Add illustration of the effect of scaling data

[ArturoAmorQ]

closes #446

Adds code to visualize the effect of StandardScaler on the adult_census dataset

[glemaitre]

Side note @ArturoAmorQ Instead of adding "Fixes #xxx" in the title, you can add "closes #xxx" in the description of the summary of the first PR message. It will have the advantage that issue #xxx will be close when we are going to merge.

[glemaitre]

If we go with this synthetic example, that would be my comments. However I will propose an alternative

[glemaitre]

I would not import `matplotlib that early. I would delay it to put it in the cell where we do the first plot

[glemaitre]

I think that we should not have comments in the code itself. It would be better to be a real sentence in markdown

[glemaitre]

Suggested change

	X, _ =make_blobs(n_samples=100, n_features=2, centers=centers,
	X, _ = make_blobs(n_samples=100, n_features=2, centers=centers,

[glemaitre]

At this stage, I think that we should plot the original dataset.
Then add some text to do the scikit-learn scaling and finally a new cell with the plotting of the scaling

[glemaitre]

In the first notebook, we did use plt.hist. Instead of generating a new dataset a bit dissociated from the notebook, we could focus on a single feature. It avoids having to explain anything regarding Gaussian blobs and will be more intuitive.

In short, we could plot the histogram of the "age" columns before and after scaling. Basically, it will give these figures:

# %%
fig, axs = plt.subplots(ncols=2, sharey=True, figsize=(6, 4))
axs[0].hist(data_train["age"], bins=15)
axs[1].hist(data_train_scaled[:, 0], bins=15)
axs[0].set_xlabel("Age")
axs[1].set_xlabel("Normalized Age")
axs[0].set_ylabel("Frequency")
fig.suptitle("Histogram of the age feature \nbefore and after normalization", y=1.05)

(I would not use the code above and instead do 2 separate figures to have more basic matplotlib code.)

The nice part is that we show that the distribution does change. Only the x-axis values are changing. We could add use the transformer to transform the minimum age and maximum age on the x-axis to explain how do we get these new values in the scaled data. We can then easily emphasize that the values becomes negative.

[ArturoAmorQ]

The idea of this PR and #446 is to show a figure similar to the one we show in Quiz M1.2 Q4, i.e., using two features to create a plot in the Cartesian plane. The goal is to improve the score for both Q4 (64.7%) and Q5 (40.7%).

I am not sure if people will be able to see the connection between an hist plot and said figures. The fact is that the text explanation has shown not to suffice for passing the concept, so I would assume this connection is not that easy to make.

It avoids having to explain anything regarding Gaussian blobs and will be more intuitive.

Using the data-set could be a good idea as long as we plot it in the Cartesian plane, but letting people play with the position of the centers is worth it in my opinion. Maybe we can find a turnaround like creating using the data-set and encouraging people to visit this example in the documentation, or just adding a fixed image as mentioned in #446. Thoughts on that?

[glemaitre]

The goal is to improve the score for both Q4 (64.7%) and Q5 (40.7%).

65% is fine. The second question is difficult because you need to think that features can become negative and this aspect was discussed in the course before. Thus, I am fine with adding basically the answer in the notebook with the data at hand.

I am not sure if people will be able to see the connection between an hist plot and said figures. The fact is that the text explanation has shown not to suffice for passing the concept, so I would assume this connection is not that easy to make.

Adding the new dataset and figure just allow to answer the quiz without not much thinking but it is completely disconnected from the course. I would really not do that just for the sake of people getting the right answer. Instead, we should make it explicit on the data at hand what we missed to explain at first.

Using the data-set could be a good idea as long as we plot it in the Cartesian plane

The histogram is useful there. It allows showing that there is no change in the distribution indeed. We can still plot thing in the feature space thought. I could imagine a strip plot together with the marginal distribution on the top

but letting people play with the position of the centers is worth it in my opinion

IMO, he does not bring any values

Maybe we can find a turnaround like creating using the data-set and encouraging people to visit this example in the documentation, or just adding a fixed image as mentioned in #446.

This example is quite complex but it is worth to link to it explaining that StandardScaler is only an option and other preprocessors are existing.

[ArturoAmorQ]

I committed a new illustration using the adult_census data-set to avoid creating an ad hoc data-set with make_blobs.

[lesteve]

A few comments

[lesteve]

I think before this you can add something to say that in the previous cell the mean of all the columns is close to 0 and the standard deviation of all the columns is close to 1 which is the StandardScaler's purpose

[ArturoAmorQ]

Done, thanks for the comments!