Ex_09_26_22.ipynb

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        "# Data Privacy\n",
        "## In-Class"
      ]
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            "<ipython-input-1-c4969c0f00bf>:6: MatplotlibDeprecationWarning: The seaborn styles shipped by Matplotlib are deprecated since 3.6, as they no longer correspond to the styles shipped by seaborn. However, they will remain available as 'seaborn-v0_8-<style>'. Alternatively, directly use the seaborn API instead.\n",
            "  plt.style.use('seaborn-whitegrid')\n"
          ]
        }
      ],
      "source": [
        "# Load the data and libraries\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "from scipy import stats\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('seaborn-whitegrid')\n",
        "\n",
        "def laplace_mech(v, sensitivity, epsilon):\n",
        "    return v + np.random.laplace(loc=0, scale=sensitivity / epsilon)\n",
        "\n",
        "def pct_error(orig, priv):\n",
        "    return np.abs(orig - priv)/orig * 100.0\n",
        "\n",
        "adult = pd.read_csv('https://github.com/jnear/cs211-data-privacy/raw/master/homework/adult_with_pii.csv')"
      ]
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        "adult\n"
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              "                    Name         DOB          SSN    Zip  Age  \\\n",
              "0       Karrie Trusslove    9/7/1967  732-14-6110  64152   39   \n",
              "1       Brandise Tripony    6/7/1988  150-19-2766  61523   50   \n",
              "2          Brenn McNeely    8/6/1991  725-59-9860  95668   38   \n",
              "3            Dorry Poter    4/6/2009  659-57-4974  25503   53   \n",
              "4            Dick Honnan   9/16/1951  220-93-3811  75387   28   \n",
              "...                  ...         ...          ...    ...  ...   \n",
              "32556       Ardyce Golby  10/29/1961  212-61-8338  41328   27   \n",
              "32557      Jean O'Connor   6/28/1952  737-32-2919  94735   40   \n",
              "32558   Reuben Skrzynski    8/9/1966  314-48-0219  49628   58   \n",
              "32559        Caye Biddle   5/19/1978  647-75-3550   8213   22   \n",
              "32560  Hortense Hardesty   5/11/2012  690-42-5638  86153   52   \n",
              "\n",
              "              Workclass  fnlwgt   Education  Education-Num  \\\n",
              "0             State-gov   77516   Bachelors             13   \n",
              "1      Self-emp-not-inc   83311   Bachelors             13   \n",
              "2               Private  215646     HS-grad              9   \n",
              "3               Private  234721        11th              7   \n",
              "4               Private  338409   Bachelors             13   \n",
              "...                 ...     ...         ...            ...   \n",
              "32556           Private  257302  Assoc-acdm             12   \n",
              "32557           Private  154374     HS-grad              9   \n",
              "32558           Private  151910     HS-grad              9   \n",
              "32559           Private  201490     HS-grad              9   \n",
              "32560      Self-emp-inc  287927     HS-grad              9   \n",
              "\n",
              "           Marital Status         Occupation   Relationship   Race     Sex  \\\n",
              "0           Never-married       Adm-clerical  Not-in-family  White    Male   \n",
              "1      Married-civ-spouse    Exec-managerial        Husband  White    Male   \n",
              "2                Divorced  Handlers-cleaners  Not-in-family  White    Male   \n",
              "3      Married-civ-spouse  Handlers-cleaners        Husband  Black    Male   \n",
              "4      Married-civ-spouse     Prof-specialty           Wife  Black  Female   \n",
              "...                   ...                ...            ...    ...     ...   \n",
              "32556  Married-civ-spouse       Tech-support           Wife  White  Female   \n",
              "32557  Married-civ-spouse  Machine-op-inspct        Husband  White    Male   \n",
              "32558             Widowed       Adm-clerical      Unmarried  White  Female   \n",
              "32559       Never-married       Adm-clerical      Own-child  White    Male   \n",
              "32560  Married-civ-spouse    Exec-managerial           Wife  White  Female   \n",
              "\n",
              "       Capital Gain  Capital Loss  Hours per week        Country Target  \n",
              "0              2174             0              40  United-States  <=50K  \n",
              "1                 0             0              13  United-States  <=50K  \n",
              "2                 0             0              40  United-States  <=50K  \n",
              "3                 0             0              40  United-States  <=50K  \n",
              "4                 0             0              40           Cuba  <=50K  \n",
              "...             ...           ...             ...            ...    ...  \n",
              "32556             0             0              38  United-States  <=50K  \n",
              "32557             0             0              40  United-States   >50K  \n",
              "32558             0             0              40  United-States  <=50K  \n",
              "32559             0             0              20  United-States  <=50K  \n",
              "32560         15024             0              40  United-States   >50K  \n",
              "\n",
              "[32561 rows x 19 columns]"
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              "      <th>0</th>\n",
              "      <td>Karrie Trusslove</td>\n",
              "      <td>9/7/1967</td>\n",
              "      <td>732-14-6110</td>\n",
              "      <td>64152</td>\n",
              "      <td>39</td>\n",
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              "      <td>77516</td>\n",
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              "      <td>2174</td>\n",
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              "      <td>40</td>\n",
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              "      <td>Brandise Tripony</td>\n",
              "      <td>6/7/1988</td>\n",
              "      <td>150-19-2766</td>\n",
              "      <td>61523</td>\n",
              "      <td>50</td>\n",
              "      <td>Self-emp-not-inc</td>\n",
              "      <td>83311</td>\n",
              "      <td>Bachelors</td>\n",
              "      <td>13</td>\n",
              "      <td>Married-civ-spouse</td>\n",
              "      <td>Exec-managerial</td>\n",
              "      <td>Husband</td>\n",
              "      <td>White</td>\n",
              "      <td>Male</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>13</td>\n",
              "      <td>United-States</td>\n",
              "      <td>&lt;=50K</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Brenn McNeely</td>\n",
              "      <td>8/6/1991</td>\n",
              "      <td>725-59-9860</td>\n",
              "      <td>95668</td>\n",
              "      <td>38</td>\n",
              "      <td>Private</td>\n",
              "      <td>215646</td>\n",
              "      <td>HS-grad</td>\n",
              "      <td>9</td>\n",
              "      <td>Divorced</td>\n",
              "      <td>Handlers-cleaners</td>\n",
              "      <td>Not-in-family</td>\n",
              "      <td>White</td>\n",
              "      <td>Male</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>40</td>\n",
              "      <td>United-States</td>\n",
              "      <td>&lt;=50K</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Dorry Poter</td>\n",
              "      <td>4/6/2009</td>\n",
              "      <td>659-57-4974</td>\n",
              "      <td>25503</td>\n",
              "      <td>53</td>\n",
              "      <td>Private</td>\n",
              "      <td>234721</td>\n",
              "      <td>11th</td>\n",
              "      <td>7</td>\n",
              "      <td>Married-civ-spouse</td>\n",
              "      <td>Handlers-cleaners</td>\n",
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              "      <td>Black</td>\n",
              "      <td>Male</td>\n",
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              "      <td>0</td>\n",
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              "      <td>United-States</td>\n",
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              "      <th>4</th>\n",
              "      <td>Dick Honnan</td>\n",
              "      <td>9/16/1951</td>\n",
              "      <td>220-93-3811</td>\n",
              "      <td>75387</td>\n",
              "      <td>28</td>\n",
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              "      <td>338409</td>\n",
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              "      <td>Prof-specialty</td>\n",
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              "      <td>Black</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>Cuba</td>\n",
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              "      <td>Ardyce Golby</td>\n",
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              "      <td>41328</td>\n",
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              "      <td>White</td>\n",
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              "      <td>Jean O'Connor</td>\n",
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              "      <td>Reuben Skrzynski</td>\n",
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              "      <th>32559</th>\n",
              "      <td>Caye Biddle</td>\n",
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              "      <td>20</td>\n",
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              "      <th>32560</th>\n",
              "      <td>Hortense Hardesty</td>\n",
              "      <td>5/11/2012</td>\n",
              "      <td>690-42-5638</td>\n",
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              "      <td>52</td>\n",
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              "      <td>&gt;50K</td>\n",
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              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
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              "    }\n",
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              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-351b66ed-9ade-4e43-87d4-54b3d6191e35 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JEcjKTfDk0wn"
      },
      "source": [
        "## Question 1\n",
        "\n",
        "For various values of $b$, write code to print out the percent error of summing the ages in the `adult` dataset,\n",
        "clipped to each value of $b$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "5017dfb00b9fa0c28dc47d5e03672bcc",
          "grade": false,
          "grade_id": "cell-bb6f4fe4b3beb456",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "_AlgOsMZk0wo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3e896393-11f7-4e97-8638-6dfc9332085b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "For b = 1, Clipped Sum = 32561, Percent Error = 97.4080940444511%\n",
            "For b = 11, Clipped Sum = 358171, Percent Error = 71.48903448896206%\n",
            "For b = 21, Clipped Sum = 678374, Percent Error = 46.000380495392264%\n",
            "For b = 31, Clipped Sum = 935798, Percent Error = 25.509031989473492%\n",
            "For b = 41, Clipped Sum = 1108069, Percent Error = 11.7959939725709%\n",
            "For b = 51, Clipped Sum = 1201865, Percent Error = 4.329687317165198%\n",
            "For b = 61, Clipped Sum = 1241700, Percent Error = 1.1587597123836921%\n",
            "For b = 71, Clipped Sum = 1253315, Percent Error = 0.2341877497996031%\n",
            "For b = 81, Clipped Sum = 1255772, Percent Error = 0.03860675005194001%\n",
            "For b = 91, Clipped Sum = 1256257, Percent Error = 0.0%\n"
          ]
        }
      ],
      "source": [
        "bs = range(1, 100, 10)\n",
        "real_sum = adult['Age'].sum()\n",
        "for b in bs:\n",
        "    # Clip the ages to the current value of b\n",
        "    clipped_sum = adult['Age'].clip(lower=0, upper=b).sum()\n",
        "\n",
        "    Percent_error=((real_sum-clipped_sum)/real_sum)*100\n",
        "     # Print the result\n",
        "    print(f\"For b = {b}, Clipped Sum = {clipped_sum}, Percent Error = {Percent_error}%\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "THaNLyAQk0wp"
      },
      "source": [
        "What value of $b$ is the best?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "b5ae2ac2b16c4f62b326bccf0184692b",
          "grade": true,
          "grade_id": "cell-250b062d06204617",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "l5iUw7Uck0wq"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zM4MZsmjk0wq"
      },
      "source": [
        "## Question 2\n",
        "\n",
        "For various values of $b$, print the result of a *differentially private* sum of ages, clipped to each value of $b$. Use $\\epsilon = 0.1$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "fce2c03e38136df9fa6c79119866a44c",
          "grade": false,
          "grade_id": "cell-dca4f1bfa29d353d",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "8E1cCfjNk0wr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e564d4d2-49e4-436d-a57a-bae380908650"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "For b = 1, Clipped Sum = 32561, differentially private sum =  32568.50577921981\n",
            "For b = 11, Clipped Sum = 358171, differentially private sum =  358181.9451314483\n",
            "For b = 21, Clipped Sum = 678374, differentially private sum =  678379.3176448656\n",
            "For b = 31, Clipped Sum = 935798, differentially private sum =  935788.6217624572\n",
            "For b = 41, Clipped Sum = 1108069, differentially private sum =  1108056.166257963\n",
            "For b = 51, Clipped Sum = 1201865, differentially private sum =  1201865.3782098033\n",
            "For b = 61, Clipped Sum = 1241700, differentially private sum =  1241702.9232992597\n",
            "For b = 71, Clipped Sum = 1253315, differentially private sum =  1253316.3727774047\n",
            "For b = 81, Clipped Sum = 1255772, differentially private sum =  1255772.190136209\n",
            "For b = 91, Clipped Sum = 1256257, differentially private sum =  1256255.7797449704\n"
          ]
        }
      ],
      "source": [
        "bs = range(1, 100, 10)\n",
        "real_sum = adult['Age'].sum()\n",
        "for b in bs:\n",
        "    # Clip the ages to the current value of b\n",
        "    clipped_sum = adult['Age'].clip(lower=0, upper=b).sum()\n",
        "\n",
        "    noise_add=clipped_sum+np.random.laplace(loc=0, scale=1/0.1)\n",
        "     # Print the result\n",
        "    print(f\"For b = {b}, Clipped Sum = {clipped_sum}, differentially private sum = \",noise_add)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tTfWVhXkk0ws"
      },
      "source": [
        "Which value of $b$ is the best now? Does it differ?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "a6614c5f0fba0ddceddde10ee8626362",
          "grade": true,
          "grade_id": "cell-fee4808b879b0a04",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "PbEGVhlYk0ws"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-mvgz7Kyk0wt"
      },
      "source": [
        "## Question 3\n",
        "\n",
        "Write an algorithm to *automatically pick the clipping parameter* for the age column. Your algorithm should satisfy differential privacy."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "0da086ab81420b019466185a8bbaf8c1",
          "grade": false,
          "grade_id": "cell-9a41939138d41f6f",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "n6zm96tSk0wt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca45ca93-16ce-4871-84db-f43e0311365e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "36    898.453217\n",
              "31    888.453217\n",
              "34    886.453217\n",
              "23    877.453217\n",
              "35    876.453217\n",
              "         ...    \n",
              "83      6.453217\n",
              "88      3.453217\n",
              "85      3.453217\n",
              "86      1.453217\n",
              "87      1.453217\n",
              "Name: Age, Length: 73, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ],
      "source": [
        "def pick_b(epsilon):\n",
        "\n",
        "    clipped_sum = adult['Age'].clip(lower=0, upper=100).value_counts()\n",
        "\n",
        "    return clipped_sum + np.random.laplace(loc=0,scale=1/epsilon)\n",
        "\n",
        "pick_b(1.0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "692492fba66dc0685be8dee946edbed7",
          "grade": true,
          "grade_id": "cell-136e29134703a26b",
          "locked": true,
          "points": 5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "OR-SPRJnk0wt"
      },
      "outputs": [],
      "source": [
        "# TEST CASE for question 3\n",
        "\n",
        "many_trials = np.mean([pick_b(1.0) for _ in range(100)])\n",
        "assert many_trials > 70\n",
        "assert many_trials < 500"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d7MKYkQxk0wu"
      },
      "source": [
        "## Question 4\n",
        "\n",
        "What is the privacy cost of your algorithm, and why?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "e3b3bf3b0934d4a2d9429867fd118ab4",
          "grade": true,
          "grade_id": "cell-5e3ac9bbd3f179e9",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "DqS2TjCEk0wu"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wtLHLN7Dk0wu"
      },
      "source": [
        "## Question 5\n",
        "\n",
        "Write code to generate a *histogram* of education numbers in the `adult` dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "a4c084311f288978d7388707ed803dc4",
          "grade": false,
          "grade_id": "cell-ee86a67be2f997fb",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "YTlGhEZmk0wv"
      },
      "outputs": [],
      "source": [
        "def education_hist():\n",
        "    # Generate a histogram of education numbers\n",
        "    education_counts = adult['Education'].value_counts()\n",
        "\n",
        "    # Convert the result to a dictionary for easy access\n",
        "    education_dict = education_counts.to_dict()\n",
        "\n",
        "    return education_dict"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "9ca7a5909d65acf22b40eef95b77ef24",
          "grade": true,
          "grade_id": "cell-7e1309ee016dc1b0",
          "locked": true,
          "points": 5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "P_Lf7xOBk0wv"
      },
      "outputs": [],
      "source": [
        "# TEST CASE for question 5\n",
        "h = education_hist()\n",
        "assert h['HS-grad'] == 10501\n",
        "assert h['12th'] == 433\n",
        "assert h['Doctorate'] == 413"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0GSXA70dk0wv"
      },
      "source": [
        "## Question 6\n",
        "\n",
        "Write code to release a *differentially private histogram* of education numbers."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "78135ffc0ddb6f5f824c4380c31fa067",
          "grade": false,
          "grade_id": "cell-e5d6ede7edcdc46e",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "6vZ4SQYrk0ww",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d749b1a6-69e8-4251-cf2a-b56edd6c1cc4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "HS-grad         10498.657176\n",
              "Some-college     7288.657176\n",
              "Bachelors        5352.657176\n",
              "Masters          1720.657176\n",
              "Assoc-voc        1379.657176\n",
              "11th             1172.657176\n",
              "Assoc-acdm       1064.657176\n",
              "10th              930.657176\n",
              "7th-8th           643.657176\n",
              "Prof-school       573.657176\n",
              "9th               511.657176\n",
              "12th              430.657176\n",
              "Doctorate         410.657176\n",
              "5th-6th           330.657176\n",
              "1st-4th           165.657176\n",
              "Preschool          48.657176\n",
              "Name: Education, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ],
      "source": [
        "def dp_education_hist(epsilon):\n",
        "    return adult['Education'].value_counts()+ np.random.laplace(loc=0,scale=1/epsilon)\n",
        "\n",
        "dp_education_hist(1.0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "b6d8b325844651b39c4e402d3bfac373",
          "grade": true,
          "grade_id": "cell-3d994871e2ce6873",
          "locked": true,
          "points": 5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "NIlKHZGHk0ww"
      },
      "outputs": [],
      "source": [
        "# TEST CASE for question 6\n",
        "h = dp_education_hist(1.0)\n",
        "assert abs(h['HS-grad'] - 10501) < 100\n",
        "assert abs(h['Doctorate'] - 413) < 100"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yr8E6cnhk0ww"
      },
      "source": [
        "## Question 7\n",
        "\n",
        "What is the total privacy cost of `dp_education_hist`, and why?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "b260643b7d27a6d1ba3d243471dd2758",
          "grade": true,
          "grade_id": "cell-892ecfb572a7e900",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "BIA47Yl_k0wx"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SXve0BHzk0wx"
      },
      "source": [
        "## Question 8\n",
        "\n",
        "Write code to generate a differentially private *contingency table* for the Education and Sex columns of the `adult` dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "f1d36e02ba769a0419701627a6a54a5c",
          "grade": false,
          "grade_id": "cell-8ee68bcf1e36b660",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "rWh-PxTgk0wx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 576
        },
        "outputId": "243b37df-7db0-4bc3-b838-9fa5c7f22682"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Sex                Female         Male\n",
              "Education                             \n",
              "10th           295.937866   638.937866\n",
              "11th           432.937866   743.937866\n",
              "12th           144.937866   289.937866\n",
              "1st-4th         46.937866   122.937866\n",
              "5th-6th         84.937866   249.937866\n",
              "7th-8th        160.937866   486.937866\n",
              "9th            144.937866   370.937866\n",
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              "Preschool       16.937866    35.937866\n",
              "Prof-school     92.937866   484.937866\n",
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            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "def dp_crosstab_education_sex(epsilon):\n",
        "     return pd.crosstab(adult['Education'], adult['Sex'])+np.random.laplace(loc=0,scale=1/epsilon)\n",
        "dp_crosstab_education_sex(1.0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "c75206f511320740052bb35011d31e14",
          "grade": true,
          "grade_id": "cell-8793de8189968533",
          "locked": true,
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          "task": false
        },
        "id": "LhJWALoUk0wx"
      },
      "outputs": [],
      "source": [
        "# TEST CASE for question 8\n",
        "ct = dp_crosstab_education_sex(1.0)\n",
        "assert abs(ct['Female']['10th'] - 295) < 100\n",
        "assert abs(ct['Male']['10th'] - 638) < 100\n",
        "assert abs(ct['Female']['Bachelors'] - 1619) < 100\n",
        "\n",
        "assert abs(ct['Female']['10th'] - 295) > 0\n",
        "assert abs(ct['Male']['10th'] - 638) > 0\n",
        "assert abs(ct['Female']['Bachelors'] - 1619) > 0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NO2aVxMuk0wx"
      },
      "source": [
        "## Question 9\n",
        "\n",
        "Does parallel composition apply for the contingency table in question 1? Why or why not?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "9d45318df4e423bfde4cf13a8527fc60",
          "grade": true,
          "grade_id": "cell-ad80affc47428f91",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "9JrwfedHk0wx"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pAlYv9Sok0wy"
      },
      "source": [
        "## Question 10\n",
        "\n",
        "Does the number of columns used in constructing the contingency table matter for privacy cost? Does it matter for accuracy?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "851d5bf06ada00ac761cf695bf3bb8ab",
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          "grade_id": "cell-5dead8598d0dbda8",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "ctFLObp9k0wy"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ysi9jGA9k0wy"
      },
      "source": [
        "## Question 11\n",
        "\n",
        "Implement the Gaussian mechanism for $(\\epsilon, \\delta)$-differential privacy."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "31d4967e3d4bf6c87e8f17c5a8869a92",
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          "grade_id": "cell-8a747c92ab199a91",
          "locked": false,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "KkV0luRAk0wy"
      },
      "outputs": [],
      "source": [
        "def gaussian_mech(count, sensitivity, epsilon, delta):\n",
        "    # Calculate the scale parameter for Laplace noise\n",
        "    beta = sensitivity / epsilon\n",
        "\n",
        "    # Generate Laplace noise\n",
        "    laplace_noise = np.random.laplace(scale=beta)\n",
        "\n",
        "    # Calculate the standard deviation of Gaussian noise\n",
        "    sigma = np.sqrt(2 * np.log(1.25 / delta)) * beta\n",
        "\n",
        "    # Generate Gaussian noise\n",
        "    gaussian_noise = np.random.normal(loc=0, scale=sigma)\n",
        "\n",
        "    # Add Laplace and Gaussian noise to the count\n",
        "    noisy_count = count + laplace_noise + gaussian_noise\n",
        "\n",
        "    return noisy_count"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "deletable": false,
        "editable": false,
        "nbgrader": {
          "cell_type": "code",
          "checksum": "1adc60d692e5bf0e529ed61ad082a8ac",
          "grade": true,
          "grade_id": "cell-f991d474ed13d0ed",
          "locked": true,
          "points": 5,
          "schema_version": 3,
          "solution": false,
          "task": false
        },
        "id": "5RhgHiLak0wy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7abf7913-b9d2-4830-f90a-695e7702ad2c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "mean error: 0.05886428876069715\n"
          ]
        }
      ],
      "source": [
        "# TEST CASE\n",
        "\n",
        "results = [gaussian_mech(len(adult[adult['Age'] > 50]), 1, 1.0, 10e-5) for _ in range(100)]\n",
        "errors = [pct_error(len(adult[adult['Age'] > 50]), r) for r in results]\n",
        "print('mean error:', np.mean(errors))\n",
        "\n",
        "assert np.mean(errors) > 0\n",
        "assert np.mean(errors) < 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DIT0w1Qyk0wy"
      },
      "source": [
        "## Question 12\n",
        "\n",
        "How do the Laplace and Gaussian mechanisms compare in terms of relative error on the query \"how many individuals are over 50 years old\" with $\\epsilon = 1$ and $\\delta = 10^{-5}$?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "id": "TR9f0VZ_k0wz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 425
        },
        "outputId": "e93e4c63-c0e3-42ab-e9f0-688c76485108"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "true_answer = len(adult[adult['Age'] > 50])\n",
        "\n",
        "laplace_answers = [laplace_mech(true_answer, 1, 1) for _ in range(200)]\n",
        "gaussian_answers = [gaussian_mech(true_answer, 1, 1, 10e-5) for _ in range(200)]\n",
        "\n",
        "laplace_error = [pct_error(true_answer, a) for a in laplace_answers]\n",
        "gaussian_error = [pct_error(true_answer, a) for a in gaussian_answers]\n",
        "\n",
        "_, bins, _ = plt.hist(gaussian_error, bins=20, label='Gaussian')\n",
        "plt.hist(laplace_error, bins=bins, label='Laplace', alpha=0.5)\n",
        "plt.legend();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "nbgrader": {
          "cell_type": "markdown",
          "checksum": "1153ff5988a844b33435df5d8de63f06",
          "grade": true,
          "grade_id": "cell-aa96c49ecf1a6d2c",
          "locked": false,
          "points": 5,
          "schema_version": 3,
          "solution": true,
          "task": false
        },
        "id": "Kh_qh2kCk0wz"
      },
      "source": [
        "YOUR ANSWER HERE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TeTzZXudk0wz"
      },
      "source": [
        "## Not a Question - Just for reference\n",
        "\n",
        "[Reference](https://uvm-plaid.github.io/programming-dp/notebooks/ch6.html#the-gaussian-mechanism)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "SAxoZd8qk0wz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "outputId": "e6725f49-eca5-4495-f5e0-1bb24f01fc62"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "e^epsilon = 2.718281828459045\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "epsilon = 1\n",
        "sensitivity = 1\n",
        "delta = 1e-5\n",
        "sigma_squared = 2 * sensitivity**2 * np.log(1.25 / delta) / (epsilon**2)\n",
        "sigma = np.sqrt(sigma_squared)\n",
        "\n",
        "def gauss_pdf(x):\n",
        "    return 1/(sigma*np.sqrt(2*np.pi)) * np.exp(-(1/2)*(x/sigma)**2)\n",
        "\n",
        "xs = np.linspace(-50, 50, 200)\n",
        "ys1 = [gauss_pdf(x) for x in xs]\n",
        "ys2 = [gauss_pdf(x+1) for x in xs]\n",
        "\n",
        "plt.plot(xs,ys1)\n",
        "plt.plot(xs,ys2)\n",
        "\n",
        "# ratio < e^epsilon should hold\n",
        "print('e^epsilon =', np.exp(epsilon))\n",
        "ratios = [(x, y1 / y2) for x, y1, y2 in zip(xs, ys1, ys2)]\n",
        "#ratios"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "sg09SQJEk0wz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "outputId": "c3646ea9-653b-4764-9ced-6eda76e14dd1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "e^epsilon = 2.718281828459045\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def laplace_pdf(x):\n",
        "    return (1/2)*epsilon * np.exp(-np.abs(x)*epsilon)\n",
        "\n",
        "xs = np.linspace(-50, 50, 200)\n",
        "ys1 = [laplace_pdf(x) for x in xs]\n",
        "ys2 = [laplace_pdf(x+1) for x in xs]\n",
        "\n",
        "plt.plot(xs,ys1)\n",
        "plt.plot(xs,ys2)\n",
        "\n",
        "# ratio < e^epsilon should hold\n",
        "print('e^epsilon =', np.exp(epsilon))\n",
        "ratios = [(x, y1 / y2) for x, y1, y2 in zip(xs, ys1, ys2)]\n",
        "#ratios"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.11"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}