_Exo1_Descente_de_gradient.ipynb

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        "<a href=\"https://colab.research.google.com/github/roxin/psm-machine-learning/blob/master/_Exo1_Descente_de_gradient.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
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        "id": "jpoYHDHo6Ya0"
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      "source": [
        "# Algorithme de la descente de gradient\n",
        "### Source d'inspiration :\n",
        "### https://www.bogotobogo.com/python/python_numpy_batch_gradient_descent_algorithm.php"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oFq5HwUE6Ya1"
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      "source": [
        "### Descente du gradient (descente graduelle)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HCoo_tO26Ya2"
      },
      "source": [
        "### Fonction coût"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OIno64Rp6ihR"
      },
      "source": [
        "\\begin{equation*}\n",
        "J \\left(\\theta_0, \\theta_1\\right) = \\frac{1}{2m}\\sum_{i=1}^m ( h_\\theta(x_i)- y_i)^2\n",
        "\\end{equation*}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0IEYRPXs79S7"
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      "source": [
        "Algorithme de la descente du gradient :\n",
        "\n",
        "     Répeter jusqu'à la convergence :\n",
        "\\begin{equation*}\n",
        "\\theta_0 := \\theta_0 - \\alpha \\frac{1}{m}\\sum_{i=1}^m ( h_\\theta(x_i)- y_i)\n",
        "\\end{equation*}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pPhugYuc-G1-"
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      "source": [
        "\\begin{equation*}\n",
        "\\theta_1 := \\theta_1 - \\alpha \\frac{1}{m}\\sum_{i=1}^m ( h_\\theta(x_i)- y_i)x_i\n",
        "\\end{equation*}"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# importation des bibliothéques\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "P0Bv_xNS4oc_"
      },
      "execution_count": 1,
      "outputs": []
    },
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          "end_time": "2020-09-13T12:52:05.213359Z",
          "start_time": "2020-09-13T12:52:05.207791Z"
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      "source": [
        "# déclaration d'une fonction pour la descente de gradient\n",
        "def descente_de_gradient(alpha, X, y, iterations):\n",
        "    m = X.shape[0] # number d'echantillons\n",
        "    theta = np.ones(2)\n",
        "    X_transpose = X.transpose()\n",
        "    for iter in range(0, iterations):\n",
        "        hypothesis = # TODO\n",
        "        differences = # TODO\n",
        "        # fonction coût (objectif)\n",
        "        J = # TODO  \n",
        "        valJ.append(J)\n",
        "        # print (\"iter %s | J: %.3f\" % (iter, J))      \n",
        "        gradients = #TODO\n",
        "        # mise à jour / nouveau theta \n",
        "        theta = #TODO  \n",
        "        valTheta_0.append(theta[0])\n",
        "        valTheta_1.append(theta[1])\n",
        "    return theta\n",
        "#"
      ],
      "execution_count": null,
      "outputs": []
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      "source": [
        "# Serie longue de données\n",
        "X = 3 * np.random.rand(100, 1)  # genère un vecteur colonne avec 100 éléments (valeurs de 0 à 1) \n",
        "y = 2 + 5 * X + np.random.randn(100, 1)\n",
        "print(np.shape(y))\n",
        "y = y.reshape(100,)\n",
        "print(np.shape(y))"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(100, 1)\n",
            "(100,)\n"
          ]
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      "source": [
        "# Série courte de données\n",
        "X = np.array([[3], [4], [6], [10]]) \n",
        "y = np.array([7, 9, 10, 17]) \n",
        "print('X = ',X)\n",
        "print('y = ', y)\n",
        "              "
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "X =  [[ 3]\n",
            " [ 4]\n",
            " [ 6]\n",
            " [10]]\n",
            "y =  [ 7  9 10 17]\n"
          ]
        }
      ]
    },
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      "source": [
        "#print(X, \"\\n\", y)\n",
        "m = np.shape(X)\n",
        "print(m)"
      ],
      "execution_count": 4,
      "outputs": [
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          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(4, 1)\n"
          ]
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      "source": [
        "# concatenation de deux matrices\n",
        "X_b = np.c_[ np.ones(m), X] # insérer une colonne\n",
        "valJ = []                   # mémorisera les valeurs de la fonction objectif J(theta0, theta1)\n",
        "alpha = 0.005               # pas d'apprentissage\n",
        "valTheta_0 = []\n",
        "valTheta_1 = []\n",
        "nombreIterations = 1000\n",
        "#print(valTheta)\n",
        "theta = descente_de_gradient(alpha, X_b, y, nombreIterations)\n",
        "print(X_b.transpose())"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-5-13d41055588f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mnombreIterations\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;31m#print(valTheta)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mtheta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdescente_de_gradient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX_b\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnombreIterations\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_b\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'descente_de_gradient' is not defined"
          ]
        }
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        "id": "LUKJRaZw6YbG",
        "outputId": "8c1c0dc4-64f6-42d5-a197-e0e3750a6d52"
      },
      "source": [
        "# visualisation\n",
        "for i in range(X_b.shape[1]):\n",
        "    y_predict = theta[0] + theta[1]*X_b \n",
        "\n",
        "plt.plot(X_b[:,1],y,'o',label=\"Prédictions\")\n",
        "plt.plot(X_b,y_predict,'k-')\n",
        "plt.xlabel(\"$X$\", fontsize=18)\n",
        "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
        "plt.legend(loc=\"upper left\", fontsize=14)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2020-09-13T12:54:33.721290Z",
          "start_time": "2020-09-13T12:54:33.584014Z"
        },
        "id": "t_JXLMFz6YbJ",
        "outputId": "fb3a7041-6ac3-4bb5-c40e-bc5f81f805bd"
      },
      "source": [
        "# fonction coût\n",
        "plt.plot(range(nombreIterations), valJ)\n",
        "#plt.title('Pas d\\'apprentissage = ', alpha)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2020-09-13T12:54:39.673414Z",
          "start_time": "2020-09-13T12:54:39.526014Z"
        },
        "id": "NhyMFbaY6YbM",
        "outputId": "906fe8ad-c3a4-437e-995c-975d3145650c"
      },
      "source": [
        "# valTheta [0] valTheta [1]\n",
        "\"\"\"plt.plot(range(nombreIterations), valTheta_0)\n",
        "plt.show()\n",
        "\"\"\"\n",
        "#print(valTheta_1)\n",
        "plt.plot(range(nombreIterations), valTheta_0)\n",
        "plt.plot(range(nombreIterations), valTheta_1)\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2020-09-13T03:53:42.991083Z",
          "start_time": "2020-09-13T03:53:42.750358Z"
        },
        "id": "Z5RDxCcT6YbP",
        "outputId": "5b7303ac-0de2-4b84-c46a-49475e15c580"
      },
      "source": [
        "print(theta)\n",
        "print(\"Terminé !\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "[2.77577901 4.51506986]\n",
            "Terminé !\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}