About

This notebook demonstrates stacking machine learning algorithm - folding, which physics use in their analysis.



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

Loading data

download particle identification Data Set from UCI



In [2]:

    
!cd toy_datasets; wget -O MiniBooNE_PID.txt -nc MiniBooNE_PID.txt https://archive.ics.uci.edu/ml/machine-learning-databases/00199/MiniBooNE_PID.txt









    



File `MiniBooNE_PID.txt' already there; not retrieving.



In [3]:

    
import numpy, pandas
from rep.utils import train_test_split
from sklearn.metrics import roc_auc_score

data = pandas.read_csv('toy_datasets/MiniBooNE_PID.txt', sep='\s*', skiprows=[0], header=None, engine='python')
labels = pandas.read_csv('toy_datasets/MiniBooNE_PID.txt', sep=' ', nrows=1, header=None)
labels = [1] * labels[1].values[0] + [0] * labels[2].values[0]
data.columns = ['feature_{}'.format(key) for key in data.columns]

train_data, test_data, train_labels, test_labels = train_test_split(data, labels, train_size=0.5)

Training variables



In [4]:

    
variables = list(data.columns)

Folding strategy - stacking algorithm

It implements the same interface as all classifiers, but with some difference:

all prediction methods have additional parameter "vote_function" (example folder.predict(X, vote_function=None)), which is used to combine all classifiers' predictions. By default "mean" is used as "vote_function"



In [5]:

    
from rep.estimators import SklearnClassifier
from sklearn.ensemble import GradientBoostingClassifier

Define folding model



In [6]:

    
from rep.metaml import FoldingClassifier



In [7]:

    
n_folds = 4
folder = FoldingClassifier(GradientBoostingClassifier(), n_folds=n_folds, features=variables)
folder.fit(train_data, train_labels)









    Out[7]:





FoldingClassifier(base_estimator=GradientBoostingClassifier(init=None, learning_rate=0.1, loss='deviance',
              max_depth=3, max_features=None, max_leaf_nodes=None,
              min_samples_leaf=1, min_samples_split=2,
              min_weight_fraction_leaf=0.0, n_estimators=100,
              random_state=None, subsample=1.0, verbose=0,
              warm_start=False),
         features=['feature_0', 'feature_1', 'feature_2', 'feature_3', 'feature_4', 'feature_5', 'feature_6', 'feature_7', 'feature_8', 'feature_9', 'feature_10', 'feature_11', 'feature_12', 'feature_13', 'feature_14', 'feature_15', 'feature_16', 'feature_17', 'feature_18', 'feature_19', 'feature_20', 'featu...', 'feature_43', 'feature_44', 'feature_45', 'feature_46', 'feature_47', 'feature_48', 'feature_49'],
         ipc_profile=None, n_folds=4, random_state=None)

Default prediction (predict ith fold by ith classifier)



In [8]:

    
folder.predict_proba(train_data)









    



KFold prediction using folds column






    Out[8]:





array([[ 0.96744155,  0.03255845],
       [ 0.9254746 ,  0.0745254 ],
       [ 0.98048878,  0.01951122],
       ..., 
       [ 0.98744345,  0.01255655],
       [ 0.99227938,  0.00772062],
       [ 0.02780023,  0.97219977]])

Voting prediction (predict i-fold by all classifiers and take value, which is calculated by `vote_function`)



In [9]:

    
# definition of mean function, which combines all predictions
def mean_vote(x):
    return numpy.mean(x, axis=0)



In [10]:

    
folder.predict_proba(test_data, vote_function=mean_vote)









    



Using voting KFold prediction






    Out[10]:





array([[ 0.14722266,  0.85277734],
       [ 0.95026913,  0.04973087],
       [ 0.99504987,  0.00495013],
       ..., 
       [ 0.17173721,  0.82826279],
       [ 0.94682241,  0.05317759],
       [ 0.07535153,  0.92464847]])

Comparison of folds

Again use ClassificationReport class to compare different results. For folding classifier this report uses only default prediction.

Report training dataset



In [11]:

    
from rep.data.storage import LabeledDataStorage
from rep.report import ClassificationReport
# add folds_column to dataset to use mask
train_data["FOLDS"] = folder._get_folds_column(len(train_data))
lds = LabeledDataStorage(train_data, train_labels)

report = ClassificationReport({'folding': folder}, lds)









    



KFold prediction using folds column

Signal distribution for each fold

Use mask parameter to plot distribution for the specific fold



In [12]:

    
for fold_num in range(n_folds):
    report.prediction_pdf(mask="FOLDS == %d" % fold_num, labels_dict={1: 'sig fold %d' % fold_num}).plot()

Background distribution for each fold



In [13]:

    
for fold_num in range(n_folds):
    report.prediction_pdf(mask="FOLDS == %d" % fold_num, labels_dict={0: 'bck fold %d' % fold_num}).plot()

ROCs (each fold used as test dataset)



In [14]:

    
for fold_num in range(n_folds):
    report.roc(mask="FOLDS == %d" % fold_num).plot()

Report for test dataset

NOTE: Here vote function is None, so default prediction is used



In [15]:

    
lds = LabeledDataStorage(test_data, test_labels)

report = ClassificationReport({'folding': folder}, lds)









    



KFold prediction using folds column



In [16]:

    
report.prediction_pdf().plot(new_plot=True, figsize = (9, 4))



In [17]:

    
report.roc().plot(xlim=(0.5, 1))