles(noise=0.2, factor=0.5, random_state=1),
linearly_separable
]
datasets_name=['Moons ',
'Circle',
'LinSep']
In [5]:
def showComparison(names,classifiers,datasets,datasets_name):# the results
bnres=[None]*len(datasets_name)
h = .02 # step size in the mesh
fs=6
figure = plt.figure(figsize=(12, 4))
i = 1
# iterate over datasets
for ds_cnt, ds in enumerate(datasets):
print(datasets_name[ds_cnt]+' : ',end='')
# preprocess dataset, split into training and test part
X, y = ds
X = StandardScaler().fit_transform(X)
X_train, X_test, y_train, y_test = \
train_test_split(X, y, test_size=.4, random_state=42)
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# just plot the dataset first
cm = plt.cm.RdBu
cm_bright = ListedColormap(['#FF0000', '#0000FF'])
ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
if ds_cnt == 0:
ax.set_title("Input data",fontsize=fs)
ax.set_ylabel(datasets_name[ds_cnt])
# Plot the training points
ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright,
edgecolors='k',marker=".")
# Plot the testing points
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.6,
edgecolors='k',marker=".")
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xticks(())
ax.set_yticks(())
i += 1
# iterate over classifiers
for name, clf in zip(names, classifiers):
print(".",end="",flush=True)
ax = plt.subplot(len(datasets), len(classifiers) + 1, i)
clf.fit(X_train, y_train)
score = clf.score(X_test, y_test)
# 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].
if hasattr(clf, "decision_function"):
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
else:
Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
# Put the result into a color plot
Z = Z.reshape(xx.shape)
ax.contourf(xx, yy, Z, cmap=cm, alpha=.7)
# Plot the training points
#ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright,
# edgecolors='k', alpha=0.2,marker='.')
# Plot the testing points
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright,
edgecolors='k',marker='.')
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xticks(())
ax.set_yticks(())
if ds_cnt == 0:
ax.set_title(name,fontsize=fs)
ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
size=12, horizontalalignment='right',color="white",
path_effects=[pe.withStroke(linewidth=2, foreground="black")])
i += 1
bnres[ds_cnt]=gum.BayesNet(classifiers[-1].bn)
print()
plt.tight_layout()
plt.show()
return bnres
In [6]:
# the classifiers
names = ["Nearest Neighbors", "Linear SVM", "RBF SVM", "Gaussian Process",
"Decision Tree", "Random Forest", "Neural Net", "AdaBoost",
"Naive Bayes", "QDA","BNClassifier"
]
classifiers = [
KNeighborsClassifier(3),
SVC(kernel="linear", C=0.025),
SVC(gamma=2, C=1),
GaussianProcessClassifier(1.0 * RBF(1.0)),
DecisionTreeClassifier(max_depth=5),
RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1),
MLPClassifier(alpha=1, max_iter=1000),
AdaBoostClassifier(),
GaussianNB(),
QuadraticDiscriminantAnalysis(),
BNClassifier(learningMethod='MIIC', prior='Smoothing', priorWeight=0.01, discretizationNbBins=5,
discretizationStrategy="kmeans", # 'kmeans', 'uniform', 'quantile', 'NML', 'MDLP', 'CAIM', 'NoDiscretization'
usePR=False)
]
bnres=showComparison(names,classifiers,datasets,datasets_name)
Moons : ...........
/Users/phw/.virtualenvs/devAgrum/lib/python3.12/site-packages/sklearn/ensemble/_weight_boosting.py:527: FutureWarning: The SAMME.R algorithm (the default) is deprecated and will be removed in 1.6. Use the SAMME algorithm to circumvent this warning.
warnings.warn(
Circle : ...........
/Users/phw/.virtualenvs/devAgrum/lib/python3.12/site-packages/sklearn/ensemble/_weight_boosting.py:527: FutureWarning: The SAMME.R algorithm (the default) is deprecated and will be removed in 1.6. Use the SAMME algorithm to circumvent this warning.
warnings.warn(
LinSep : ...........
/Users/phw/.virtualenvs/devAgrum/lib/python3.12/site-packages/sklearn/ensemble/_weight_boosting.py:527: FutureWarning: The SAMME.R algorithm (the default) is deprecated and will be removed in 1.6. Use the SAMME algorithm to circumvent this warning.
warnings.warn(
The three BNs learned for each task:
In [7]:
gnb.sideBySide(*bnres,captions=datasets_name)
Note that, for LinSep, the BNClassifier has correctly learned that \(x1\) and \(y\) are independent (no need of \(x1\) to predict \(y\)). \(x1\) is not a relevant feature for this classification.
### A zoom of one of this BN classifiers
In [8]:
h=0.2
ds=make_moons(noise=0.3, random_state=0)
X, y = ds
X = StandardScaler().fit_transform(X)
X_train, X_test, y_train, y_test =train_test_split(X, y, test_size=.4, random_state=42)
x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
clf=BNClassifier(learningMethod='MIIC', prior='Smoothing', priorWeight=0.01, discretizationNbBins=5,discretizationStrategy="kmeans",usePR=False)
clf.fit(X_train,y_train)
score = clf.score(X_test, y_test)
Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]
clf.bn
Z = Z.reshape(xx.shape)
ax = plt.subplot(1, 1,1)
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xticks(())
ax.set_yticks(())
ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, alpha=0.6,edgecolors='k',marker=".")
ax.contourf(xx, yy, Z, alpha=.7)
ax.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),
size=12, horizontalalignment='right',color="white",
path_effects=[pe.withStroke(linewidth=2, foreground="black")]);
n-ary classifiers on IRIS dataset
In [9]:
# From https://scikit-learn.org/stable/auto_examples/classification/plot_classification_probability.html#sphx-glr-auto-examples-classification-plot-classification-probability-py
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# License: BSD 3 clause
In [10]:
import matplotlib.pyplot as plt
import numpy as np
from sklearn.metrics import accuracy_score
from sklearn.linear_model import LogisticRegression
from sklearn.svm import SVC
from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF
from sklearn import datasets
iris = datasets.load_iris()
X = iris.data[:, 0:2] # we only take the first two features for visualization
y = iris.target
n_features = X.shape[1]
C = 10
kernel = 1.0 * RBF([1.0, 1.0]) # for GPC
# Create different classifiers.
classifiers = {
'L1 logistic': LogisticRegression(C=C, penalty='l1',
solver='saga',
multi_class='multinomial',
max_iter=10000),
'L2 logistic (Multinomial)': LogisticRegression(C=C, penalty='l2',
solver='saga',
multi_class='multinomial',
max_iter=10000),
'L2 logistic (OvR)': LogisticRegression(C=C, penalty='l2',
solver='saga',
multi_class='ovr',
max_iter=10000),
'Linear SVC': SVC(kernel='linear', C=C, probability=True,random_state=0),
# 'GPC': GaussianProcessClassifier(kernel), # too long
'BN' : BNClassifier(learningMethod='MIIC',
prior='Smoothing', priorWeight=1,
discretizationNbBins=9,
discretizationStrategy="quantile",
discretizationThreshold=10)
}
n_classifiers = len(classifiers)
plt.figure(figsize=(3 * 2, n_classifiers * 2))
plt.subplots_adjust(bottom=.2, top=.95)
xx = np.linspace(3, 9, 100)
yy = np.linspace(1, 5, 100).T
xx, yy = np.meshgrid(xx, yy)
Xfull = np.c_[xx.ravel(), yy.ravel()]
for index, (name, classifier) in enumerate(classifiers.items()):
classifier.fit(X, y)
y_pred = classifier.predict(X)
accuracy = accuracy_score(y, y_pred)
print("Accuracy (train) for %s: %0.1f%% " % (name, accuracy * 100))
# View probabilities:
probas = classifier.predict_proba(Xfull)
n_classes = np.unique(y_pred).size
for k in range(n_classes):
plt.subplot(n_classifiers, n_classes, index * n_classes + k + 1)
plt.title("Class %d" % k)
if k == 0:
plt.ylabel(name)
imshow_handle = plt.imshow(probas[:, k].reshape((100, 100)),
extent=(3, 9, 1, 5), origin='lower')
plt.xticks(())
plt.yticks(())
idx = (y_pred == k)
if idx.any():
plt.scatter(X[idx, 0], X[idx, 1], marker='o', c='w', edgecolor='k')
ax = plt.axes([0.15, 0.04, 0.7, 0.05])
plt.title("Probability")
plt.colorbar(imshow_handle, cax=ax, orientation='horizontal')
plt.show()
/Users/phw/.virtualenvs/devAgrum/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:1247: FutureWarning: 'multi_class' was deprecated in version 1.5 and will be removed in 1.7. From then on, it will always use 'multinomial'. Leave it to its default value to avoid this warning.
warnings.warn(
/Users/phw/.virtualenvs/devAgrum/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:1247: FutureWarning: 'multi_class' was deprecated in version 1.5 and will be removed in 1.7. From then on, it will always use 'multinomial'. Leave it to its default value to avoid this warning.
warnings.warn(
/Users/phw/.virtualenvs/devAgrum/lib/python3.12/site-packages/sklearn/linear_model/_logistic.py:1256: FutureWarning: 'multi_class' was deprecated in version 1.5 and will be removed in 1.7. Use OneVsRestClassifier(LogisticRegression(..)) instead. Leave it to its default value to avoid this warning.
warnings.warn(
Accuracy (train) for L1 logistic: 82.7%
Accuracy (train) for L2 logistic (Multinomial): 82.7%
Accuracy (train) for L2 logistic (OvR): 79.3%
Accuracy (train) for Linear SVC: 82.0%
Accuracy (train) for BN: 83.3%
So the BNClassifier gives the ‘best’ accuracy (even if discretized). Moreover, once again, it propose a structural representation of the classification mechanism.
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classifiers['BN'].bn
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Recognizing hand-written digits with Bayesian Networks
In [12]:
#From https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html#sphx-glr-auto-examples-classification-plot-digits-classification-py
# Author: Gael Varoquaux <gael dot varoquaux at normalesup dot org>
# License: BSD 3 clause
In [13]:
# Standard scientific Python imports
import matplotlib.pyplot as plt
# Import datasets, classifiers and performance metrics
from sklearn import datasets, metrics
from sklearn.model_selection import train_test_split
digits = datasets.load_digits()
_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))
for ax, image, label in zip(axes, digits.images, digits.target):
ax.set_axis_off()
ax.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
ax.set_title('Training: %i' % label)
In [14]:
# flatten the images
n_samples = len(digits.images)
data = digits.images.reshape((n_samples, -1)).astype(int)
# Create a classifier: a support vector classifier
#clf = svm.SVC(gamma=0.001)
clf = BNClassifier(learningMethod='MIIC', prior='Smoothing', priorWeight=1,
discretizationNbBins=3,discretizationStrategy="kmeans",discretizationThreshold=10)
# Split data into 50% train and 50% test subsets
X_train, X_test, y_train, y_test = train_test_split(
data, digits.target, test_size=0.5, shuffle=False)
# Learn the digits on the train subset
clf.fit(X_train, y_train)
# Predict the value of the digit on the test subset
predicted = clf.predict(X_test)
_, axes = plt.subplots(nrows=1, ncols=4, figsize=(10, 3))
for ax, image, prediction in zip(axes, X_test, predicted):
ax.set_axis_off()
image = image.reshape(8, 8)
ax.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
ax.set_title(f'Prediction: {int(prediction)}')
cm = metrics.confusion_matrix(y_test, predicted)
disp = metrics.ConfusionMatrixDisplay(confusion_matrix=cm)
disp.plot()
plt.show()
print(f"Classification report for classifier {clf}:\n"
f"{metrics.classification_report(y_test, predicted)}\n")
Classification report for classifier BNClassifier(discretizationNbBins=3, discretizationStrategy='kmeans',
discretizationThreshold=10, prior='Smoothing'):
precision recall f1-score support
0 0.98 0.95 0.97 88
1 0.86 0.80 0.83 91
2 0.91 0.85 0.88 86
3 0.84 0.80 0.82 91
4 0.99 0.91 0.95 92
5 0.79 0.82 0.81 91
6 0.95 0.95 0.95 91
7 0.89 0.90 0.89 89
8 0.79 0.76 0.77 88
9 0.72 0.90 0.80 92
accuracy 0.87 899
macro avg 0.87 0.87 0.87 899
weighted avg 0.87 0.87 0.87 899
Focus on the pixels needed for the classification
As always, using BNClassifier make us learn a bit more about the structure of the problem.
In [15]:
gnb.show(clf.bn,size="13!")
Then, once again, the Markov Blanket gives us the relevant features (here the pixels)
In [16]:
print("Markov blanket of the classifier:")
gnb.show(clf.MarkovBlanket,size="14!")
print(f"Number of pixels used for classification : {clf.MarkovBlanket.size()-1}/64")
Markov blanket of the classifier:
Number of pixels used for classification : 33/64
It appears that many pixels are not relevant for this classification.
In [17]:
#Visualization of the pixels of the Markov Blanket
fig, ax = plt.subplots()
ax.set_axis_off()
relevant_pixels = set([int(x[1:]) for x in clf.MarkovBlanket.names() if x!='y'])
ax.imshow(np.array([1 if i in relevant_pixels else 0 for i in range(64)]).reshape(8,8),
cmap=plt.cm.gray_r)
plt.show()
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