notebooks/Deeplearning_Practice_2.ipynb

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      "name": "python3",
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "$sigmoid(x) = \\frac{1}{1+e^{-x}}$ is sometimes also known as the logistic function. It is a non-linear function used not only in Machine Learning (Logistic Regression), but also in Deep Learning.\n",
        "\n",
        "Let's first build a function to compute $sigmoid(x)$."
      ],
      "metadata": {
        "id": "ice7hpl7aZm2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "import numpy as np\n",
        "\n",
        "x = np.array([1, 2, 3])\n",
        "# try to run this first line\n",
        "#print(math.exp(x))\n",
        "print(np.exp(x))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zZObZh59jRVa",
        "outputId": "6d76276a-55c1-4fbc-eb3b-ef5ab64699c3"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 2.71828183  7.3890561  20.08553692]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K_u8HmIjZxvr",
        "outputId": "c158168d-06a7-41dc-e3e1-f533cbcd4e40"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9525741268224334"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "# using math package\n",
        "def basic_sigmoid(x):\n",
        "    return 1/(1+math.exp(-x))\n",
        "\n",
        "basic_sigmoid(3)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# using numpy package\n",
        "def sigmoid(x):\n",
        "    return 1/(1+np.exp(-x))\n",
        "\n",
        "sigmoid(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wwZBhSgQj1Ra",
        "outputId": "c071b961-69fb-4cea-b738-700b89e9befe"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.73105858, 0.88079708, 0.95257413])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# compute z for one element using loop\n",
        "x = np.array([1, 2, 3])\n",
        "w= np.array([0.5, 0.3, 0.2])\n",
        "b = 0.4\n",
        "z = b\n",
        "\n",
        "for i in range(len(x)):\n",
        "    z += x[i]*w[i]\n",
        "\n",
        "print(z)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xYRSVvcpkfVf",
        "outputId": "a59e6177-1634-4f94-a9ac-4d9a6279cfa9"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# compute the activation\n",
        "a = sigmoid(z)\n",
        "print(a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kFfyXdTIlq0k",
        "outputId": "db9e4ca5-1374-4dfe-a999-c3780aba79b1"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.8909031788043871\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# compute the activation but using vectorize approach\n",
        "sigmoid(np.dot(w.T, x) + b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ObdOGVjNl9s_",
        "outputId": "3b9113ca-3c20-4b2a-c0d2-89783779ca9d"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8909031788043871"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's generalize the activation calculation to a set of elements (your training data) using vectorization"
      ],
      "metadata": {
        "id": "vkzGQNnsVBMe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# build the X matrix with the right orientation (dimensions)\n",
        "X = np.array([[1, 2, 3], [1.5, 3.1, 4], [5, 6, 3]]).T\n",
        "print(X)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Eluhunvzomiu",
        "outputId": "83871a9d-5a94-4ec4-df80-57c2e5ac7da5"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.  1.5 5. ]\n",
            " [2.  3.1 6. ]\n",
            " [3.  4.  3. ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"x(1,1) :\",X[0,0])\n",
        "print(\"x(2,3) :\",X[1,2])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MbfW3l05rIcj",
        "outputId": "edcf7349-903e-4e1c-aab4-24459eb78214"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x(1,1) : 1.0\n",
            "x(2,3) : 6.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# check the shape of w.\n",
        "w.shape# ===> but this is the dim we need (3 , 1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "by_kL6rhsFxN",
        "outputId": "76c7f661-a78c-4172-a2b5-a617c0ad58b9"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# use reshape to adjust the dimensions\n",
        "w= w.reshape(len(w),1)"
      ],
      "metadata": {
        "id": "u1kc_DTetL1Q"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"w dim: \", w.shape)\n",
        "print(\"X dim: \", X.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qw_vCTSitlkq",
        "outputId": "8177f94f-64b6-4096-c5bf-581f819153bc"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "w dim:  (3, 1)\n",
            "X dim:  (3, 3)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# compute Z of all elements\n",
        "Z = np.dot(w.T, X) + b\n",
        "print(Z)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RWa3jOfcuJ9V",
        "outputId": "1fb44d56-58d9-43d8-94c6-fadc3d7fa6a6"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[2.1  2.88 5.3 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Z.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z6_YHWAPutPQ",
        "outputId": "a4b37ad6-e7e6-45ea-c261-cc203d0ac81b"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# compute activation of all elements\n",
        "A = sigmoid(Z)\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DFUjYcCcvKfm",
        "outputId": "dd8c0809-b28c-400b-8e99-84c44e9a6942"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.89090318 0.94684886 0.9950332 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's now compute the two versions of cost function:  \n",
        "- Least square: $\\text{Cost} =  \\sum_{i=1}^{m} (y_i - \\hat{y}_i)^2$\n",
        "- Log loos: $- \\frac{1}{m} \\sum_{i=1}^{m} \\left( y_i \\log(\\hat{y}_i) + (1 - y_i) \\log(1 - \\hat{y}_i) \\right)$"
      ],
      "metadata": {
        "id": "GBocPoL4Vv47"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Y is the vector that contains the real values\n",
        "Y = np.array([[1, 0, 1]])\n",
        "print(Y.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B7o08lHOy8yX",
        "outputId": "9491452e-ec70-47df-df84-f82672984483"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(1, 3)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "D = A - Y\n",
        "print(D)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SYzJzWP5zbpn",
        "outputId": "df73af71-9627-4fa0-d882-3eaab24de4ed"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.10909682  0.94684886 -0.0049668 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Least square\n",
        "np.dot(D,D.T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZrdaSxSZzpmS",
        "outputId": "1c7756db-78e3-4744-b4ab-69d0c757105f"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.90844956]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.sum(D*D)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "miaDz7xyzyKw",
        "outputId": "baefa522-6c95-48c0-bd10-49c04d9b0a0b"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9084495560178965"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# log loss\n",
        "m = Y.shape[1]\n",
        "\n",
        "-1/m * np.sum(Y*np.log(A) + (1-Y)*np.log(1-A))\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M1MjtrE70v5f",
        "outputId": "23e9647c-c341-4e70-8229-13757477eab0"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0183714979486944"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "2QSr_QTW5Yjk"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Initial state of the params"
      ],
      "metadata": {
        "id": "2-MLRRe85ZUl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"W: \", w)\n",
        "print(\"b: \", b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DnoZ8ukJ5O6G",
        "outputId": "51b80e98-33e4-45f0-b8a1-0ee257f59e03"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "W:  [[0.5]\n",
            " [0.3]\n",
            " [0.2]]\n",
            "b:  0.4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Compute gradients:\n",
        "- $w_j := w_j - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} (a_i - y_i) x_{ij}$\n",
        "\n",
        "- $b := b - \\alpha \\frac{1}{m} \\sum_{i=1}^{m} (a_i - y_i)$\n"
      ],
      "metadata": {
        "id": "jU0uuAQB5n09"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 0.01"
      ],
      "metadata": {
        "id": "iHITZ16-6h-l"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "epmblwqR5lC9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "delta_b = np.sum(A-Y)/m\n",
        "delta_w = np.dot(X, (A-Y).T)/m"
      ],
      "metadata": {
        "id": "VQrjUY1m5O8N"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w - alpha * delta_w"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AxLzvcuj6Ecm",
        "outputId": "ed217448-b637-4f5c-94e8-8022626020f4"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.49571219],\n",
              "       [0.29104254],\n",
              "       [0.18851598]])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b - alpha * delta_b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "asbLGy6v6CGV",
        "outputId": "4ffdcdf4-72c2-4f66-d3f3-457bec2dc4b8"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3972240491974791"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create forward and Backward propagantion fronctions"
      ],
      "metadata": {
        "id": "obO-i9U08ayy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def forward(w, b, X, Y):\n",
        "  predictions = sigmoid(np.dot(w.T, X) + b)\n",
        "  cost = -1/m * np.sum(Y*np.log(predictions) + (1-Y)*np.log(1-predictions))\n",
        "  return predictions, cost"
      ],
      "metadata": {
        "id": "LCwScjt98lWr"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def backward(w, b, X, Y, A):\n",
        "  m = X.shape[1]  # number of examples\n",
        "  delta_w = np.dot(X, (A - Y).T) / m\n",
        "  delta_b = np.sum(A - Y) / m\n",
        "  new_w = w - alpha * delta_w\n",
        "  new_b = b - alpha * delta_b\n",
        "  return new_w, new_b"
      ],
      "metadata": {
        "id": "-FBHzfOm8lhK"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0qKkWRMO_TcN",
        "outputId": "2717a0ac-4356-4bd4-da90-e11cfb5b36c8"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.5],\n",
              "       [0.3],\n",
              "       [0.2]])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# run a loop of 100 steps using backward and forward and plot the cost function\n",
        "w_it=np.random.rand(3,1)\n",
        "b_it=0\n",
        "cost_values = []\n",
        "alpha = 0.01\n",
        "for i in range(1000):\n",
        "  predictions, cost = forward(w_it, b_it, X, Y)\n",
        "  w_it, b_it = backward(w_it, b_it, X, Y, predictions)\n",
        "  cost_values.append(cost)"
      ],
      "metadata": {
        "id": "4iAuJIsf-ap3"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#plot cost_values\n",
        "import matplotlib.pyplot as plt\n",
        "plt.plot(cost_values)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "OODSrVCjA38G",
        "outputId": "215f8889-d88c-4043-c365-736f3b0a66c9"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7a0a6df76e00>]"
            ]
          },
          "metadata": {},
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}