ImportError: cannot import name cross_validation

This happens because there is no cross_validation object in sklearn. You're likely looking for something more like the cross_validate function. You can access that through

from sklearn.model_selection import cross_validate

However, you don't need to import any cross-validation software to perform the train-test split, since that will just randomly sample from the data. Try

from sklearn.model_selection import train_test_split

followed by

features_train, features_test, labels_train, labels_test = train_test_split(word_data, authors, test_size=0.1, random_state=42)

In my case, I was using some files from a Udacity course, which used an older version of sklearn. Instead of spending unnecessary time reformatting code usage to meet the latest versions of all their dependencies, it was easier to install the old version.

This was possible because they provide a requirements.txt file.

python -m pip install -r requirements.txt

cross_validation used to exist as a Scikit package*, but was deprecated at some point.

If you're looking for train_test_split as your code indicates, it's in model_selection:

from sklearn import model_selection

features_train, features_test, labels_train, labels_test = model_selection.train_test_split(
    word_data, authors, test_size=0.1, random_state=42)

_{*Looks like this changed in 0.18.}