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<body>
  <!-- Cover Page -->
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    <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>

  <!-- Content -->
  <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>
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