# π Exercise 01ΒΆ

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 help you feature algorithm to decide which feature to select.

On purpose, we will make you program the wrong way of doing feature selection to 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 donβt have a link between the data and the target. Thus, the statistical performance of any machine learning model should not perform better than the chance-level.

```
import numpy as np
# Write your code here.
```

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

```
# Write your code here.
```

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 featuresβ subset. Finally,
train and test a logistic regression model.

You should get some surprising results.

```
# Write your code here.
```

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 to train and test the logistic regression.

```
# Write your code here.
```

This is not a surprise that our model is not working. We see that selecting feature 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 statistical performance.

```
# Write your code here.
```