📃 Solution for Exercise 01

📃 Solution for Exercise 01#

The aim of this exercise is to highlight caveats to have in mind when using feature selection. You have to be extremely careful regarding the set of data on which you will compute the statistic that helps your feature selection algorithm to decide which feature to select.

On purpose, we will make you program the wrong way of doing feature selection to gain insights.

First, you will create a completely random dataset using NumPy. Using the function np.random.randn, generate a matrix data containing 100 samples and 100,000 features. Then, using the function np.random.randint, generate a vector target with 100 samples containing either 0 or 1.

This type of dimensionality is typical in bioinformatics when dealing with RNA-seq. However, we will use completely randomized features such that we don’t have a link between the data and the target. Thus, the generalization performance of any machine-learning model should not perform better than the chance-level.

import numpy as np

# solution
rng = np.random.RandomState(42)
data, target = rng.randn(100, 100000), rng.randint(0, 2, size=100)

Now, create a logistic regression model and use cross-validation to check the score of such a model. It will allow use to confirm that our model cannot predict anything meaningful from random data.

# solution
from sklearn.model_selection import cross_val_score
from sklearn.linear_model import LogisticRegression

# solution
model = LogisticRegression()
test_score = cross_val_score(model, data, target, n_jobs=2)
print(f"The mean accuracy is: {test_score.mean():.3f}")

The mean accuracy is: 0.490

It is not surprising that the logistic regression model performs as bad as pure chance when we provide the full dataset.

Now, we will ask you to program the wrong pattern to select feature. Select the feature by using the entire dataset. We will choose ten features with the highest ANOVA F-score computed on the full dataset. Subsequently, subsample the dataset data by selecting the features’ subset. Finally, train and test a logistic regression model.

You should get some surprising results.

from sklearn.feature_selection import SelectKBest, f_classif

# solution
feature_selector = SelectKBest(score_func=f_classif, k=10)
data_subset = feature_selector.fit_transform(data, target)
test_score = cross_val_score(model, data_subset, target)
print(f"The mean accuracy is: {test_score.mean():.3f}")

The mean accuracy is: 0.940

Surprisingly, the logistic regression succeeded in having a fantastic accuracy using data that did not have any link with the target in the first place. We therefore know that these results are not legit.

The reasons for obtaining these results are two folds: the pool of available features is large compared to the number of samples. It is possible to find a subset of features that will link the data and the target. By not splitting the data, we leak knowledge from the entire dataset and could use this knowledge while evaluating our model.

Now, we will make you program the right way to do the feature selection. First, split the dataset into a training and testing set. Then, fit the feature selector on the training set. Then, transform both the training and testing sets before you train and test the logistic regression.

from sklearn.model_selection import train_test_split

# solution
data_train, data_test, target_train, target_test = train_test_split(
    data, target, random_state=0
)
feature_selector.fit(data_train, target_train)
data_train_subset = feature_selector.transform(data_train)
data_test_subset = feature_selector.transform(data_test)
model.fit(data_train_subset, target_train)
test_score = model.score(data_test_subset, target_test)
print(f"The mean accuracy is: {test_score:.3f}")

The mean accuracy is: 0.520

It is not a surprise that our model is not working. We see that selecting features only on the training set will not help when testing our model. In this case, we obtained the expected results.

Therefore, as with hyperparameters optimization or model selection, tuning the feature space should be done solely on the training set, keeping a part of the data left-out.

However, the previous case is not perfect. For instance, if we were asking to perform cross-validation, the manual fit/transform of the datasets will make our life hard. Indeed, the solution here is to use a scikit-learn pipeline in which the feature selection will be a pre processing stage before to train the model.

Thus, start by creating a pipeline with the feature selector and the logistic regression. Then, use cross-validation to get an estimate of the uncertainty of your model generalization performance.

from sklearn.pipeline import make_pipeline

# solution
model = make_pipeline(feature_selector, LogisticRegression())
test_score = cross_val_score(model, data, target)
print(f"The mean accuracy is: {test_score.mean():.3f}")

The mean accuracy is: 0.460

We see that using a scikit-learn pipeline removes a lot of boilerplate code and helps avoid mistakes when calling fit and transform on the different set of data.