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Cross validation and logistic regression

I am analyzing a dataset from kaggle and want to apply a logistic regression model to predict something. This is the data: https://www.kaggle.com/code/mohamedadelhosny/stroke-prediction-data-analysis-challenge/data
I split the data into train and test, and want to use cross validation to inssure highest accuracy possible. I did some pre-processing and used the dummy function over catigorical features, got to a certain point in the code, and and I don't know how to proceed. I cant figure out how to use the results of the cross validation, it's not so straight forward.
This is what I got so far:
from numpy import mean
from numpy import std
from sklearn.datasets import make_classification
from sklearn.model_selection import KFold
from sklearn.linear_model import LogisticRegression
X = data_Enco.iloc[:, data_Enco.columns != 'stroke'].values # features
Y = data_Enco.iloc[:, 6] # labels
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.20)
scaler = MinMaxScaler()
scaled_X_train = scaler.fit_transform(X_train)
scaled_X_test = scaler.transform(X_test)
# prepare the cross-validation procedure
cv = KFold(n_splits=10, random_state=1, shuffle=True)
logisticModel = LogisticRegression(class_weight='balanced')
# evaluate model
scores = cross_val_score(logisticModel, scaled_X_train, Y_train, scoring='accuracy', cv=cv)
print('average score = ', np.mean(scores))
print('std of scores = ', np.std(scores))
average score = 0.7483538453549359
std of scores = 0.0190400919099899
So far so good.. I got the results of the model for each 10 splits. But now what? how do I build a confusion matrix? how do I calculate the recall, precesion..? I have the right code without performing cross validation, I just dont know how to adapt it.. how do I use the scores of the cross_val_score function ?
logisticModel = LogisticRegression(class_weight='balanced')
logisticModel.fit(scaled_X_train, Y_train) # Train the model
predictions_log = logisticModel.predict(scaled_X_test)
## Scoring the model
logisticModel.score(scaled_X_test,Y_test)
## Confusion Matrix
Y_pred = logisticModel.predict(scaled_X_test)
real_data = Y_test
print('Observe the difference between the real data and the data predicted by the knn classifier:\n')
print('Predictions: ',Y_pred,'\n\n')
print('Real Data:m', real_data,'\n')
cmtx = pd.DataFrame(
confusion_matrix(real_data, Y_pred, labels=[0, 1]),
index = ['real 0: ', 'real 1:'], columns = ['pred 0:', 'pred 1:']
)
print(cmtx)
print('Accuracy score is: ',accuracy_score(real_data, Y_pred))
print('Precision score is: ',precision_score(real_data, Y_pred))
print('Recall Score is: ',recall_score(real_data, Y_pred))
print('F1 Score is: ',f1_score(real_data, Y_pred))

The performance of a model on the training dataset is not a good estimator of the performance on new data because of overfitting.
Cross-validation is used to obtain an estimation of the performance of your model on new data, i.e. without overfitting. And you correctly applied it to compute the mean and variance of the accuracy of your model. This should be a much better approximation of the accuracy on your test dataset than the accuracy on your training dataset. And that is it.
However, cross-validation is usually used to do model selection. Say you have two logistic regression models that use different sets of independent variables. E.g., one is using only age and gender while the other one is using age, gender, and bmi. Or you want to compare logistic regression with an SVM model.
I.e. you have several possible models and you want to decide which one is best. Of course, you cannot just compare the training dataset accuracies of all the models because those are spoiled by overfitting. And if you use the performance on the test dataset for choosing the best model, the test dataset becomes part of the training, you will have leakage, and thus the performance on the test dataset cannot be used anymore for a final, untainted performance measure. That is why cross-validation is used which creates those splits that contain different versions of validation sets.
So the idea is to
apply cross-validation to each of your candidate models,
use the scores of those cross-validations to choose the best model,
retrain that best model on the complete training dataset to get a final version of your best model, and
to finally apply this final version to the test dataset to obtain some untainted evaluation.
But note, that those three steps are for model selection. However, you have only a single model, the logistic regression, so there is nothing to select from. If you fit your model, let's call it m(p) where p denotes the parameters, to e.g. five folds of CV, you get five different fitted versions m(p1), m(p2), ..., m(p5) of the same model.
So if you have only one model, you fit it to the complete training dataset, maybe use CV to have an additional estimate for the performance on new data, but that's it. But you have already done this. There is no "selection of best model", that is only for if you have several models as described above, like e.g. logistic regression and SVM.

Cross val predict expects as input an already fitted model?

I am reading Geron's Hands-on Machine Learning. In page 90, there is a section about Confusion Matrix. He says that we need some predictions, so he does the following:
from sklearn.model_selection import cross_val_predict
y_train_pred = cross_val_predict(sgd_clf, X_train, y_train5, cv=3)
This object sgd_clf is a stochastic gradient descent classifier which was previously fitted with the train data in the previous section. My question is: why, if already fitted, it is better to split the train set in three parts and retrain (?) the sgd_clf in two of them, then make a prediction and so on, if sgd_clf is already trained? Why not just let it predict on full X_train? Or just take a new not-fitted classifier as imput? Why put sgd_clf already trained as imput to retrain? I am a bit confused.

I see your confusion and I think Geron doesn't mean you should use the fitted model for cross-validation. He just wants to compare the naive fitting method with cross-validation.
The complete code should be as follows:
from sklearn.linear_model import SGDClassifier
# No cross-validation
sgd_clf1 = SGDClassifier(random_state=42)
sgd_clf1.fit(X_train, y_train)
# With cross-validation
sgd_clf2 = SGDClassifier(random_state=42)
cross_val_score(sgd_clf2, X_train, y_train, cv=3, scoring='accuracy')

How can I explain this drop in performance on test data?

I am asking the question here, even though I hesitated to post it on CrossValidated (or DataScience) StackExchange. I have a dataset of 60 labeled objects (to be used for training) and 150 unlabeled objects (for test). The aim of the problem is to predict the labels of the 150 objects (this used to be given as a homework problem). For each object, I computed 258 features. Considering each object as a sample, I have X_train : (60,258), y_train : (60,) (labels of the objects used for training) and X_test : (150,258). Since the solution of the homework problem was given, I also have the true labels of the 150 objects, in y_test : (150,).
In order to predict the labels of the 150 objects, I choose to use a LogisticRegression (the Scikit-learn implementation). The classifier is trained on (X_train, y_train), after the data has been normalized, and used to make predictions for the 150 objects. Those predictions are compared to y_test to assess the performance of the model. For reproducibility, I copy the code I have used.
from sklearn import metrics
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.pipeline import make_pipeline
from sklearn.model_selection import cross_val_score, crosss_val_predict
# Fit classifier
LogReg = LogisticRegression(C=1, class_weight='balanced')
scaler = StandardScaler()
clf = make_pipeline(StandardScaler(), LogReg)
LogReg.fit(X_train, y_train)
# Performance on training data
CV_score = cross_val_score(clf, X_train, y_train, cv=10, scoring='roc_auc')
print(CV_score)
# Performance on test data
probas = LogReg.predict_proba(X_test)[:, 1]
AUC = metrics.roc_auc_score(y_test, probas)
print(AUC)
The matrices X_train,y_train,X_test and y_test are saved in a .mat file available at this link. My problem is the following :
Using this approach, I get a good performance on training data (CV_score = 0.8) but the performance on the test data is much worse : AUC = 0.54 for C=1 in LogReg and AUC = 0.40 for C=0.01. How can I get AUC<0.5 if a naive classifier should score AUC = 0.5 ? Is this due to the fact that I have a small number of samples for training ?
I have noticed that the performance on test data improves if I change the code for :
y_pred = cross_val_predict(clf, X_test, y_test, cv=5)
AUC = metrics.roc_auc_score(y_test, y_pred)
print(AUC)
Indeed, AUC=0.87 for C=1 and 0.9 for C=0.01. Why is the AUC score so much better using cross validation predictions ? Is it because cross validation allows to make predictions on subsets of the test data which do not contain objects/samples which decrease the AUC ?

Looks like you are encountering an overfitting problem, i.e. the classifier trained using the training data is overfitting to the training data. It has poor generalization ability. That is why the performance on the testing dataset isn't good.
cross_val_predict is actually training the classifier using part of your testing data and then predict on the rest. So the performance is much better.
Overall, there seems to be quite some difference between your training and testing datasets. So the classifier with the highest training accuracy doesn't work well on your testing set.
Another point not directly related with your question: since the number of your training samples is much smaller than the feature dimensions, it may be helpful to perform dimension reduction before feeding to classifier.

It looks like your training and test process are inconsistent. Although from your code you intend to standardize your data, you fail to do so during testing. What I mean:
clf = make_pipeline(StandardScaler(), LogReg)
LogReg.fit(X_train, y_train)
Although you define a pipeline, you do not fit the pipeline (clf.fit) but only the Logistic Regression. This matters, because your cross-validated score is calculated with the pipeline (CV_score = cross_val_score(clf, X_train, y_train, cv=10, scoring='roc_auc')) but during test instead of using the pipeline as expected to predict, you use only LogReg, hence the test data are not standardized.
The second point you raise is different. In y_pred = cross_val_predict(clf, X_test, y_test, cv=5)
you get predictions by doing cross-validation on the test data, while ignoring the train data. Here, you do data standardization since you use clf and thus your score is high; this is evidence that the standardization step is important.
To summarize, standardizing the test data, I believe will improve your test score.

Firstly it makes no sense to have 258 features for 60 training items. Secondly CV=10 for 60 items means you split the data into 10 train/test sets. Each of these has 6 items only in the test set. So whatever results you obtain will be useless. You need more training data and less features.

how to properly use sklearn to predict the error of a fit

I'm using sklearn to fit a linear regression model to some data. In particular, my response variable is stored in an array y and my features in a matrix X.
I train a linear regression model with the following piece of code
from sklearn.linear_model import LinearRegression
model = LinearRegression()
model.fit(X,y)
and everything seems to be fine.
Then let's say I have some new data X_new and I want to predict the response variable for them. This can easily done by doing
predictions = model.predict(X_new)
My question is, what is this the error associated to this prediction?
From my understanding I should compute the mean squared error of the model:
from sklearn.metrics import mean_squared_error
model_mse = mean_squared_error(model.predict(X),y)
And basically my real predictions for the new data should be a random number computed from a gaussian distribution with mean predictions and sigma^2 = model_mse. Do you agree with this and do you know if there's a faster way to do this in sklearn?

You probably want to validate your model on your training data set. I would suggest exploring the cross-validation submodule sklearn.cross_validation.
The most basic usage is:
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y)

It depends on you training data-
If it's distribution is a good representation of the "real world" and of a sufficient size (see learning theories, as PAC), then I would generally agree.
That said- if you are looking for a practical way to evaluate your model, why won't you use the test set as Kris has suggested?
I usually use grid search for optimizing parameters:
#split to training and test sets
X_train, X_test, y_train, y_test =train_test_split(
X_data[indices], y_data[indices], test_size=0.25)
#cross validation gridsearch
params = dict(logistic__C=[0.1,0.3,1,3, 10,30, 100])
grid_search = GridSearchCV(clf, param_grid=params,cv=5)
grid_search.fit(X_train, y_train)
#print scores and best estimator
print 'best param: ', grid_search.best_params_
print 'best train score: ', grid_search.best_score_
print 'Test score: ', grid_search.best_estimator_.score(X_test,y_test)
The Idea is hiding the test set from your learning algorithm (and yourself)- Don't train and don't optimize parameters using this data.
Finally you should use the test set for performance evaluation (error) only, it should provide an unbiased mse.

sklearn: How to reset a Regressor or classifier object in sknn

I have defined a regressor as follows:
nn1 = Regressor(
layers=[
Layer("Rectifier", units=150),
Layer("Rectifier", units=100),
Layer("Linear")],
regularize="L2",
# dropout_rate=0.25,
learning_rate=0.01,
valid_size=0.1,
learning_rule="adagrad",
verbose=False,
weight_decay=0.00030,
n_stable=10,
f_stable=0.00010,
n_iter=200)
I am using this regressor in a k-fold cross-validation. In order for cross-validation to work properly and not learn from the previous folds, it's necessary that the regressor to be reset after each fold.
How can I reset the regressor object?

sklearn.base.clone should achieve what you're looking to achieve

The pattern that I use for cross validation instantiates a new classifier for each training/test pair:
from sklearn.cross_validation import KFold
kf = KFold(len(labels),n_folds=5, shuffle=True)
for train, test in kf:
clf = YourClassifierClass()
clf.fit(data[train],labels[train])
# Do evaluation with data[test] and labels[test]
You can save your current best classifier in a separate variable and access its parameters after cross validation (this is also useful if you want to try different parameters).