Understanding Mutual Information on Titanic Dataset - data-analysis

Question

I was reading about Mutual Information on the Kaggle courses: https://www.kaggle.com/code/ryanholbrook/mutual-information
After that I tried it out on the Titanic Competition Dataset and I encountered a weird behaviour .
I will post the code further below.
I ranked all the features with mutual information and received the following output:
PassengerId 0.665912
Name 0.665912
Ticket 0.572496
Cabin 0.165236
Sex 0.150870
Fare 0.141621
Age 0.066269
Pclass 0.058107
SibSp 0.023197
Embarked 0.016668
Parch 0.016366
According to the documentation
Mutual information (MI) [1] between two random variables is a non-negative value, which measures the dependency between the variables. It is equal to zero if and only if two random variables are independent, and higher values mean higher dependency.
From my point of view at least PassengerId should be independent as well as the name. because I used factorize() on all objects. Which leaves me with 100% unique values for both Id and Names. There are in total 891 rows in the training dataset.
# number of unique values for top 2 MI
print(X_mi["PassengerId"].nunique())
print(X_mi["Name"].nunique())
891
891
My question is how does this happen? And why does PassengerId and Name with all unique values score even higher than lets say Age or Sex?
I followerd the Kaggle course on the link above. Only difference should be that I used
from sklearn.feature_selection import mutual_info_classif
instead of
from sklearn.feature_selection import mutual_info_regression
because my target is a discrete target.
Here is the relevant code:
X_train_full = pd.read_csv("/kaggle/input/titanic/train.csv")
X_test_full = pd.read_csv("/kaggle/input/titanic/test.csv")
X_mi = X_train_full.copy()
y_mi = X_mi.pop("Survived")
# Label encoding for categoricals
for colname in X_mi.select_dtypes("object"):
X_mi[colname], _ = X_mi[colname].factorize()
# fill all NaN values of age with mean and cast type to int
X_mi["Age"] = X_mi["Age"].transform(lambda age: age.fillna(age.mean()))
X_mi["Age"] = X_mi["Age"].transform(lambda age: age.astype("int"))
# cast fare type to int
X_mi["Fare"] = X_mi["Fare"].transform(lambda fare: fare.astype("int"))
# All discrete features should now have integer dtypes (double-check this before using MI!)
discrete_features = X_mi.dtypes == int
from sklearn.feature_selection import mutual_info_classif
def make_mi_scores(X, y, discrete_features):
mi_scores = mutual_info_classif(X, y, discrete_features=discrete_features)
mi_scores = pd.Series(mi_scores, name="MI Scores", index=X.columns)
mi_scores = mi_scores.sort_values(ascending=False)
return mi_scores
mi_scores = make_mi_scores(X_mi, y_mi, discrete_features)
print(mi_scores) # show features with their MI scores
Any explanation or suggestions what I might have done wrong?
From Data Analytics point of view I might have some mistakes but how does a fully unrelated feature like PassengerId score so high and higher than the others?
Thank you :)