📃 Solution for Exercise M3.02#

The goal is to find the best set of hyperparameters which maximize the generalization performance on a training set.

Here again with limit the size of the training set to make computation run faster. Feel free to increase the train_size value if your computer is powerful enough.

import numpy as np
import pandas as pd

adult_census = pd.read_csv("../datasets/adult-census.csv")

target_name = "class"
target = adult_census[target_name]
data = adult_census.drop(columns=[target_name, "education-num"])
from sklearn.model_selection import train_test_split

data_train, data_test, target_train, target_test = train_test_split(
    data, target, train_size=0.2, random_state=42)

In this exercise, we will progressively define the classification pipeline and later tune its hyperparameters.

Our pipeline should:

  • preprocess the categorical columns using a OneHotEncoder and use a StandardScaler to normalize the numerical data.

  • use a LogisticRegression as a predictive model.

Start by defining the columns and the preprocessing pipelines to be applied on each group of columns.

from sklearn.compose import make_column_selector as selector

# solution
categorical_columns_selector = selector(dtype_include=object)
categorical_columns = categorical_columns_selector(data)

numerical_columns_selector = selector(dtype_exclude=object)
numerical_columns = numerical_columns_selector(data)
from sklearn.preprocessing import OneHotEncoder
from sklearn.preprocessing import StandardScaler

# solution
categorical_processor = OneHotEncoder(handle_unknown="ignore")
numerical_processor = StandardScaler()

Subsequently, create a ColumnTransformer to redirect the specific columns a preprocessing pipeline.

from sklearn.compose import ColumnTransformer

# solution
preprocessor = ColumnTransformer(
    [('cat_preprocessor', categorical_processor, categorical_columns),
     ('num_preprocessor', numerical_processor, numerical_columns)]

Assemble the final pipeline by combining the above preprocessor with a logistic regression classifier. Force the maximum number of iterations to 10_000 to ensure that the model will converge.

from sklearn.pipeline import make_pipeline
from sklearn.linear_model import LogisticRegression

# solution
model = make_pipeline(preprocessor, LogisticRegression(max_iter=10_000))

Use RandomizedSearchCV with n_iter=20 to find the best set of hyperparameters by tuning the following parameters of the model:

  • the parameter C of the LogisticRegression with values ranging from 0.001 to 10. You can use a log-uniform distribution (i.e. scipy.stats.loguniform);

  • the parameter with_mean of the StandardScaler with possible values True or False;

  • the parameter with_std of the StandardScaler with possible values True or False.

Once the computation has completed, print the best combination of parameters stored in the best_params_ attribute.

from sklearn.model_selection import RandomizedSearchCV
from scipy.stats import loguniform

# solution
param_distributions = {
    "logisticregression__C": loguniform(0.001, 10),
    "columntransformer__num_preprocessor__with_mean": [True, False],
    "columntransformer__num_preprocessor__with_std": [True, False],

model_random_search = RandomizedSearchCV(
    model, param_distributions=param_distributions,
    n_iter=20, error_score=np.nan, n_jobs=2, verbose=1, random_state=1)
model_random_search.fit(data_train, target_train)
Fitting 5 folds for each of 20 candidates, totalling 100 fits
{'columntransformer__num_preprocessor__with_mean': False,
 'columntransformer__num_preprocessor__with_std': False,
 'logisticregression__C': 7.465283462691551}

So the best hyperparameters give a model where the features are scaled but not centered and the final model is regularized.

Getting the best parameter combinations is the main outcome of the hyper-parameter optimization procedure. However it is also interesting to assess the sensitivity of the best models to the choice of those parameters. The following code, not required to answer the quiz question shows how to conduct such an interactive analysis for this this pipeline using a parallel coordinate plot using the plotly library.

We could use cv_results = model_random_search.cv_results_ to make a parallel coordinate plot as we did in the previous notebook (you are more than welcome to try!). Instead we are going to load the results obtained from a similar search with many more iterations (1,000 instead of 20).

cv_results = pd.read_csv(

To simplify the axis of the plot, we will rename the column of the dataframe and only select the mean test score and the value of the hyperparameters.

column_name_mapping = {
    "param_logisticregression__C": "C",
    "param_columntransformer__num_preprocessor__with_mean": "centering",
    "param_columntransformer__num_preprocessor__with_std": "scaling",
    "mean_test_score": "mean test accuracy",

cv_results = cv_results.rename(columns=column_name_mapping)
cv_results = cv_results[column_name_mapping.values()].sort_values(
    "mean test accuracy", ascending=False)

In addition, the parallel coordinate plot from plotly expects all data to be numeric. Thus, we convert the boolean indicator informing whether or not the data were centered or scaled into an integer, where True is mapped to 1 and False is mapped to 0.

We also take the logarithm of the C values to span the data on a broader range for a better visualization.

column_scaler = ["centering", "scaling"]
cv_results[column_scaler] = cv_results[column_scaler].astype(np.int64)
cv_results['log C'] = np.log10(cv_results['C'])
import plotly.express as px

fig = px.parallel_coordinates(
    color="mean test accuracy",
    dimensions=["log C", "centering", "scaling", "mean test accuracy"],