What is the default scoring criteria for cross_validate() method? How can we define a different criteria like AUC for scoring?
The default strategy used in any scoring function is determined by the estimator, for instance you can look at the documentation for the .score() method of the LogisticRegression to find out that the default strategy for such estimator is the Mean accuracy.
Additionally, functions such as cross_validate accept a scoring parameter where you can personalize the strategy. This is covered a bit more in detail in Module 7.
To complete the answer of Arturo. The default is the accuracy score for the classifier and the R2 score for the regressor.
You can specify the ROC AUC using scoring="roc_auc".
But you should probably have a deeper look to the links provided by Arturo for more details.