Python pour la data science

Lino Galiana

doi:10.5281/zenodo.8229676

If you want to try the examples in this tutorial:

1 Introduction

This chapter aims to very briefly introduce the principle of training models in a classification context. The goal is to illustrate the process using an algorithm with an intuitive principle. It seeks to demonstrate some of the concepts discussed in previous chapters, particularly those related to model training. Other courses in your curriculum will allow you to explore additional classification algorithms and the limitations of each technique.

1.1 Data

Ce chapitre utilise toujours le même jeu de données, présenté dans l’introduction de cette partie : les données de vote aux élections présidentielles américaines croisées à des variables sociodémographiques. Le code est disponible sur Github.

!pip install --upgrade xlrd #colab bug verson xlrd
!pip install geopandas

import requests

url = 'https://raw.githubusercontent.com/linogaliana/python-datascientist/main/content/modelisation/get_data.py'
r = requests.get(url, allow_redirects=True)
open('getdata.py', 'wb').write(r.content)

import getdata
votes = getdata.create_votes_dataframes()

1.2 The SVM Method (Support Vector Machines)

SVM (Support Vector Machines) is part of the traditional toolkit for data scientists. The principle of this technique is relatively intuitive thanks to its geometric interpretation. The goal is to find a line, with margins (supports), that best separates the point cloud in our data. Of course, in real life, it is rare to have well-organized point clouds that can be separated by a line. However, an appropriate projection (a kernel) can transform the data to enable separation.

Mathematical formalization

SVM is one of the most intuitive machine learning methods due to its simple geometric interpretation. It is also one of the least complex machine learning algorithms in terms of formalization for practitioners familiar with traditional statistics. This note provides an overview, though it is not essential for understanding this chapter. In machine learning, more than the mathematical details, the key is to build intuitions.

The goal of SVM, let us recall, is to find a hyperplane that best separates the different classes. For example, in a two-dimensional space, it aims to find a line with margins that best divides the space into regions with homogeneous labels.

Without loss of generality, we can assume the problem involves a probability distribution \(\mathbb{P}(x,y)\) (\(\mathbb{P} \to \{-1,1\}\)) that is unknown. The goal of classification is to build an estimator of the ideal decision function that minimizes the probability of error. In other words

\[ \theta = \arg\min_\Theta \mathbb{P}(h_\theta(X) \neq y |x) \]

The simplest SVMs are linear SVMs. In this case, it is assumed that a linear separator exists that can assign each class based on its sign:

\[ h_\theta(x) = \text{signe}(f_\theta(x)) ; \text{ avec } f_\theta(x) = \theta^T x + b \] avec \(\theta \in \mathbb{R}^p\) et \(w \in \mathbb{R}\).

When observations are linearly separable, there is an infinite number of linear decision boundaries separating the two classes. The “best” choice is to select the maximum margin that separates the data. The distance between the two margins is \(\frac{2}{||\theta||}\). Thus, maximizing this distance between two hyperplanes is equivalent to minimizing \(||\theta||^2\) under the constraint \(y_i(\theta^Tx_i + b) \geq 1\).

In the non-linearly separable case, the hinge loss \(\max\big(0,y_i(\theta^Tx_i + b)\big)\) allows for linearizing the loss function, resulting in the following optimization problem:

\[ \frac{1}{n} \sum_{i=1}^n \max\big(0,y_i(\theta^Tx_i + b)\big) + \lambda ||\theta||^2 \]

Generalization to the non-linear case involves introducing kernels that transform the coordinate space of the observations.

2 Application

To apply a classification model, we need to find a dichotomous variable. The natural choice is to use the dichotomous variable of a party’s victory or defeat.

Even though the Republicans lost in 2020, they won in more counties (less populated ones). We will consider a Republican victory as our label 1 and a defeat as 0.

from sklearn import svm
import sklearn.metrics
from sklearn.model_selection import train_test_split
from sklearn.model_selection import cross_val_score
import matplotlib.pyplot as plt

Exercise 1: First classification algorithm

Create a dummy variable called y with a value of 1 when the Republicans win.
Using the ready-to-use function train_test_split from the sklearn.model_selection library, create test samples (20% of the observations) and training samples (80%) with the following features:

vars = [
  "Unemployment_rate_2019", "Median_Household_Income_2021",
  "Percent of adults with less than a high school diploma, 2018-22",
  "Percent of adults with a bachelor's degree or higher, 2018-22"
]

and use the variable y as the label.

Note: You may encounter the following warning:

A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel()

Note: To avoid this warning every time you train your model, you can use DataFrame[['y']].values.ravel() instead of DataFrame[['y']] when preparing your samples.

Train an SVM classifier with a regularization parameter C = 1. Examine the following performance metrics: accuracy, f1, recall, and precision.
Check the confusion matrix: despite seemingly reasonable scores, you should notice a significant issue.
Repeat the previous steps using normalized variables. Are the results different?
[OPTIONAL] Perform 5-fold cross-validation to determine the ideal C parameter.
Change the x variables. Use only the previous Democratic vote result (2016) and income. The variables in question are share_2016_republican and Median_Household_Income_2021. Examine the results, particularly the confusion matrix.

We thus obtain a set of training features with the following structure:

	Unemployment_rate_2019	Median_Household_Income_2021	Percent of adults with less than a high school diploma, 2018-22	Percent of adults with a bachelor's degree or higher, 2018-22
2588	3.7	48166.0	14.928228	19.153438
1216	3.7	42225.0	24.007613	11.025014
1535	3.5	63984.0	9.895525	21.062488
1473	3.7	57465.0	14.014559	18.742772
1224	4.5	58741.0	7.777468	24.420876

And the associated labels are as follows:

array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,
       1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
       0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1,
       1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0,
       1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1,
       1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
       1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
       0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0,
       1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1,
       0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1,
       0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
       1, 1, 1, 1])

At the end of question 3, our classifier completely misses the 0 labels, which are in the minority. One possible reason is the scale of the variables. Income, in particular, has a distribution that can dominate the others in a linear model. Therefore, at a minimum, it is necessary to standardize the variables, which is the focus of question 4.

Standardizing the variables ultimately does not bring any improvement:

It is therefore necessary to go further: the problem does not lie in the scale but in the choice of variables. This is why the step of variable selection is crucial and why a chapter is dedicated to it.

At the end of question 6, the new classifier should have the following performance:

Informations additionnelles

environment files have been tested on.

Latest built version: 2025-03-19

Python version used:

'3.12.6 | packaged by conda-forge | (main, Sep 30 2024, 18:08:52) [GCC 13.3.0]'

Package	Version
affine	2.4.0
aiobotocore	2.21.1
aiohappyeyeballs	2.6.1
aiohttp	3.11.13
aioitertools	0.12.0
aiosignal	1.3.2
alembic	1.13.3
altair	5.4.1
aniso8601	9.0.1
annotated-types	0.7.0
anyio	4.8.0
appdirs	1.4.4
archspec	0.2.3
asttokens	2.4.1
attrs	25.3.0
babel	2.17.0
bcrypt	4.2.0
beautifulsoup4	4.12.3
black	24.8.0
blinker	1.8.2
blis	1.2.0
bokeh	3.5.2
boltons	24.0.0
boto3	1.37.1
botocore	1.37.1
branca	0.7.2
Brotli	1.1.0
bs4	0.0.2
cachetools	5.5.0
cartiflette	0.0.2
Cartopy	0.24.1
catalogue	2.0.10
cattrs	24.1.2
certifi	2025.1.31
cffi	1.17.1
charset-normalizer	3.4.1
chromedriver-autoinstaller	0.6.4
click	8.1.8
click-plugins	1.1.1
cligj	0.7.2
cloudpathlib	0.21.0
cloudpickle	3.0.0
colorama	0.4.6
comm	0.2.2
commonmark	0.9.1
conda	24.9.1
conda-libmamba-solver	24.7.0
conda-package-handling	2.3.0
conda_package_streaming	0.10.0
confection	0.1.5
contextily	1.6.2
contourpy	1.3.1
cryptography	43.0.1
cycler	0.12.1
cymem	2.0.11
cytoolz	1.0.0
dask	2024.9.1
dask-expr	1.1.15
databricks-sdk	0.33.0
dataclasses-json	0.6.7
debugpy	1.8.6
decorator	5.1.1
Deprecated	1.2.14
diskcache	5.6.3
distributed	2024.9.1
distro	1.9.0
docker	7.1.0
duckdb	1.2.1
en_core_web_sm	3.8.0
entrypoints	0.4
et_xmlfile	2.0.0
exceptiongroup	1.2.2
executing	2.1.0
fastexcel	0.11.6
fastjsonschema	2.21.1
fiona	1.10.1
Flask	3.0.3
folium	0.17.0
fontawesomefree	6.6.0
fonttools	4.56.0
fr_core_news_sm	3.8.0
frozendict	2.4.4
frozenlist	1.5.0
fsspec	2023.12.2
geographiclib	2.0
geopandas	1.0.1
geoplot	0.5.1
geopy	2.4.1
gitdb	4.0.11
GitPython	3.1.43
google-auth	2.35.0
graphene	3.3
graphql-core	3.2.4
graphql-relay	3.2.0
graphviz	0.20.3
great-tables	0.12.0
greenlet	3.1.1
gunicorn	22.0.0
h11	0.14.0
h2	4.1.0
hpack	4.0.0
htmltools	0.6.0
httpcore	1.0.7
httpx	0.28.1
httpx-sse	0.4.0
hyperframe	6.0.1
idna	3.10
imageio	2.37.0
importlib_metadata	8.6.1
importlib_resources	6.5.2
inflate64	1.0.1
ipykernel	6.29.5
ipython	8.28.0
itsdangerous	2.2.0
jedi	0.19.1
Jinja2	3.1.6
jmespath	1.0.1
joblib	1.4.2
jsonpatch	1.33
jsonpointer	3.0.0
jsonschema	4.23.0
jsonschema-specifications	2024.10.1
jupyter-cache	1.0.0
jupyter_client	8.6.3
jupyter_core	5.7.2
kaleido	0.2.1
kiwisolver	1.4.8
langchain	0.3.20
langchain-community	0.3.9
langchain-core	0.3.45
langchain-text-splitters	0.3.6
langcodes	3.5.0
langsmith	0.1.147
language_data	1.3.0
lazy_loader	0.4
libmambapy	1.5.9
locket	1.0.0
loguru	0.7.3
lxml	5.3.1
lz4	4.3.3
Mako	1.3.5
mamba	1.5.9
mapclassify	2.8.1
marisa-trie	1.2.1
Markdown	3.6
markdown-it-py	3.0.0
MarkupSafe	3.0.2
marshmallow	3.26.1
matplotlib	3.10.1
matplotlib-inline	0.1.7
mdurl	0.1.2
menuinst	2.1.2
mercantile	1.2.1
mizani	0.11.4
mlflow	2.16.2
mlflow-skinny	2.16.2
msgpack	1.1.0
multidict	6.1.0
multivolumefile	0.2.3
munkres	1.1.4
murmurhash	1.0.12
mypy-extensions	1.0.0
narwhals	1.30.0
nbclient	0.10.0
nbformat	5.10.4
nest_asyncio	1.6.0
networkx	3.4.2
nltk	3.9.1
numpy	2.2.3
opencv-python-headless	4.10.0.84
openpyxl	3.1.5
opentelemetry-api	1.16.0
opentelemetry-sdk	1.16.0
opentelemetry-semantic-conventions	0.37b0
orjson	3.10.15
outcome	1.3.0.post0
OWSLib	0.28.1
packaging	24.2
pandas	2.2.3
paramiko	3.5.0
parso	0.8.4
partd	1.4.2
pathspec	0.12.1
patsy	1.0.1
Pebble	5.1.0
pexpect	4.9.0
pickleshare	0.7.5
pillow	11.1.0
pip	24.2
platformdirs	4.3.6
plotly	5.24.1
plotnine	0.13.6
pluggy	1.5.0
polars	1.8.2
preshed	3.0.9
prometheus_client	0.21.0
prometheus_flask_exporter	0.23.1
prompt_toolkit	3.0.48
propcache	0.3.0
protobuf	4.25.3
psutil	7.0.0
ptyprocess	0.7.0
pure_eval	0.2.3
py7zr	0.20.8
pyarrow	17.0.0
pyarrow-hotfix	0.6
pyasn1	0.6.1
pyasn1_modules	0.4.1
pybcj	1.0.3
pycosat	0.6.6
pycparser	2.22
pycryptodomex	3.21.0
pydantic	2.10.6
pydantic_core	2.27.2
pydantic-settings	2.8.1
Pygments	2.19.1
PyNaCl	1.5.0
pynsee	0.1.8
pyogrio	0.10.0
pyOpenSSL	24.2.1
pyparsing	3.2.1
pyppmd	1.1.1
pyproj	3.7.1
pyshp	2.3.1
PySocks	1.7.1
python-dateutil	2.9.0.post0
python-dotenv	1.0.1
python-magic	0.4.27
pytz	2025.1
pyu2f	0.1.5
pywaffle	1.1.1
PyYAML	6.0.2
pyzmq	26.3.0
pyzstd	0.16.2
querystring_parser	1.2.4
rasterio	1.4.3
referencing	0.36.2
regex	2024.9.11
requests	2.32.3
requests-cache	1.2.1
requests-toolbelt	1.0.0
retrying	1.3.4
rich	13.9.4
rpds-py	0.23.1
rsa	4.9
rtree	1.4.0
ruamel.yaml	0.18.6
ruamel.yaml.clib	0.2.8
s3fs	2023.12.2
s3transfer	0.11.3
scikit-image	0.24.0
scikit-learn	1.6.1
scipy	1.13.0
seaborn	0.13.2
selenium	4.29.0
setuptools	76.0.0
shapely	2.0.7
shellingham	1.5.4
six	1.17.0
smart-open	7.1.0
smmap	5.0.0
sniffio	1.3.1
sortedcontainers	2.4.0
soupsieve	2.5
spacy	3.8.4
spacy-legacy	3.0.12
spacy-loggers	1.0.5
SQLAlchemy	2.0.39
sqlparse	0.5.1
srsly	2.5.1
stack-data	0.6.2
statsmodels	0.14.4
tabulate	0.9.0
tblib	3.0.0
tenacity	9.0.0
texttable	1.7.0
thinc	8.3.4
threadpoolctl	3.6.0
tifffile	2025.3.13
toolz	1.0.0
topojson	1.9
tornado	6.4.2
tqdm	4.67.1
traitlets	5.14.3
trio	0.29.0
trio-websocket	0.12.2
truststore	0.9.2
typer	0.15.2
typing_extensions	4.12.2
typing-inspect	0.9.0
tzdata	2025.1
Unidecode	1.3.8
url-normalize	1.4.3
urllib3	1.26.20
uv	0.6.8
wasabi	1.1.3
wcwidth	0.2.13
weasel	0.4.1
webdriver-manager	4.0.2
websocket-client	1.8.0
Werkzeug	3.0.4
wheel	0.44.0
wordcloud	1.9.3
wrapt	1.17.2
wsproto	1.2.0
xgboost	2.1.1
xlrd	2.0.1
xyzservices	2025.1.0
yarl	1.18.3
yellowbrick	1.5
zict	3.0.0
zipp	3.21.0
zstandard	0.23.0

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md`Ce fichier a été modifié __${table_commit.length}__ fois depuis sa création le ${creation_string} (dernière modification le ${last_modification_string})`

creation = d3.min(
  table_commit.map(d => new Date(d.Date))
)

last_modification = d3.max(
  table_commit.map(d => new Date(d.Date))
)

creation_string = creation.toLocaleString("fr", {
  "day": "numeric",
  "month": "long",
  "year": "numeric"
})

last_modification_string = last_modification.toLocaleString("fr", {
  "day": "numeric",
  "month": "long",
  "year": "numeric"
})

html`<div>${git_history_table}</div>`

html`<div>${git_history_plot}</div>`

SHA	Date	Author	Description
48dccf14	2025-01-14 21:45:34	lgaliana	Fix bug in modeling section
8c8ca4c0	2024-12-20 10:45:00	lgaliana	Traduction du chapitre clustering
a5ecaedc	2024-12-20 09:36:42	Lino Galiana	Traduction du chapitre modélisation (#582)
ff0820bc	2024-11-27 15:10:39	lgaliana	Mise en forme chapitre régression
bb943aab	2024-11-26 15:18:41	Lino Galiana	hope works (#579)
e7fd1ff3	2024-11-25 18:20:32	lgaliana	rename classification chapter

git_history_table = Inputs.table(
  table_commit,
  {
    format: {
      SHA: x => md`[${x}](${github_repo}/commit/${x})`,
      Description: x => md`${replacePullRequestPattern(x, github_repo)}`,
      /*Date: x => x.toLocaleString("fr", {
        "month": "numeric",
        "day": "numeric",
        "year": "numeric"
        })
      */
    }
  }
)

git_history_plot = Plot.plot({
  marks: [
    Plot.ruleY([0], {stroke: "royalblue"}),
    Plot.dot(
          table_commit,
          Plot.pointerX({x: (d) => new Date(d.date), y: 0, stroke: "red"})),
    Plot.dot(table_commit, {x: (d) => new Date(d.Date), y: 0, fill: "royalblue"})
  ]
})

function replacePullRequestPattern(inputString, githubRepo) {
    // Use a regular expression to match the pattern #digit
    var pattern = /#(\d+)/g;

    // Replace the pattern with ${github_repo}/pull/#digit
    var replacedString = inputString.replace(pattern, '[#$1](' + githubRepo + '/pull/$1)');

    return replacedString;
}

github_repo = "https://github.com/linogaliana/python-datascientist"

table_commit = {

// Get the HTML table by its class name
var table = document.querySelector('.commit-table');

// Check if the table exists
if (table) {
    // Initialize an array to store the table data
    var dataArray = [];

    // Extract headers from the first row
    var headers = [];
    for (var i = 0; i < table.rows[0].cells.length; i++) {
        headers.push(table.rows[0].cells[i].textContent.trim());
    }

    // Iterate through the rows, starting from the second row
    for (var i = 1; i < table.rows.length; i++) {
        var row = table.rows[i];
        var rowData = {};

        // Iterate through the cells in the row
        for (var j = 0; j < row.cells.length; j++) {
            // Use headers as keys and cell content as values
            rowData[headers[j]] = row.cells[j].textContent.trim();
        }

        // Push the rowData object to the dataArray
        dataArray.push(rowData);
    }
  }

  return dataArray

}

// Get the element with class 'git-details'
{
  var gitDetails = document.querySelector('.commit-table');

  // Check if the element exists
  if (gitDetails) {
      // Hide the element
      gitDetails.style.display = 'none';
  }
}

Plot = require('@observablehq/plot@0.6.12/dist/plot.umd.min.js')

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Citation

BibTeX citation:

@book{galiana2023,
  author = {Galiana, Lino},
  title = {Python Pour La Data Science},
  date = {2023},
  url = {https://pythonds.linogaliana.fr/},
  doi = {10.5281/zenodo.8229676},
  langid = {en}
}

For attribution, please cite this work as:

Galiana, Lino. 2023. Python Pour La Data Science. https://doi.org/10.5281/zenodo.8229676.