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| |
| <div class="cover"> |
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| <div class="cover-circle cover-circle-1"></div> |
| <div class="cover-circle cover-circle-2"></div> |
| <div class="cover-circle cover-circle-3"></div> |
| </div> |
| <div class="cover-content"> |
| <div class="cover-badge">Formation 2025/2026</div> |
| <h1 class="cover-title">Cours de<br>Machine Learning</h1> |
| <p class="cover-subtitle">De la theorie a la pratique — Algorithmes fondamentaux et techniques avancees</p> |
| <p class="cover-author">Formateur : Imad Maalouf</p> |
| <p class="cover-info">ML Academy — GE-MCI 4A</p> |
| </div> |
| </div> |
|
|
| |
| <div class="content"> |
| <h1>1. Introduction au Machine Learning</h1> |
| |
| <p> |
| Le <strong>Machine Learning (ML)</strong> est une branche de l'intelligence artificielle |
| qui permet aux machines d'apprendre a partir de donnees <em>sans etre explicitement programmees</em> |
| pour chaque tache. Au lieu de coder des regles a la main, on montre des exemples au modele |
| et il decouvre lui-meme les patterns. |
| </p> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Idee fondamentale</div> |
| <p> |
| On cherche a approximer une fonction inconnue $f$ telle que $\hat{y} = f(x_1, x_2, \ldots, x_n)$. |
| Le modele ML apprend cette fonction a partir d'exemples $(x, y)$ connus. |
| </p> |
| </div> |
|
|
| <h2>1.1 Types d'apprentissage</h2> |
|
|
| <div class="cards-grid"> |
| <div class="card"> |
| <div class="card-icon">S</div> |
| <div class="card-title">Supervise</div> |
| <div class="card-text">Donnees labellisees $(x, y)$ : regression et classification.</div> |
| </div> |
| <div class="card"> |
| <div class="card-icon">N</div> |
| <div class="card-title">Non supervise</div> |
| <div class="card-text">Pas de labels : clustering, reduction de dimension.</div> |
| </div> |
| <div class="card"> |
| <div class="card-icon">R</div> |
| <div class="card-title">Par renforcement</div> |
| <div class="card-text">Agent apprend via actions-recompenses.</div> |
| </div> |
| </div> |
|
|
| <h2>1.2 Pipeline ML typique</h2> |
|
|
| <div class="pipeline"> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">1</div> |
| <div class="pipeline-label">Donnees</div> |
| <div class="pipeline-desc">Collecte & nettoyage</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">2</div> |
| <div class="pipeline-label">Features</div> |
| <div class="pipeline-desc">Engineering</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">3</div> |
| <div class="pipeline-label">Split</div> |
| <div class="pipeline-desc">Train / Test</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">4</div> |
| <div class="pipeline-label">Modele</div> |
| <div class="pipeline-desc">Entrainement</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">5</div> |
| <div class="pipeline-label">Evaluation</div> |
| <div class="pipeline-desc">Metriques</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">6</div> |
| <div class="pipeline-label">Production</div> |
| <div class="pipeline-desc">Deploiement</div> |
| </div> |
| </div> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>2. Regression Lineaire</h1> |
| |
| <p> |
| La <strong>regression lineaire</strong> modelise la relation entre les features et la cible |
| par une fonction affine. C'est l'algorithme le plus simple mais souvent tres efficace |
| comme baseline. |
| </p> |
|
|
| <div class="equation-block"> |
| $$\hat{y} = w_0 + w_1 x_1 + w_2 x_2 + \cdots + w_n x_n = \mathbf{w}^T \mathbf{x}$$ |
| <span class="equation-label">Modele lineaire avec coefficients $\mathbf{w}$</span> |
| </div> |
|
|
| <p> |
| L'objectif est de minimiser l'erreur quadratique moyenne (MSE) : |
| </p> |
|
|
| <div class="equation-block"> |
| $$\text{MSE} = \frac{1}{m} \sum_{i=1}^{m} (y_i - \hat{y}_i)^2$$ |
| <span class="equation-label">Fonction de cout : moyenne des erreurs quadratiques</span> |
| </div> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Solution analytique</div> |
| <p> |
| La regression lineaire admet une solution fermee : |
| $\mathbf{w}^* = (X^T X)^{-1} X^T Y$. Pas besoin d'iterations ! |
| </p> |
| </div> |
|
|
| <h2>2.1 Avantages et limitations</h2> |
|
|
| <div class="comparison-grid"> |
| <div class="comparison-box"> |
| <h4>[+] Avantages</h4> |
| <ul> |
| <li>Tres rapide a entrainer</li> |
| <li>Interpretable (coefficients)</li> |
| <li>Pas d'hyperparametres</li> |
| <li>Excellent baseline</li> |
| </ul> |
| </div> |
| <div class="comparison-box"> |
| <h4>[-] Limitations</h4> |
| <ul> |
| <li>Relation lineaire uniquement</li> |
| <li>Sensible aux outliers</li> |
| <li>Performance decroit en haute dimension</li> |
| </ul> |
| </div> |
| </div> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>3. Regression Logistique</h1> |
| |
| <p> |
| Malgre son nom, la <strong>regression logistique</strong> est un algorithme de <em>classification</em>. |
| Elle predit la probabilite d'appartenance a une classe en utilisant la fonction sigmoide. |
| </p> |
|
|
| <div class="equation-block"> |
| $$P(y=1|\mathbf{x}) = \sigma(\mathbf{w}^T \mathbf{x}) = \frac{1}{1 + e^{-\mathbf{w}^T \mathbf{x}}}$$ |
| <span class="equation-label">Fonction sigmoide pour la classification binaire</span> |
| </div> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Cas d'usage : Dataset Titanic</div> |
| <p> |
| Predire la survie des passagers du Titanic a partir de leur age, sexe, |
| classe de billet, etc. Un classique du ML pour debuter ! |
| </p> |
| </div> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>4. Random Forest</h1> |
| |
| <p> |
| <strong>Random Forest</strong> est un ensemble d'arbres de decision qui votent pour predire. |
| C'est l'un des algorithmes les plus populaires en ML applique : performant, robuste, |
| peu sensible au tuning. |
| </p> |
|
|
| <h2>4.1 Algorithme : Bagging + Random Splits</h2> |
|
|
| <div class="pipeline"> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">1</div> |
| <div class="pipeline-label">Bootstrap</div> |
| <div class="pipeline-desc">Echantillons aleatoires</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">2</div> |
| <div class="pipeline-label">Splits</div> |
| <div class="pipeline-desc">Features aleatoires</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">3</div> |
| <div class="pipeline-label">Arbres</div> |
| <div class="pipeline-desc">N arbres independants</div> |
| </div> |
| <div class="pipeline-step"> |
| <div class="pipeline-num">4</div> |
| <div class="pipeline-label">Vote</div> |
| <div class="pipeline-desc">Moyenne ou mode</div> |
| </div> |
| </div> |
|
|
| <h2>4.2 Hyperparametres cles</h2> |
|
|
| <div class="metric-row"> |
| <div class="metric-card"> |
| <div class="metric-name">n_estimators</div> |
| <div class="metric-formula">100 - 500</div> |
| <div class="metric-desc">Nombre d'arbres</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">max_depth</div> |
| <div class="metric-formula">10 - 30</div> |
| <div class="metric-desc">Profondeur max</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">min_samples_split</div> |
| <div class="metric-formula">2 - 10</div> |
| <div class="metric-desc">Min pour splitter</div> |
| </div> |
| </div> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Feature Importance</div> |
| <p> |
| Random Forest fournit automatiquement l'importance de chaque feature, |
| ce qui aide a comprendre quelles variables influencent le plus les predictions. |
| </p> |
| </div> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>5. Reseaux de Neurones</h1> |
| |
| <p> |
| Les <strong>reseaux de neurones</strong> sont inspires du cerveau humain : des couches de neurones |
| interconnectes executent des transformations non-lineaires. Ils excellent pour les patterns complexes. |
| </p> |
|
|
| <h2>5.1 Fonctionnement : Forward + Backprop</h2> |
|
|
| <div class="cards-grid"> |
| <div class="card"> |
| <div class="card-icon">F</div> |
| <div class="card-title">Forward Pass</div> |
| <div class="card-text">Donnees traversent les couches : $\mathbf{h}_1 = \sigma(W_1 \mathbf{x} + b_1)$</div> |
| </div> |
| <div class="card"> |
| <div class="card-icon">L</div> |
| <div class="card-title">Loss Computation</div> |
| <div class="card-text">Compare prediction vs realite : $L = \frac{1}{m} \sum (y - \hat{y})^2$</div> |
| </div> |
| <div class="card"> |
| <div class="card-icon">B</div> |
| <div class="card-title">Backpropagation</div> |
| <div class="card-text">Calcule les gradients via la chaine de derivation</div> |
| </div> |
| </div> |
|
|
| <h2>5.2 Fonctions d'activation</h2> |
|
|
| <div class="metric-row"> |
| <div class="metric-card"> |
| <div class="metric-name">ReLU</div> |
| <div class="metric-formula">$f(x) = \max(0, x)$</div> |
| <div class="metric-desc">Couches cachees</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">Sigmoid</div> |
| <div class="metric-formula">$f(x) = \frac{1}{1 + e^{-x}}$</div> |
| <div class="metric-desc">Classification binaire</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">Softmax</div> |
| <div class="metric-formula">$f(x_i) = \frac{e^{x_i}}{\sum_j e^{x_j}}$</div> |
| <div class="metric-desc">Classification multi-classe</div> |
| </div> |
| </div> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>6. LSTM et Series Temporelles</h1> |
| |
| <p> |
| <strong>LSTM (Long Short-Term Memory)</strong> est un type de reseau neuronal pour series temporelles. |
| Il peut "retenir" l'information sur de longues periodes — crucial pour les predictions temporelles. |
| </p> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Probleme des RNN vanilla</div> |
| <p> |
| Les gradients disparaissent (vanishing) ou explosent (exploding) sur de longues sequences. |
| Le LSTM resout ce probleme avec son <strong>cell state</strong>. |
| </p> |
| </div> |
|
|
| <h2>6.1 Les trois portes du LSTM</h2> |
|
|
| <div class="metric-row"> |
| <div class="metric-card"> |
| <div class="metric-name">Forget Gate</div> |
| <div class="metric-formula">$f_t = \sigma(W_f [h_{t-1}, x_t] + b_f)$</div> |
| <div class="metric-desc">Quoi oublier ?</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">Input Gate</div> |
| <div class="metric-formula">$i_t = \sigma(W_i [h_{t-1}, x_t] + b_i)$</div> |
| <div class="metric-desc">Quoi ajouter ?</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">Output Gate</div> |
| <div class="metric-formula">$o_t = \sigma(W_o [h_{t-1}, x_t] + b_o)$</div> |
| <div class="metric-desc">Quoi exposer ?</div> |
| </div> |
| </div> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Cas d'usage</div> |
| <p> |
| Prediction de prix boursiers, meteo, consommation energetique, |
| traitement du langage naturel (NLP)... |
| </p> |
| </div> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>7. Metriques de Performance</h1> |
| |
| <p> |
| Evaluer correctement un modele est crucial. Les bonnes metriques dependent du type de probleme |
| (regression vs classification) et des objectifs metier. |
| </p> |
|
|
| <h2>7.1 Regression</h2> |
|
|
| <div class="metric-row"> |
| <div class="metric-card"> |
| <div class="metric-name">MAE</div> |
| <div class="metric-formula">$\frac{1}{n}\sum|y_i - \hat{y}_i|$</div> |
| <div class="metric-desc">Robuste aux outliers</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">RMSE</div> |
| <div class="metric-formula">$\sqrt{\frac{1}{n}\sum(y_i - \hat{y}_i)^2}$</div> |
| <div class="metric-desc">Penalise les grandes erreurs</div> |
| </div> |
| <div class="metric-card"> |
| <div class="metric-name">R2</div> |
| <div class="metric-formula">$1 - \frac{SS_{res}}{SS_{tot}}$</div> |
| <div class="metric-desc">% variance expliquee</div> |
| </div> |
| </div> |
|
|
| <h2>7.2 Classification</h2> |
|
|
| <table> |
| <thead> |
| <tr> |
| <th>Metrique</th> |
| <th>Formule</th> |
| <th>Usage</th> |
| </tr> |
| </thead> |
| <tbody> |
| <tr> |
| <td><strong>Accuracy</strong></td> |
| <td>$(TP + TN) / Total$</td> |
| <td>Classes equilibrees</td> |
| </tr> |
| <tr> |
| <td><strong>Precision</strong></td> |
| <td>$TP / (TP + FP)$</td> |
| <td>Minimiser faux positifs</td> |
| </tr> |
| <tr> |
| <td><strong>Recall</strong></td> |
| <td>$TP / (TP + FN)$</td> |
| <td>Minimiser faux negatifs</td> |
| </tr> |
| <tr> |
| <td><strong>F1-Score</strong></td> |
| <td>$2 \cdot \frac{P \cdot R}{P + R}$</td> |
| <td>Classes desequilibrees</td> |
| </tr> |
| </tbody> |
| </table> |
|
|
| <div class="page-break"></div> |
|
|
| <h1>8. Optimisation et Regularisation</h1> |
| |
| <p> |
| Pour eviter le <strong>surapprentissage (overfitting)</strong> et ameliorer la generalisation, |
| plusieurs techniques existent. |
| </p> |
|
|
| <div class="cards-grid"> |
| <div class="card"> |
| <div class="card-icon">D</div> |
| <div class="card-title">Dropout</div> |
| <div class="card-text">Desactive aleatoirement des neurones pendant l'entrainement.</div> |
| </div> |
| <div class="card"> |
| <div class="card-icon">E</div> |
| <div class="card-title">Early Stopping</div> |
| <div class="card-text">Arrete l'entrainement quand la validation stagne.</div> |
| </div> |
| <div class="card"> |
| <div class="card-icon">L</div> |
| <div class="card-title">L2 Regularization</div> |
| <div class="card-text">Penalise les grands poids : $L_{total} = L_{data} + \lambda \sum w^2$</div> |
| </div> |
| </div> |
|
|
| <div class="info-box"> |
| <div class="info-box-title">Regle d'or</div> |
| <p> |
| Toujours comparer les metriques sur <strong>train</strong> ET <strong>test</strong>. |
| Un grand ecart = overfitting. Objectif : R2 train ≈ R2 test. |
| </p> |
| </div> |
|
|
| <div class="author-footer"> |
| <div class="author-name">Imad Maalouf</div> |
| <div class="author-contact"> |
| imadmaalouf02@gmail.com | github.com/imadmaalouf02 | huggingface.co/spaces/MAALOOUF/ML_Training |
| </div> |
| </div> |
| </div> |
| </body> |
| </html> |
|
|
