π Solution for Exercise M1.05
Contents
π Solution for Exercise M1.05#
The goal of this exercise is to evaluate the impact of feature preprocessing on a pipeline that uses a decisiontreebased classifier instead of a logistic regression.
The first question is to empirically evaluate whether scaling numerical features is helpful or not;
The second question is to evaluate whether it is empirically better (both from a computational and a statistical perspective) to use integer coded or onehot encoded categories.
import pandas as pd
adult_census = pd.read_csv("../datasets/adultcensus.csv")
target_name = "class"
target = adult_census[target_name]
data = adult_census.drop(columns=[target_name, "educationnum"])
As in the previous notebooks, we use the utility make_column_selector
to select only columns with a specific data type. Besides, we list in
advance all categories for the categorical columns.
from sklearn.compose import make_column_selector as selector
numerical_columns_selector = selector(dtype_exclude=object)
categorical_columns_selector = selector(dtype_include=object)
numerical_columns = numerical_columns_selector(data)
categorical_columns = categorical_columns_selector(data)
Reference pipeline (no numerical scaling and integercoded categories)#
First letβs time the pipeline we used in the main notebook to serve as a reference:
import time
from sklearn.model_selection import cross_validate
from sklearn.pipeline import make_pipeline
from sklearn.compose import ColumnTransformer
from sklearn.preprocessing import OrdinalEncoder
from sklearn.ensemble import HistGradientBoostingClassifier
categorical_preprocessor = OrdinalEncoder(handle_unknown="use_encoded_value",
unknown_value=1)
preprocessor = ColumnTransformer([
('categorical', categorical_preprocessor, categorical_columns)],
remainder="passthrough")
model = make_pipeline(preprocessor, HistGradientBoostingClassifier())
start = time.time()
cv_results = cross_validate(model, data, target)
elapsed_time = time.time()  start
scores = cv_results["test_score"]
print("The mean crossvalidation accuracy is: "
f"{scores.mean():.3f} Β± {scores.std():.3f} "
f"with a fitting time of {elapsed_time:.3f}")
The mean crossvalidation accuracy is: 0.873 Β± 0.002 with a fitting time of 4.954
Scaling numerical features#
Letβs write a similar pipeline that also scales the numerical features using
StandardScaler
(or similar):
# solution
import time
from sklearn.preprocessing import StandardScaler
preprocessor = ColumnTransformer([
('numerical', StandardScaler(), numerical_columns),
('categorical', OrdinalEncoder(handle_unknown="use_encoded_value",
unknown_value=1),
categorical_columns)])
model = make_pipeline(preprocessor, HistGradientBoostingClassifier())
start = time.time()
cv_results = cross_validate(model, data, target)
elapsed_time = time.time()  start
scores = cv_results["test_score"]
print("The mean crossvalidation accuracy is: "
f"{scores.mean():.3f} Β± {scores.std():.3f} "
f"with a fitting time of {elapsed_time:.3f}")
The mean crossvalidation accuracy is: 0.873 Β± 0.003 with a fitting time of 4.973
Analysis#
We can observe that both the accuracy and the training time are approximately the same as the reference pipeline (any time difference you might observe is not significant).
Scaling numerical features is indeed useless for most decision tree models in
general and for HistGradientBoostingClassifier
in particular.
Onehot encoding of categorical variables#
We observed that integer coding of categorical variables can be very
detrimental for linear models. However, it does not seem to be the case for
HistGradientBoostingClassifier
models, as the crossvalidation score
of the reference pipeline with OrdinalEncoder
is reasonably good.
Letβs see if we can get an even better accuracy with OneHotEncoder
.
Hint: HistGradientBoostingClassifier
does not yet support sparse input
data. You might want to use
OneHotEncoder(handle_unknown="ignore", sparse=False)
to force the use of a
dense representation as a workaround.
# solution
import time
from sklearn.preprocessing import OneHotEncoder
categorical_preprocessor = OneHotEncoder(handle_unknown="ignore", sparse=False)
preprocessor = ColumnTransformer([
('onehotencoder', categorical_preprocessor, categorical_columns)],
remainder="passthrough")
model = make_pipeline(preprocessor, HistGradientBoostingClassifier())
start = time.time()
cv_results = cross_validate(model, data, target)
elapsed_time = time.time()  start
scores = cv_results["test_score"]
print("The mean crossvalidation accuracy is: "
f"{scores.mean():.3f} Β± {scores.std():.3f} "
f"with a fitting time of {elapsed_time:.3f}")
The mean crossvalidation accuracy is: 0.873 Β± 0.002 with a fitting time of 19.101
Analysis#
From an accuracy point of view, the result is almost exactly the same.
The reason is that HistGradientBoostingClassifier
is expressive
and robust enough to deal with misleading ordering of integer coded
categories (which was not the case for linear models).
However from a computation point of view, the training time is
much longer: this is caused by the fact that OneHotEncoder
generates approximately 10 times more features than OrdinalEncoder
.
Note that the current implementation HistGradientBoostingClassifier
is still incomplete, and once sparse representation are handled
correctly, training time might improve with such kinds of encodings.
The main take away message is that arbitrary integer coding of
categories is perfectly fine for HistGradientBoostingClassifier
and yields fast training times.
Important
Which encoder should I use?
Meaningful order 
Nonmeaningful order 


Treebased model 


Linear model 


OneHotEncoder
: will always do something meaningful, but can be unnecessary slow with trees.OrdinalEncoder
: can be detrimental for linear models unless your category has a meaningful order and you make sure thatOrdinalEncoder
respects this order. Trees can deal withOrdinalEncoder
fine as long as they are deep enough.