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    "# Exercice 1 : \n",
    "Autre fonctions d'erreurs : \n",
    "- Erreur résiduelle : ei = f(xi)-yi\n",
    "- Erreur logarithmique : ei = log(1+|f(xi)-yi|)\n",
    "- Erreur relative : ei = (f(xi)-yi)/yi\n",
    "\n",
    "# Exercice 2 : \n",
    "Autre fonctions de couts : \n",
    "- Erreur Log-Cosh, Log-Cosh est similaire à MAE pour de petites erreurs\n",
    "- Erreur Huber (𝛿=1), Huber réduit l’impact des grandes erreurs\n",
    "- Erreur de Poisson, Poisson est adaptée aux distributions asymétriques\n",
    "  "
   ]
  },
  {
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   "id": "3aa6d565-ac05-48ca-9f10-ece048a7eff2",
   "metadata": {},
   "source": [
    "# Exercice 3 : \n"
   ]
  },
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     "text": [
      "iteration =  1\n",
      "a= 50  b= 75\n",
      "iteration =  2\n",
      "a= -25.75309997451889  b= 74.9568945\n",
      "iteration =  3\n",
      "a= 13.539805289078245  b= 74.97929653630847\n",
      "iteration =  4\n",
      "a= -6.841306604859323  b= 74.9677200103882\n",
      "iteration =  5\n",
      "a= 3.730314856415273  b= 74.97376806255475\n",
      "iteration =  6\n",
      "a= -1.7531534482568194  b= 74.9706742990146\n",
      "iteration =  7\n",
      "a= 1.0911050566712879  b= 74.97232236778468\n",
      "iteration =  8\n",
      "a= -0.3842033063747208  b= 74.97151086236455\n",
      "iteration =  9\n",
      "a= 0.3810346829632343  b= 74.97197513066288\n",
      "iteration =  10\n",
      "a= -0.015891986938224745  b= 74.97177765894565\n",
      "iteration =  11\n",
      "a= 0.1899926591360049  b= 74.9719234297637\n",
      "iteration =  12\n",
      "a= 0.08320088730389696  b= 74.97189116168829\n",
      "iteration =  13\n",
      "a= 0.13859343372153637  b= 74.97195124182983\n",
      "iteration =  14\n",
      "a= 0.10986146169209325  b= 74.97196342120678\n",
      "iteration =  15\n",
      "a= 0.12476462455318163  b= 74.97200044654436\n",
      "iteration =  16\n",
      "a= 0.1170343740876787  b= 74.97202458433483\n",
      "iteration =  17\n",
      "a= 0.12104400709218902  b= 74.97205540683525\n",
      "iteration =  18\n",
      "a= 0.11896419782388343  b= 74.97208276197472\n",
      "iteration =  19\n",
      "a= 0.12004296396127893  b= 74.97211191560189\n",
      "Paramètre a : 0.11948338652853815\n",
      "Paramètre b : 74.97214013633689\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Données d'exemple (à remplacer par vos propres données)\n",
    "# xi : les valeurs d'entrée\n",
    "# yi : les valeurs de sortie cibles\n",
    "xi = np.array([313, 2384, 342, 420])  # Exemple\n",
    "yi = np.array([124, 339, 179, 186])  # Exemple\n",
    "\n",
    "# Hyperparamètres\n",
    "alpha = 0.000001  # Taux d'apprentissage\n",
    "m = len(xi)  # Nombre d'exemples\n",
    "\n",
    "# Initialisation des paramètres\n",
    "a = 50  # Paramètre a initial\n",
    "b =  75 # Paramètre b initial\n",
    "\n",
    "# Seuils d'arrêt\n",
    "epsilon_threshold = 1e-3\n",
    "\n",
    "# Initialisation des erreurs\n",
    "epsilon_1 = float('inf')\n",
    "epsilon_2 = float('inf')\n",
    "tmp = 0\n",
    "\n",
    "# Boucle principale\n",
    "while epsilon_1 > epsilon_threshold or epsilon_2 > epsilon_threshold:\n",
    "    a_prev = a\n",
    "    b_prev = b\n",
    "    tmp += 1\n",
    "    print(\"iteration = \",tmp)\n",
    "    print(\"a=\",a,\" b=\",b)\n",
    "    \n",
    "\n",
    "\n",
    "    # Calcul des gradients et mise à jour des paramètres\n",
    "    b = b - alpha * (1 / m) * np.sum(a * xi + b - yi)\n",
    "    a = a - alpha * (1 / m) * np.sum((a * xi + b - yi) * xi)\n",
    "\n",
    "    # Calcul des erreurs\n",
    "    epsilon_1 = abs(a_prev - a)\n",
    "    epsilon_2 = abs(b_prev - b)\n",
    "\n",
    "# Résultats finaux\n",
    "print(f\"Paramètre a : {a}\")\n",
    "print(f\"Paramètre b : {b}\")"
   ]
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    "| Itération | A | B |\n",
    "| :--------------- |:---------------:| -----:|\n",
    "| 1  | 50 | 75 |\n",
    "| 9  | 0.38103 | 74.97197 |\n",
    "| 19 | 0.12004 | 74.97214 |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9fed1c7-6c60-4589-8086-3f8fefec8fca",
   "metadata": {},
   "source": [
    "# Exercice 4 :\n",
    "## 1)\n",
    "![image](Illustration_sans_titre.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04ea9f05-9b2d-43a9-86bf-afa9f17f0336",
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   "source": [
    "## 2)\n",
    "\n",
    "data : 01 11 10 00\n",
    "\n",
    "| _ | 01 | 11 | 10 | 00 |\n",
    "| :--------------- |:---------------:| -----:| -----:| -----:|\n",
    "| W0 | 2 | 1 | 1 | 0 |\n",
    "| W1 | 0 | 0 | 0 | 1 |\n",
    "| W2 | 0 | 1 | 1 | 1 |\n",
    "| RF |-2 | 0 | -1 | 0 |\n",
    "| RO | 0 | 0 | 0 | 0 |\n",
    "| RA | 1 | 0 | 1 | 0 |\n",
    "| W0' | 2+(1-0)*-1 = 1 | 1 | 1+(1-0)*-1 = 0 | 0 |\n",
    "| W1' | 0+(1-0)*0 = 0 | 0 | 0+(1-0)*1 = 1 | 1 |\n",
    "| W2' | 0+(1-0)*1 = 1 | 1 | 1+(1-0)*0 = 1 | 1 |"
   ]
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