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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')

Using Custom Metric for Score Method in XGBoost

I am using xgboost for a classification problem with an imbalanced dataset. I plan on using some combination of an f1-score or roc-auc as my primary criteria for judging the model.
Currently the default value returned from the score method is accuracy, but I would really like to have a specific evaluation metric returned instead. My big motivation for doing this is that I presume the feature_importances_ attribute from the model is determined from what's affecting the score method, and the columns that impact predictive accuracy might very well be different from the columns that impact roc-auc. Right now I am passing in values to eval_metric but it does not seem to be making a difference.
Here is some sample code:
from sklearn.model_selection import train_test_split
from xgboost import XGBClassifier
from sklearn.datasets import load_breast_cancer
from sklearn.metrics import roc_auc_score
data = load_breast_cancer()
X = data['data']
y = data['target']
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42, test_size=0.2, stratify=y)
mod.fit(X_train, y_train)
Now at this point, mod.score(X_test, y_test) will return a value of ~ 0.96, and the roc_auc_score is ~ 0.99.
I was hoping the following snippet:
mod.fit(X_train, y_train, eval_metric='auc')
Would then allow mod.score(X_test, y_test) to return the roc_auc_score value, but it is still returning predictive accuracy, not roc_auc.
The purpose of this exercise is estimating the influence of different columns on the outcome, so if I could get feature_importances_ returned using f1 or roc_auc as the measure of impact this would be a huge boon, but I do not seem to be on the right path as of now.
Thank you.

There are two parts to your question, to use eval_metric, you need to provide data to evaluate using eval_set = :
mod = XGBClassifier()
mod.fit(X_train, y_train,eval_set=[(X_test,y_test)],eval_metric="auc")
You can check the auc using evals_result(), and it gives the auc for every iteration:
mod.evals_result()
{'validation_0': OrderedDict([('auc',
[0.965939,
0.9833,
0.984788,
[...]
0.991402,
0.991071,
0.991402,
0.991733])])}
The importance score is calculated based on the average gain across all splits the feature is used in see help page. From your question, I suppose you need the mdoel to maximize auc, like in cross-validation, but you cannot use the auc as an objective in xgboost. Gradient boosting methods require a differentiable loss function.
With imbalanced dataset, you can try to adjust the parameter scale_pos_weight, to adjust the balance of positive and negative weights. This is discussed in xgboost website

Basic Sklearn: How to Pass Scoring Function to Fit Method

I'm using sklearn to do some machine learning. I often use GridSearchCV to explore hyperparameters and perform cross-validation. Using this, I can specify a scoring function, like this:
scores = -cross_val_score(svr, X, Y, cv=10, scoring='neg_mean_squared_error')
However, I want to train my SVR model using mean squared error. Unfortunately, there's no scoring parameter in either the constructor for SVR or the fit method.
How should I do this?
Thanks!

I typically use Pipeline to do it. You can create list of pipelines including SVR model (and others if you want). Then, you can apply GridSearchCV where putting pipeline in as your argument.
Here, you can add params_grid where searching space can be defined as pipelinename__paramname (double underscore in between). For example, I have pipeline name svr and I want to search on parameter C, I can put the key in my parameter dictionary as svr__C.
from sklearn.pipeline import Pipeline
from sklearn.model_selection import cross_val_score, GridSearchCV
from sklearn.svm import SVR
c_range = np.arange(1, 10, 1)
pipeline = Pipeline([('svr', SVR())])
params_grid = {'svr__C': c_range}
# grid search with 3-fold cross validation
gridsearch_model = GridSearchCV(pipeline, params_grid,
cv=3, scoring='neg_mean_squared_error')
Then, you can do the same procedure by fitting training data and find best score and parameters
gridsearch_model.fit(X_train, y_train)
print(gridsearch_model.best_params_, gridsearch_model.best_score_)
You can also use cross_val_score to find the score:
cross_val_score(gridsearch_model, X_train, y_train,
cv=3, scoring='neg_mean_squared_error')
Hope this helps!

Using cross_val_predict against test data set

I'm confused about using cross_val_predict in a test data set.
I created a simple Random Forest model and used cross_val_predict to make predictions:
from sklearn.ensemble import RandomForestClassifier
from sklearn.cross_validation import cross_val_predict, KFold
lr = RandomForestClassifier(random_state=1, class_weight="balanced", n_estimators=25, max_depth=6)
kf = KFold(train_df.shape[0], random_state=1)
predictions = cross_val_predict(lr,train_df[features_columns], train_df["target"], cv=kf)
predictions = pd.Series(predictions)
I'm confused on the next step here. How do I use what is learnt above to make predictions on the test data set?

I don't think cross_val_score or cross_val_predict uses fit before predicting. It does it on the fly. If you look at the documentation (section 3.1.1.1), you'll see that they never mention fit anywhere.

As #DmitryPolonskiy commented, the model has to be trained (with the fit method) before it can be used to predict.
# Train the model (a.k.a. `fit` training data to it).
lr.fit(train_df[features_columns], train_df["target"])
# Use the model to make predictions based on testing data.
y_pred = lr.predict(test_df[feature_columns])
# Compare the predicted y values to actual y values.
accuracy = (y_pred == test_df["target"]).mean()
cross_val_predict is a method of cross validation, which lets you determine the accuracy of your model. Take a look at sklearn's cross-validation page.

I am not sure the question was answered. I had a similar thought. I want compare the results (Accuracy for example) with the method that does not apply CV. The CV valiadte accuracy is on the X_train and y_train. The other method fit the model using X_trian and y_train, tested on the X_test and y_test. So the comparison is not fair since they are on different datasets.
What you can do is using the estimator returned by the cross_validate
lr_fit = cross_validate(lr, train_df[features_columns], train_df["target"], cv=kf, return_estimator=Ture)
y_pred = lr_fit.predict(test_df[feature_columns])
accuracy = (y_pred == test_df["target"]).mean()

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.