In this notebook we compute the Standard Error for Cross Validation based on

CMU Notes from Ryan Tibshirani

Note: Tibshirani's father at Stanford worked on 632bootstrap

  • [1] Efron, Bradley, and Robert Tibshirani. 1997. "Improvements on Cross-Validation: The .632+ Bootstrap Method." Journal of the American Statistical Association 92 (438): 548. doi:10.2307/2965703.

The standard error is the standard deviation of the Student t-distribution. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample.

In [ ]:
!pip install git+
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In [ ]:
import pandas as pd

import numpy as np
from sklearn.metrics import confusion_matrix
from sklearn.metrics import roc_curve, auc
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression

#from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
from sklearn.model_selection import KFold, cross_val_score, GridSearchCV, train_test_split
from sklearn.metrics import accuracy_score, classification_report, confusion_matrix
from sklearn.utils import resample
from sklearn.dummy import DummyClassifier

from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer

from sklearn.metrics import average_precision_score
from sklearn.metrics import precision_recall_curve
from sklearn.metrics import plot_precision_recall_curve
from sklearn.metrics import roc_curve, auc, confusion_matrix

from matplotlib import pyplot

import ml_valuation

from ml_valuation import model_valuation
from ml_valuation import model_visualization
In [ ]:
arr_X, arr_y = load_breast_cancer(return_X_y=True)
In [ ]:
#X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

print("X: " + str(arr_X.shape))
#print("X_test: " + str(X.shape))
X: (569, 30)
In [ ]:
[[1.799e+01 1.038e+01 1.228e+02 ... 2.654e-01 4.601e-01 1.189e-01]
 [2.057e+01 1.777e+01 1.329e+02 ... 1.860e-01 2.750e-01 8.902e-02]
 [1.969e+01 2.125e+01 1.300e+02 ... 2.430e-01 3.613e-01 8.758e-02]
 [1.660e+01 2.808e+01 1.083e+02 ... 1.418e-01 2.218e-01 7.820e-02]
 [2.060e+01 2.933e+01 1.401e+02 ... 2.650e-01 4.087e-01 1.240e-01]
 [7.760e+00 2.454e+01 4.792e+01 ... 0.000e+00 2.871e-01 7.039e-02]]
In [ ]:
unique, counts = np.unique(arr_y, return_counts=True)
dict(zip(unique, counts))
Out[ ]:
{0: 212, 1: 357}
In [ ]:
from sklearn.model_selection import KFold, train_test_split, RandomizedSearchCV, StratifiedKFold

# fit a model
classifier_kfold_LR = LogisticRegression(solver='newton-cg')

k = 10
cv = StratifiedKFold( n_splits=k )
stats = list()

X = pd.DataFrame(arr_X)
y = pd.DataFrame(arr_y)
#for train_index, test_index in cv.split(X, y):
for i, (train_index, test_index) in enumerate(cv.split(X, y)):

  # convert the data indexes into references
  Xtrain, Xtest = X.iloc[train_index], X.iloc[test_index]
  ytrain, ytest = y.iloc[train_index], y.iloc[test_index]

  print("Running CV Fold-" + str(i))
  #x_train_scaled, x_test_scaled, y_train_scaled, y_test_scaled = train_test_split(df_full_scaled, y_train_full, test_size=1 - train_ratio)

  # X.iloc[ train_index ], y.iloc[ train_index ])
  # fit the model on the training data (Xtrain) and labels (ytrain) Xtrain, ytrain.values.ravel() )

  # now get the probabilites of the predictions for the text input (data: Xtest, labels: ytest)
  #probas_ = classifier_kfold_LR.predict_proba( Xtest )

  #print( "prediction probabilities: " + str(yhat.shape) )

  #prediction_est_prob = probas_[:, 1]

  y_pred = classifier_kfold_LR.predict(Xtest)

  accuracy_fold = accuracy_score(ytest, y_pred)

  #scmtrx_lr_full_testset = model_valuation.standard_confusion_matrix_for_top_ranked_percent(y_test_scaled, yhat, 0.5, 1.0)
  print("Accuracy: " + str(accuracy_fold))


mean_score = np.mean(stats)
print("\n\nAverage Accuracy Across All Folds: " + str("{:.4f}".format(mean_score)))

std_dev_score = np.std(stats)
print("\n\nSTD DEV: " + str(std_dev_score))
standard_error_score = (1/np.sqrt(k)) * std_dev_score

print("\n\nStandard Error (Accuracy) Across All Folds: ( " + str("{:.4f}".format(standard_error_score)) + ")")

# 95% of values will lie within ±1.96
ci_95 = 1.96 * standard_error_score
print("CI Ranges 95%:")

low_end_range = mean_score - ci_95
high_end_range = mean_score + ci_95

print("High: " + str(high_end_range))
print("Low : " + str(low_end_range))
Running CV Fold-0
Accuracy: 0.9824561403508771
Running CV Fold-1
/usr/local/lib/python3.7/dist-packages/scipy/optimize/ LineSearchWarning: The line search algorithm did not converge
  warn('The line search algorithm did not converge', LineSearchWarning)
/usr/local/lib/python3.7/dist-packages/sklearn/utils/ UserWarning: Line Search failed
  warnings.warn('Line Search failed')
Accuracy: 0.9122807017543859
Running CV Fold-2
Accuracy: 0.9298245614035088
Running CV Fold-3
Accuracy: 0.9473684210526315
Running CV Fold-4
Accuracy: 0.9824561403508771
Running CV Fold-5
Accuracy: 0.9824561403508771
Running CV Fold-6
Accuracy: 0.9298245614035088
Running CV Fold-7
Accuracy: 0.9473684210526315
Running CV Fold-8
Accuracy: 0.9649122807017544
Running CV Fold-9
Accuracy: 0.9642857142857143

Average Accuracy Across All Folds: 0.9543

STD DEV: 0.023770661464399972

Standard Error (Accuracy) Across All Folds: ( 0.0075)
CI Ranges 95%:
High: 0.969056516887071
Low : 0.9395900996542824