bayesian_linear_regression.ipynb

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        "<a href=\"https://colab.research.google.com/github/Antony-gitau/probabilistic_AI_playgraound/blob/main/bayesian_linear_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "In this notebook, we are going to tackle an example of bayesian linear regression using pyro, a probabilistic programming tool.\n",
        "\n",
        "We want to confirm that the terrain ruggedness is related to poorer economic perfomance outside Africa, but reverse effects on income for African countries.  (as that was the conclusion of this [paper](https://diegopuga.org/papers/rugged.pdf))\n",
        "\n",
        "*We are following an example on pyro webpage.*"
      ],
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      "source": [
        "%%capture\n",
        "!pip install -q --upgrade pyro-ppl torch\n",
        "\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "\n",
        "import pyro\n",
        "import pyro.distributions as dist\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Data:\n",
        "We will use rugged data in which we only care about:\n",
        "1. rugged index - quantifies the ruggedness of geographical location in and out of Africa.\n",
        "2. list of nation in and out of Africa\n",
        "3. The GDP per capita of the nations for the year 2000 "
      ],
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        "id": "j0wvBqTtNEe3"
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      "source": [
        "data_url = \"https://d2hg8soec8ck9v.cloudfront.net/datasets/rugged_data.csv\"\n",
        "\n",
        "# We encode the data in the url with the latin-1, character encoding standard\n",
        "rugged_data = pd.read_csv(data_url, encoding=\"ISO-8859-1\")"
      ],
      "metadata": {
        "id": "nD-Lmd23KHuL"
      },
      "execution_count": 3,
      "outputs": []
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      "source": [
        "rugged_data.head()"
      ],
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              "  isocode  isonum      country  rugged  rugged_popw  rugged_slope  rugged_lsd  \\\n",
              "0     ABW     533        Aruba   0.462        0.380         1.226       0.144   \n",
              "1     AFG       4  Afghanistan   2.518        1.469         7.414       0.720   \n",
              "2     AGO      24       Angola   0.858        0.714         2.274       0.228   \n",
              "3     AIA     660     Anguilla   0.013        0.010         0.026       0.006   \n",
              "4     ALB       8      Albania   3.427        1.597        10.451       1.006   \n",
              "\n",
              "   rugged_pc  land_area     lat  ...  africa_region_w  africa_region_e  \\\n",
              "0      0.000       18.0  12.508  ...                0                0   \n",
              "1     39.004    65209.0  33.833  ...                0                0   \n",
              "2      4.906   124670.0 -12.299  ...                0                0   \n",
              "3      0.000        9.0  18.231  ...                0                0   \n",
              "4     62.133     2740.0  41.143  ...                0                0   \n",
              "\n",
              "   africa_region_c  slave_exports  dist_slavemkt_atlantic  \\\n",
              "0                0            0.0                     NaN   \n",
              "1                0            0.0                     NaN   \n",
              "2                1      3610000.0                   5.669   \n",
              "3                0            0.0                     NaN   \n",
              "4                0            0.0                     NaN   \n",
              "\n",
              "   dist_slavemkt_indian  dist_slavemkt_saharan  dist_slavemkt_redsea  \\\n",
              "0                   NaN                    NaN                   NaN   \n",
              "1                   NaN                    NaN                   NaN   \n",
              "2                 6.981                  4.926                 3.872   \n",
              "3                   NaN                    NaN                   NaN   \n",
              "4                   NaN                    NaN                   NaN   \n",
              "\n",
              "    pop_1400  european_descent  \n",
              "0      614.0               NaN  \n",
              "1  1870829.0               0.0  \n",
              "2  1223208.0               2.0  \n",
              "3        NaN               NaN  \n",
              "4   200000.0             100.0  \n",
              "\n",
              "[5 rows x 51 columns]"
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              "      <td>4.926</td>\n",
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              "      <td>1223208.0</td>\n",
              "      <td>2.0</td>\n",
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        "rugged_data.columns"
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          "data": {
            "text/plain": [
              "Index(['isocode', 'isonum', 'country', 'rugged', 'rugged_popw', 'rugged_slope',\n",
              "       'rugged_lsd', 'rugged_pc', 'land_area', 'lat', 'lon', 'soil', 'desert',\n",
              "       'tropical', 'dist_coast', 'near_coast', 'gemstones', 'rgdppc_2000',\n",
              "       'rgdppc_1950_m', 'rgdppc_1975_m', 'rgdppc_2000_m', 'rgdppc_1950_2000_m',\n",
              "       'q_rule_law', 'cont_africa', 'cont_asia', 'cont_europe', 'cont_oceania',\n",
              "       'cont_north_america', 'cont_south_america', 'legor_gbr', 'legor_fra',\n",
              "       'legor_soc', 'legor_deu', 'legor_sca', 'colony_esp', 'colony_gbr',\n",
              "       'colony_fra', 'colony_prt', 'colony_oeu', 'africa_region_n',\n",
              "       'africa_region_s', 'africa_region_w', 'africa_region_e',\n",
              "       'africa_region_c', 'slave_exports', 'dist_slavemkt_atlantic',\n",
              "       'dist_slavemkt_indian', 'dist_slavemkt_saharan', 'dist_slavemkt_redsea',\n",
              "       'pop_1400', 'european_descent'],\n",
              "      dtype='object')"
            ]
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          "metadata": {},
          "execution_count": 5
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      "source": [
        "# lets pick three columns we care about (as we stated earlier) and create a dataframe \n",
        "ruggedness_dataframe = rugged_data[[\"cont_africa\",\"rugged\",\"rgdppc_2000\"]]\n",
        "ruggedness_dataframe.head()"
      ],
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            "text/plain": [
              "   cont_africa  rugged  rgdppc_2000\n",
              "0            0   0.462          NaN\n",
              "1            0   2.518          NaN\n",
              "2            1   0.858     1794.729\n",
              "3            0   0.013          NaN\n",
              "4            0   3.427     3703.113"
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              "                                                     [key], {});\n",
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              "\n",
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              "            + ' to learn more about interactive tables.';\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ruggedness_dataframe.isnull().sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GKJzdsLgQ3-Y",
        "outputId": "9d0525fa-ca18-4a30-8a7d-3ac0994570fc"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "cont_africa     0\n",
              "rugged          0\n",
              "rgdppc_2000    64\n",
              "dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# lets remove the nan values in the rgdppc_2000 column\n",
        "nan_values = np.isfinite(ruggedness_dataframe.rgdppc_2000)\n",
        "sum_true = np.sum(nan_values)\n",
        "sum_false = np.sum(~nan_values)\n",
        "print(\"Trues \", sum_true)\n",
        "print(\"Falses \", sum_false)\n",
        "\n",
        "# this is the dataframe before we remove the nan values on the rgdppc_2000 column\n",
        "print(ruggedness_dataframe.info())\n",
        "\n",
        "ruggedness_dataframe = ruggedness_dataframe[nan_values]\n",
        "#this is after we drop the columns\n",
        "print(ruggedness_dataframe.info())\n",
        "ruggedness_dataframe.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 623
        },
        "id": "k1CI8KFzRDCs",
        "outputId": "0bdb4831-1b5b-424a-f276-4ffee77671b8"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Trues  170\n",
            "Falses  64\n",
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 234 entries, 0 to 233\n",
            "Data columns (total 3 columns):\n",
            " #   Column       Non-Null Count  Dtype  \n",
            "---  ------       --------------  -----  \n",
            " 0   cont_africa  234 non-null    int64  \n",
            " 1   rugged       234 non-null    float64\n",
            " 2   rgdppc_2000  170 non-null    float64\n",
            "dtypes: float64(2), int64(1)\n",
            "memory usage: 5.6 KB\n",
            "None\n",
            "<class 'pandas.core.frame.DataFrame'>\n",
            "Int64Index: 170 entries, 2 to 233\n",
            "Data columns (total 3 columns):\n",
            " #   Column       Non-Null Count  Dtype  \n",
            "---  ------       --------------  -----  \n",
            " 0   cont_africa  170 non-null    int64  \n",
            " 1   rugged       170 non-null    float64\n",
            " 2   rgdppc_2000  170 non-null    float64\n",
            "dtypes: float64(2), int64(1)\n",
            "memory usage: 5.3 KB\n",
            "None\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   cont_africa  rugged  rgdppc_2000\n",
              "2            1   0.858     1794.729\n",
              "4            0   3.427     3703.113\n",
              "7            0   0.769    20604.460\n",
              "8            0   0.775    12173.680\n",
              "9            0   2.688     2421.985"
            ],
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              "      <th>cont_africa</th>\n",
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              "                                                     [key], {});\n",
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              "\n",
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              "            + ' to learn more about interactive tables.';\n",
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            ]
          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#lets normalize the rgdppc_2000 column \n",
        "ruggedness_dataframe['rgdppc_2000'] = np.log(ruggedness_dataframe['rgdppc_2000'])"
      ],
      "metadata": {
        "id": "ZDHgbPDIUH0d"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "wKOJZRonirao"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Lets get started with the bayesian linear regression"
      ],
      "metadata": {
        "id": "NFHfrSyPQ2mT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "from torch import nn\n",
        "from pyro.nn import PyroModule\n"
      ],
      "metadata": {
        "id": "wzChtbTJFlg3"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We now train with pytorch optimizers\n",
        "- adam optimizer\n",
        "- mean squared error\n",
        "\n",
        "we start of by capturing the interaction of ruggedness and whether a nation is in africa or not.\n",
        "\n",
        "Multiplying the values of \"count_africa\" with \"rugged\" creates a new feature that represents the combined effect of the two. This is useful in making the model more nuanced as the result of the new feature will show higher values for countries in Africa with rugged terrain which indicates a different effect compared to other combinations."
      ],
      "metadata": {
        "id": "BVDlJYxSSnXV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# we add a feature to capture the interaction btw cont_africa and ruggedness\n",
        "ruggedness_dataframe['cont_africa_x_ruggedness'] = ruggedness_dataframe['cont_africa'] * ruggedness_dataframe['rugged']\n"
      ],
      "metadata": {
        "id": "TZ3padCBSmi1"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ruggedness_dataframe.columns"
      ],
      "metadata": {
        "id": "0wB0Jy1xV-PL",
        "outputId": "1d14a0c6-da13-4662-8cb5-4ab5d68b71b0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['cont_africa', 'rugged', 'rgdppc_2000', 'cont_africa_x_ruggedness'], dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(ruggedness_dataframe.dtypes)\n",
        "\n",
        "# we convert the ints and float points into tensors\n",
        "ruggedness_dataframe_in_tensors = torch.tensor(np.array(ruggedness_dataframe[['cont_africa', 'rugged', 'rgdppc_2000', 'cont_africa_x_ruggedness']]))\n",
        "\n",
        "# we then split the train set from the label set\n",
        "x_data, y_data = ruggedness_dataframe_in_tensors[:,:-1], ruggedness_dataframe_in_tensors[:,-1]\n",
        "\n"
      ],
      "metadata": {
        "id": "qHI6gq02TAep",
        "outputId": "d2572ee9-33e5-4668-a121-6e76ad4a1ac5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cont_africa                   int64\n",
            "rugged                      float64\n",
            "rgdppc_2000                 float64\n",
            "cont_africa_x_ruggedness    float64\n",
            "dtype: object\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# the regression model will receive 3 features and output 1 \n",
        "linear_reg = PyroModule[nn.Linear](3, 1)\n",
        "\n",
        "# MSE loss and Adam optimizer\n",
        "loss_fn = torch.nn.MSELoss(reduction='sum')\n",
        "optimiz = torch.optim.Adam(linear_reg.parameters(), lr=0.005)\n",
        "num_iter = 1500 "
      ],
      "metadata": {
        "id": "KpmicEtJVEKM"
      },
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notes on the train function:\n",
        "- squeezing the tensor along the dimension -1 removes any singleton dimension present in the output tensor. That is what the .squeeze(-1) is doing.\n",
        "\n",
        "- forward pass on the model involves multiplying the input features by the model's weights and applying any defined activation functions or biases.\n",
        "\n",
        "- Zero grad ensures that the gradients from the previous iterations of training do not accumulate and affect the current iteration's computations."
      ],
      "metadata": {
        "id": "ZcLymArWaZPd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def train():\n",
        "  y_pred = linear_reg(x_data).squeeze(-1)\n",
        "  #print(y_pred.dtype)\n",
        "  #y_pred = linear_reg(x_data.to(linear_reg.weight.dtype)).squeeze(-1)\n",
        "  loss_calc = loss_fn(y_pred, y_data)\n",
        "  # set the gradients to zero for the upcoming iteration\n",
        "  optimiz.zero_grad\n",
        "  loss_calc.backward()\n",
        "  optimiz.step()\n",
        "  return loss_calc\n",
        "\n"
      ],
      "metadata": {
        "id": "JZmk9jI4Va_G"
      },
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for iter in range(num_iter):\n",
        "  loss_calc = train()\n",
        "\n",
        "  # we print in the iterations of 50\n",
        "  if (iter + 1) % 50 == 0:\n",
        "    print(\"Iteration %04d, loss %.4f\" %(iter + 1, loss_calc.item()))"
      ],
      "metadata": {
        "id": "eYa5VQR6crq6",
        "outputId": "c39e8b2f-71bb-407e-983a-2f689a3d934d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 432
        }
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "error",
          "ename": "RuntimeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-60-124a4b294f14>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0miter\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_iter\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;32m----> 2\u001b[0;31m   \u001b[0mloss_calc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain\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[0m\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m   \u001b[0;31m# we print in the iterations of 50\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m   \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0miter\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;36m50\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-53-2a1646c651e3>\u001b[0m in \u001b[0;36mtrain\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mtrain\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;32m----> 2\u001b[0;31m   \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlinear_reg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqueeze\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\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      3\u001b[0m   \u001b[0;31m#print(y_pred.dtype)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m   \u001b[0;31m#y_pred = linear_reg(x_data.to(linear_reg.weight.dtype)).squeeze(-1)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m   \u001b[0mloss_calc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloss_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_pred\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/pyro/nn/module.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    446\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\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[1;32m    447\u001b[0m         \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_pyro_context\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 448\u001b[0;31m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\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    449\u001b[0m         if (\n\u001b[1;32m    450\u001b[0m             \u001b[0mpyro\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msettings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"validate_poutine\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/torch/nn/modules/module.py\u001b[0m in \u001b[0;36m_call_impl\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1499\u001b[0m                 \u001b[0;32mor\u001b[0m \u001b[0m_global_backward_pre_hooks\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0m_global_backward_hooks\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1500\u001b[0m                 or _global_forward_hooks or _global_forward_pre_hooks):\n\u001b[0;32m-> 1501\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mforward_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\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   1502\u001b[0m         \u001b[0;31m# Do not call functions when jit is used\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1503\u001b[0m         \u001b[0mfull_backward_hooks\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnon_full_backward_hooks\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[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/torch/nn/modules/linear.py\u001b[0m in \u001b[0;36mforward\u001b[0;34m(self, input)\u001b[0m\n\u001b[1;32m    112\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    113\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mforward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mTensor\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mTensor\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 114\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mF\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinear\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mweight\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbias\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    115\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    116\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mextra_repr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mRuntimeError\u001b[0m: mat1 and mat2 must have the same dtype"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "lOt9nJKGeg-m"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}