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).

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

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.naive_bayes import GaussianNB

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=(10, 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),
GaussianNB(),
BNClassifier(learningMethod='MIIC', prior='Smoothing', priorWeight=1, discretizationNbBins=5,
discretizationStrategy="uniform", # 'kmeans', 'uniform', 'quantile', 'NML', 'MDLP', 'CAIM', 'NoDiscretization'
usePR=False)
]

bnres=showComparison(names,classifiers,datasets,datasets_name)

Moons  : ...........
Circle : ...........
LinSep : ...........


The three BNs learned for each task:

In [7]:

gnb.sideBySide(*bnres,captions=datasets_name)

 G x0 x0 y y x0->y x1 x1 x1->y Moons G x0 x0 y y x0->y x1 x1 x1->y Circle G x0 x0 y y x0->y x1 x1 LinSep

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=1, discretizationNbBins=5,discretizationStrategy="uniform",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>

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

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),
'BN' : BNClassifier(learningMethod='MIIC',
prior='Smoothing', priorWeight=1,
discretizationNbBins=6,
discretizationStrategy="kmeans",
discretizationThreshold=10)
}

n_classifiers = len(classifiers)

plt.figure(figsize=(3 * 2, n_classifiers * 2))

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()

Accuracy (train) for L1 logistic: 83.3%
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 GPC: 82.7%
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.

In [11]:

classifiers['BN'].bn

Out[11]:


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>

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

_, 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, learningMethod='MIIC',
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()