04.first-neural-network.ipynb

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  "metadata": {
    "colab": {
      "name": "04.first-neural-network.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fz7Xygqo3s3b",
        "colab_type": "text"
      },
      "source": [
        "# Build Your First Neural Network with PyTorch\n",
        "\n",
        "In this tutorial, you'll build your first Neural Network using PyTorch. You'll use it to predict whether or not is going to rain tomorrow using real weather information.\n",
        "\n",
        "- [Run the complete notebook in your browser (Google Colab)](https://colab.research.google.com/drive/1lDXVkdt7GC8jK_nGmOMKeDywXse-DY-u)\n",
        "- [Read the Getting Things Done with Pytorch book](https://github.com/curiousily/Getting-Things-Done-with-Pytorch)\n",
        "\n",
        "You'll learn how to:\n",
        "\n",
        "- Preprocess CSV files and convert the data to Tensors\n",
        "- Build your own Neural Network model with PyTorch\n",
        "- Use a loss function and an optimizer to train your model\n",
        "- Evaluate your model and learn about the perils of imbalanced classification"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "izq6eneDG4LP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install -q -U watermark"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pDQQni6tG5G3",
        "colab_type": "code",
        "outputId": "00b6611b-476e-475c-c7a4-d2b38b5ee44c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "%reload_ext watermark\n",
        "%watermark -v -p numpy,pandas,torch"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "CPython 3.6.9\n",
            "IPython 5.5.0\n",
            "\n",
            "numpy 1.17.5\n",
            "pandas 0.25.3\n",
            "torch 1.4.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AePREfpPkH2b",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Heavily based on https://github.com/Prodicode/ann-visualizer\n",
        "\n",
        "def ann_viz(model, view=True, filename=\"network.gv\"):\n",
        "    \"\"\"Vizualizez a Sequential model.\n",
        "\n",
        "    # Arguments\n",
        "        model: A Keras model instance.\n",
        "\n",
        "        view: whether to display the model after generation.\n",
        "\n",
        "        filename: where to save the vizualization. (a .gv file)\n",
        "\n",
        "        title: A title for the graph\n",
        "    \"\"\"\n",
        "    from graphviz import Digraph\n",
        "\n",
        "    input_layer = 0\n",
        "    hidden_layers_nr = 0\n",
        "    layer_types = []\n",
        "    hidden_layers = []\n",
        "    output_layer = 0\n",
        "    layers = [layer for layer in model.modules() if type(layer) == torch.nn.Linear]\n",
        "\n",
        "    for layer in layers:\n",
        "        if layer == layers[0]:\n",
        "            input_layer = layer.in_features\n",
        "            hidden_layers_nr += 1\n",
        "            if type(layer) == torch.nn.Linear:                \n",
        "                hidden_layers.append(layer.out_features)\n",
        "                layer_types.append(\"Dense\")\n",
        "            else:\n",
        "                raise Exception(\"Input error\")\n",
        "\n",
        "        else:\n",
        "            if layer == layers[-1]:\n",
        "                output_layer = layer.out_features\n",
        "            else:\n",
        "                hidden_layers_nr += 1\n",
        "                if type(layer) == torch.nn.Linear:\n",
        "\n",
        "                    hidden_layers.append(layer.out_features)\n",
        "                    layer_types.append(\"Dense\")\n",
        "                else:\n",
        "                    raise Exception(\"Hidden error\")\n",
        "        last_layer_nodes = input_layer\n",
        "        nodes_up = input_layer\n",
        "\n",
        "    g = Digraph(\"g\", filename=filename)\n",
        "    n = 0\n",
        "    g.graph_attr.update(splines=\"false\", nodesep=\"0.5\", ranksep=\"0\", rankdir='LR')\n",
        "    # Input Layer\n",
        "    with g.subgraph(name=\"cluster_input\") as c:\n",
        "        if type(layers[0]) == torch.nn.Linear:\n",
        "            the_label = \"Input Layer\"\n",
        "            if layers[0].in_features > 10:\n",
        "                the_label += \" (+\" + str(layers[0].in_features - 10) + \")\"\n",
        "                input_layer = 10\n",
        "            c.attr(color=\"white\")\n",
        "            for i in range(0, input_layer):\n",
        "                n += 1\n",
        "                c.node(str(n))\n",
        "                c.attr(labeljust=\"1\")\n",
        "                c.attr(label=the_label, labelloc=\"bottom\")\n",
        "                c.attr(rank=\"same\")                \n",
        "                c.node_attr.update(\n",
        "                    width=\"0.65\",\n",
        "                    style=\"filled\",                    \n",
        "                    shape=\"circle\",\n",
        "                    color=HAPPY_COLORS_PALETTE[3],\n",
        "                    fontcolor=HAPPY_COLORS_PALETTE[3],\n",
        "                )\n",
        "    for i in range(0, hidden_layers_nr):\n",
        "        with g.subgraph(name=\"cluster_\" + str(i + 1)) as c:\n",
        "            if layer_types[i] == \"Dense\":\n",
        "                c.attr(color=\"white\")\n",
        "                c.attr(rank=\"same\")\n",
        "                the_label = f'Hidden Layer {i + 1}'\n",
        "                if layers[i].out_features > 10:\n",
        "                    the_label += \" (+\" + str(layers[i].out_features - 10) + \")\"\n",
        "                    hidden_layers[i] = 10\n",
        "                c.attr(labeljust=\"right\", labelloc=\"b\", label=the_label)\n",
        "                for j in range(0, hidden_layers[i]):\n",
        "                    n += 1\n",
        "                    c.node(\n",
        "                        str(n),\n",
        "                        width=\"0.65\",\n",
        "                        shape=\"circle\",\n",
        "                        style=\"filled\",\n",
        "                        color=HAPPY_COLORS_PALETTE[0],\n",
        "                        fontcolor=HAPPY_COLORS_PALETTE[0],\n",
        "                    )\n",
        "                    for h in range(nodes_up - last_layer_nodes + 1, nodes_up + 1):\n",
        "                        g.edge(str(h), str(n))\n",
        "                last_layer_nodes = hidden_layers[i]\n",
        "                nodes_up += hidden_layers[i]\n",
        "            else:\n",
        "                raise Exception(\"Hidden layer type not supported\")\n",
        "\n",
        "    with g.subgraph(name=\"cluster_output\") as c:\n",
        "        if type(layers[-1]) == torch.nn.Linear:\n",
        "            c.attr(color=\"white\")\n",
        "            c.attr(rank=\"same\")\n",
        "            c.attr(labeljust=\"1\")\n",
        "            for i in range(1, output_layer + 1):\n",
        "                n += 1\n",
        "                c.node(\n",
        "                    str(n),\n",
        "                    width=\"0.65\",\n",
        "                    shape=\"circle\",\n",
        "                    style=\"filled\",\n",
        "                    color=HAPPY_COLORS_PALETTE[4],\n",
        "                    fontcolor=HAPPY_COLORS_PALETTE[4],\n",
        "                    \n",
        "                )\n",
        "                for h in range(nodes_up - last_layer_nodes + 1, nodes_up + 1):\n",
        "                    g.edge(str(h), str(n))\n",
        "            c.attr(label=\"Output Layer\", labelloc=\"bottom\")\n",
        "            c.node_attr.update(\n",
        "                color=\"#2ecc71\", style=\"filled\", fontcolor=\"#2ecc71\", shape=\"circle\"\n",
        "            )\n",
        "\n",
        "    g.attr(arrowShape=\"none\")\n",
        "    g.edge_attr.update(arrowhead=\"none\", color=\"#707070\", penwidth=\"2\")\n",
        "    if view is True:\n",
        "        g.view()\n",
        "\n",
        "    return g\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tLB23K0eGrIm",
        "colab_type": "code",
        "outputId": "8e68bc2d-c917-47b2-fb2a-cc5fb82ecf3e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "import torch\n",
        "\n",
        "import os\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from tqdm import tqdm\n",
        "import seaborn as sns\n",
        "from pylab import rcParams\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import rc\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import confusion_matrix, classification_report\n",
        "\n",
        "from torch import nn, optim\n",
        "\n",
        "import torch.nn.functional as F\n",
        "\n",
        "%matplotlib inline\n",
        "%config InlineBackend.figure_format='retina'\n",
        "\n",
        "sns.set(style='whitegrid', palette='muted', font_scale=1.2)\n",
        "\n",
        "HAPPY_COLORS_PALETTE = [\"#01BEFE\", \"#FFDD00\", \"#FF7D00\", \"#FF006D\", \"#93D30C\", \"#8F00FF\"]\n",
        "\n",
        "sns.set_palette(sns.color_palette(HAPPY_COLORS_PALETTE))\n",
        "\n",
        "rcParams['figure.figsize'] = 12, 8\n",
        "\n",
        "RANDOM_SEED = 42\n",
        "np.random.seed(RANDOM_SEED)\n",
        "torch.manual_seed(RANDOM_SEED)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<torch._C.Generator at 0x7f33b7e8ddf0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I67ain8jB3bP",
        "colab_type": "text"
      },
      "source": [
        "## Data\n",
        "\n",
        "Our dataset contains daily weather information from multiple Australian weather stations. We're about to answer a simple question. *Will it rain tomorrow?*\n",
        "\n",
        "The data is hosted on [Kaggle](https://www.kaggle.com/jsphyg/weather-dataset-rattle-package) and created by [Joe Young](https://www.kaggle.com/jsphyg). I've uploaded the dataset to Google Drive. Let's get it:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wMB_XqAqG05R",
        "colab_type": "code",
        "outputId": "8f5953e1-d9ce-443f-8a1d-da8e5f62916f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "!gdown --id 1Q1wUptbNDYdfizk5abhmoFxIQiX19Tn7"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading...\n",
            "From: https://drive.google.com/uc?id=1Q1wUptbNDYdfizk5abhmoFxIQiX19Tn7\n",
            "To: /content/weatherAUS.csv\n",
            "14.2MB [00:00, 38.9MB/s]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6GxdXyHRGlp2",
        "colab_type": "text"
      },
      "source": [
        "And load it into a data frame:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pb7qBnsKIb_4",
        "colab_type": "code",
        "outputId": "27869fa4-59ef-41e9-87ee-1311a2f62a53",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 309
        }
      },
      "source": [
        "df = pd.read_csv('weatherAUS.csv')\n",
        "df.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Date</th>\n",
              "      <th>Location</th>\n",
              "      <th>MinTemp</th>\n",
              "      <th>MaxTemp</th>\n",
              "      <th>Rainfall</th>\n",
              "      <th>Evaporation</th>\n",
              "      <th>Sunshine</th>\n",
              "      <th>WindGustDir</th>\n",
              "      <th>WindGustSpeed</th>\n",
              "      <th>WindDir9am</th>\n",
              "      <th>WindDir3pm</th>\n",
              "      <th>WindSpeed9am</th>\n",
              "      <th>WindSpeed3pm</th>\n",
              "      <th>Humidity9am</th>\n",
              "      <th>Humidity3pm</th>\n",
              "      <th>Pressure9am</th>\n",
              "      <th>Pressure3pm</th>\n",
              "      <th>Cloud9am</th>\n",
              "      <th>Cloud3pm</th>\n",
              "      <th>Temp9am</th>\n",
              "      <th>Temp3pm</th>\n",
              "      <th>RainToday</th>\n",
              "      <th>RISK_MM</th>\n",
              "      <th>RainTomorrow</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2008-12-01</td>\n",
              "      <td>Albury</td>\n",
              "      <td>13.4</td>\n",
              "      <td>22.9</td>\n",
              "      <td>0.6</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>W</td>\n",
              "      <td>44.0</td>\n",
              "      <td>W</td>\n",
              "      <td>WNW</td>\n",
              "      <td>20.0</td>\n",
              "      <td>24.0</td>\n",
              "      <td>71.0</td>\n",
              "      <td>22.0</td>\n",
              "      <td>1007.7</td>\n",
              "      <td>1007.1</td>\n",
              "      <td>8.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>16.9</td>\n",
              "      <td>21.8</td>\n",
              "      <td>No</td>\n",
              "      <td>0.0</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2008-12-02</td>\n",
              "      <td>Albury</td>\n",
              "      <td>7.4</td>\n",
              "      <td>25.1</td>\n",
              "      <td>0.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>WNW</td>\n",
              "      <td>44.0</td>\n",
              "      <td>NNW</td>\n",
              "      <td>WSW</td>\n",
              "      <td>4.0</td>\n",
              "      <td>22.0</td>\n",
              "      <td>44.0</td>\n",
              "      <td>25.0</td>\n",
              "      <td>1010.6</td>\n",
              "      <td>1007.8</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>17.2</td>\n",
              "      <td>24.3</td>\n",
              "      <td>No</td>\n",
              "      <td>0.0</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2008-12-03</td>\n",
              "      <td>Albury</td>\n",
              "      <td>12.9</td>\n",
              "      <td>25.7</td>\n",
              "      <td>0.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>WSW</td>\n",
              "      <td>46.0</td>\n",
              "      <td>W</td>\n",
              "      <td>WSW</td>\n",
              "      <td>19.0</td>\n",
              "      <td>26.0</td>\n",
              "      <td>38.0</td>\n",
              "      <td>30.0</td>\n",
              "      <td>1007.6</td>\n",
              "      <td>1008.7</td>\n",
              "      <td>NaN</td>\n",
              "      <td>2.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>23.2</td>\n",
              "      <td>No</td>\n",
              "      <td>0.0</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2008-12-04</td>\n",
              "      <td>Albury</td>\n",
              "      <td>9.2</td>\n",
              "      <td>28.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NE</td>\n",
              "      <td>24.0</td>\n",
              "      <td>SE</td>\n",
              "      <td>E</td>\n",
              "      <td>11.0</td>\n",
              "      <td>9.0</td>\n",
              "      <td>45.0</td>\n",
              "      <td>16.0</td>\n",
              "      <td>1017.6</td>\n",
              "      <td>1012.8</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>18.1</td>\n",
              "      <td>26.5</td>\n",
              "      <td>No</td>\n",
              "      <td>1.0</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2008-12-05</td>\n",
              "      <td>Albury</td>\n",
              "      <td>17.5</td>\n",
              "      <td>32.3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>W</td>\n",
              "      <td>41.0</td>\n",
              "      <td>ENE</td>\n",
              "      <td>NW</td>\n",
              "      <td>7.0</td>\n",
              "      <td>20.0</td>\n",
              "      <td>82.0</td>\n",
              "      <td>33.0</td>\n",
              "      <td>1010.8</td>\n",
              "      <td>1006.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>29.7</td>\n",
              "      <td>No</td>\n",
              "      <td>0.2</td>\n",
              "      <td>No</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Date Location  MinTemp  ...  RainToday  RISK_MM  RainTomorrow\n",
              "0  2008-12-01   Albury     13.4  ...         No      0.0            No\n",
              "1  2008-12-02   Albury      7.4  ...         No      0.0            No\n",
              "2  2008-12-03   Albury     12.9  ...         No      0.0            No\n",
              "3  2008-12-04   Albury      9.2  ...         No      1.0            No\n",
              "4  2008-12-05   Albury     17.5  ...         No      0.2            No\n",
              "\n",
              "[5 rows x 24 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OW1qUXeYH2ME",
        "colab_type": "text"
      },
      "source": [
        "We have a large set of features/columns here. You might also notice some *NaN*s. Let's have a look at the overall dataset size:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VYs-oeNAH23q",
        "colab_type": "code",
        "outputId": "b44a8c0b-81fc-4ebf-f0d9-a9a5db6f2901",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "df.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(142193, 24)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CgZZj38qJSSs",
        "colab_type": "text"
      },
      "source": [
        "Looks like we have plenty of data. But we got to do something about those missing values."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3x-gF4Y83Ycm",
        "colab_type": "text"
      },
      "source": [
        "## Data Preprocessing\n",
        "\n",
        "We'll start by simplifying the problem by removing most of the data. We'll use only 4 columns for predicting whether or not is going to rain tomorrow:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TMozkylDI1uY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "cols = ['Rainfall', 'Humidity3pm', 'Pressure9am', 'RainToday', 'RainTomorrow']\n",
        "\n",
        "df = df[cols]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EKO3kWwDNUoy",
        "colab_type": "text"
      },
      "source": [
        "Neural Networks don't work with much else than numbers. We'll convert *yes* and *no* to 1 and 0, respectively:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BZxTNJu2J5C5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df['RainToday'].replace({'No': 0, 'Yes': 1}, inplace = True)\n",
        "df['RainTomorrow'].replace({'No': 0, 'Yes': 1}, inplace = True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "58hXrACBNfw9",
        "colab_type": "text"
      },
      "source": [
        "Let's drop the rows with missing values. There are better ways to do this, but we'll keep it simple:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sd4eBNn4NTUD",
        "colab_type": "code",
        "outputId": "81da2d18-0021-4e3b-9e13-ddd047114605",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "df = df.dropna(how='any')\n",
        "df.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Rainfall</th>\n",
              "      <th>Humidity3pm</th>\n",
              "      <th>Pressure9am</th>\n",
              "      <th>RainToday</th>\n",
              "      <th>RainTomorrow</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.6</td>\n",
              "      <td>22.0</td>\n",
              "      <td>1007.7</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.0</td>\n",
              "      <td>25.0</td>\n",
              "      <td>1010.6</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.0</td>\n",
              "      <td>30.0</td>\n",
              "      <td>1007.6</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.0</td>\n",
              "      <td>16.0</td>\n",
              "      <td>1017.6</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.0</td>\n",
              "      <td>33.0</td>\n",
              "      <td>1010.8</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Rainfall  Humidity3pm  Pressure9am  RainToday  RainTomorrow\n",
              "0       0.6         22.0       1007.7        0.0             0\n",
              "1       0.0         25.0       1010.6        0.0             0\n",
              "2       0.0         30.0       1007.6        0.0             0\n",
              "3       0.0         16.0       1017.6        0.0             0\n",
              "4       1.0         33.0       1010.8        0.0             0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "otjB4q_NRZCh",
        "colab_type": "text"
      },
      "source": [
        "Finally, we have a dataset we can work with. \n",
        "\n",
        "One important question we should answer is - *How balanced is our dataset?*. Or *How many times did it rain or not rain tomorrow?*:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A66FQPqEOydL",
        "colab_type": "code",
        "outputId": "83f8aefd-0dc5-4dc0-b0ff-a7e1ad0ef9dd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        }
      },
      "source": [
        "sns.countplot(df.RainTomorrow);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AAICCE+YDAAAAAEDBCfMB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\nHwAAAAAACk6YDwAAAAAABff/wqfCYTee3YoAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 761,
              "height": 489
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ME9fnVlg0m3F",
        "colab_type": "code",
        "outputId": "7e64a992-c4ed-4bb0-faa6-434fb353b76e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "df.RainTomorrow.value_counts() / df.shape[0]"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    0.778762\n",
              "1    0.221238\n",
              "Name: RainTomorrow, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NnJbP0QMUU_h",
        "colab_type": "text"
      },
      "source": [
        "Things are not looking good. About 78% of the data points have a non-rainy day for tomorrow. This means that a model that predicts there will be no rain tomorrow will be correct about 78% of the time.\n",
        "\n",
        "You can read and apply the [Practical Guide to Handling Imbalanced Datasets](https://www.curiousily.com/posts/practical-guide-to-handling-imbalanced-datasets/) if you want to mitigate this issue. Here, we'll just hope for the best.\n",
        "\n",
        "The final step is to split the data into train and test sets:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RdI7qBpgNTr7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = df[['Rainfall', 'Humidity3pm', 'RainToday', 'Pressure9am']]\n",
        "y = df[['RainTomorrow']]\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=RANDOM_SEED)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LwFOIU-KWt8b",
        "colab_type": "text"
      },
      "source": [
        "And convert all of it to Tensors (so we can use it with PyTorch):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GGOBFwarzrts",
        "colab_type": "code",
        "outputId": "5918e82d-77f9-4fc8-fa95-b1e2b1997a91",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "X_train = torch.from_numpy(X_train.to_numpy()).float()\n",
        "y_train = torch.squeeze(torch.from_numpy(y_train.to_numpy()).float())\n",
        "\n",
        "X_test = torch.from_numpy(X_test.to_numpy()).float()\n",
        "y_test = torch.squeeze(torch.from_numpy(y_test.to_numpy()).float())\n",
        "\n",
        "print(X_train.shape, y_train.shape)\n",
        "print(X_test.shape, y_test.shape)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([99751, 4]) torch.Size([99751])\n",
            "torch.Size([24938, 4]) torch.Size([24938])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WS3p73do3T4X",
        "colab_type": "text"
      },
      "source": [
        "## Building a Neural Network\n",
        "\n",
        "We'll build a simple Neural Network (NN) that tries to predicts will it rain tomorrow. \n",
        "\n",
        "Our input contains data from the four columns: `Rainfall, Humidity3pm, RainToday, Pressure9am`. We'll create an appropriate input layer for that.\n",
        "\n",
        "The output will be a number between 0 and 1, representing how likely (our model thinks) it is going to rain tomorrow. The prediction will be given to us by the final (output) layer of the network. \n",
        "\n",
        "We'll two (hidden) layers between the input and output layers. The parameters (neurons) of those layer will decide the final output. All layers will be fully-connected.\n",
        "\n",
        "One easy way to build the NN with PyTorch is to create a class that inherits from `torch.nn.Module`:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h1XNn_zmN7C_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Net(nn.Module):\n",
        "\n",
        "  def __init__(self, n_features):\n",
        "    super(Net, self).__init__()\n",
        "    self.fc1 = nn.Linear(n_features, 5)\n",
        "    self.fc2 = nn.Linear(5, 3)\n",
        "    self.fc3 = nn.Linear(3, 1)\n",
        "\n",
        "  def forward(self, x):\n",
        "    x = F.relu(self.fc1(x))\n",
        "    x = F.relu(self.fc2(x))\n",
        "    return torch.sigmoid(self.fc3(x))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iVF6WoxRl6bT",
        "colab_type": "code",
        "outputId": "90b6a80e-e088-4dc7-b730-ea1ff4e28833",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 612
        }
      },
      "source": [
        "net = Net(X_train.shape[1])\n",
        "\n",
        "ann_viz(net, view=False)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MJpO95ILXasL",
        "colab_type": "text"
      },
      "source": [
        "We start by creating the layers of our model in the constructor. The `forward()` method is where the magic happens. It accepts the input `x` and allows it to flow through each layer.\n",
        "\n",
        "There is a corresponding backward pass (defined for you by PyTorch) that allows the model to learn from the errors that is currently making.\n",
        "\n",
        "### Activation Functions\n",
        "\n",
        "You might notice the calls to `F.relu` and `torch.sigmoid`. Why do we need those?\n",
        "\n",
        "One of the cool *features* of Neural Networks is that they can approximate non-linear functions. In fact, [it is proven that they can approximate any function](https://en.wikipedia.org/wiki/Universal_approximation_theorem).\n",
        "\n",
        "Good luck approximating non-linear functions by stacking linear layers. Activation functions allow you to break from the linear world and learn (hopefully) more. You'll usually find them applied to an output of some layer. \n",
        "\n",
        "Those functions must be hard to define, right?\n",
        "\n",
        "#### ReLU\n",
        "\n",
        "Not at all, let start with the ReLU definition (one of the most widely used activation function):\n",
        "\n",
        "$$\n",
        "\\text{ReLU}(x) = \\max({0, x})\n",
        "$$\n",
        "\n",
        "Easy peasy, the result is the maximum value of zero and the input."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X8dFMwTrhmKv",
        "colab_type": "code",
        "outputId": "bbe157d8-2d6f-4455-cca7-2d1e6e211fc8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        }
      },
      "source": [
        "ax = plt.gca()\n",
        "\n",
        "plt.plot(\n",
        "  np.linspace(-1, 1, 5), \n",
        "  F.relu(torch.linspace(-1, 1, steps=5)).numpy()\n",
        ")\n",
        "ax.set_ylim([-1.5, 1.5]);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1IjVQLrEaAAAAYBza3F3kQ+3JxzuSPf2VW8OkwVdRr1qczKgVqYHRQawGAAAA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\nfelLG4Xo1tbWnHfeeUmShQsX5qGHHtretwgAAAA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            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 725,
              "height": 476
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ngpYTzfUCQF2",
        "colab_type": "text"
      },
      "source": [
        "#### Sigmoid\n",
        "\n",
        "The sigmoid is useful when you need to make a binary decision/classification (answering with a *yes* or a *no*). \n",
        "\n",
        "It is defined as:\n",
        "\n",
        "$$\\text{Sigmoid}(x) = \\frac{1}{1+e^{-x}}$$\n",
        "\n",
        "The sigmoid squishes the input values between 0 and 1. But in a super kind of way:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "35giPZUfAgV6",
        "colab_type": "code",
        "outputId": "618568ab-f71a-4936-9eec-532c564040e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        }
      },
      "source": [
        "ax = plt.gca()\n",
        "\n",
        "plt.plot(\n",
        "  np.linspace(-10, 10, 100), \n",
        "  torch.sigmoid(torch.linspace(-10, 10, steps=100)).numpy()\n",
        ")\n",
        "ax.set_ylim([-1.5, 1.5]);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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e0ZR8c1byyvFCNQDAYCJWAwAADWvFtuoe1Y9vq45bm5Kvz0peNUGoBgAYbMRq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\n8MO5++67s3z58rz++uuZNm1a3va2t+X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4caKefPJJq7Vf\n2N/W+Ph4vf/++5IkFxeXMl3SDaWvsM9/9+7dWrZsmaSsZRmLu+wM+Qtm6enp+v777yVlFY0DAwNL\n3Cb5CwV57rnnJGXd7b1o0aJcx/fv368tW7ZIknr37i1n5+KvxlzaY0B75PTee++9Z+tOoHw6ffq0\noqOjFRcXp7i4OB0+fNiYBRgUFKSMjAzjmKRcO/BWr15dCQkJ+t///qcjR47o4sWLqlevnjIzM/Xr\nr7/qlVdeUWJiojw9PTVjxow8F4n/5JNP1L9/f82ePVutWrVSQEBAjuNOTk6qWbOm1q9fb8xSbNCg\ngdzc3HTs2DGNGzfOuAV/4sSJuueee0rjfxVK0cmTJzVz5kxJUmhoaJELh7t371bnzp2NouPtm5mF\nh4dr2rRpSk5OlpS1Dll6erri4uK0fv16jR07VidOnJCU9Y39iy++aK23BBvr16+ffv75Z926dUuO\njo5ycnKSyWRSdHS0VqxYoTfffNNYi+6dd95Rs2bNcrVR2O+XJDVu3FgRERFKSUnRL7/8ojp16sjb\n21vnz5/XzJkztWLFCklZX+z16tWrFN8xytqkSZOML2N79+6tsLAwpaam5vufk5NTrltYyWGVj4eH\nh5ycnPTbb7/p9OnTioqKUsOGDeXk5KQDBw5ozJgxio2NlbOzs6ZPn24st2YWERGhZ555RrNnz1ad\nOnXUuHHjXDH+/ve/a/Xq1UpOTta2bdtUv359eXp66tSpU5o4caI2b94sSQoLC1P79u3L5H2j9KWn\npyssLMxYUm3UqFHq3bt3gXnJxcUlxz4vhf1+vf7661q6dKlSUlLk4OAgJycnpaWlKTY2VqtXr9bY\nsWONL9lefvllPfbYY2X3PwClLiQkRIcPH5bJZDL+pt28eVMnTpzQwoULNXnyZKWmpsrZ2Vn//ve/\njc1/zchfKKrt27cbY+ihQ4fmOU6/HfkLJ0+e1OnTp4361Z49e4ylYlu1aqVr164Zx1xdXeXh4WG8\ntkGDBoqMjFRMTIx2796ttLQ01alTRyaTSRs2bNC4ceN08+ZN1apVS9OmTZO7u3uu+OPGjdO//vUv\nzZ49Wz169Mi1rGlJx4DlERsswmJz5szRqlWr8jw2ceLEHD+PGDFCI0eOzHXem2++qbi4OG3evFkr\nVqww/rCYeXp6Kjw8PNeApTiefPJJnT59WjNnztTevXvVt2/fHMcdHR01evRoq84eQdkxz6qWrH+b\nV1RUlDELIz+hoaF65513rBoXtpWRkaEdO3Zox44d+Z7j5uamN954o0RF5Pr162vWrFkKCwvT+fPn\nNWLEiFzndOrUSePHj7c4BuzTf//7X+PxypUrtXLlygLPX7JkSZ5feBSGHFbxDB06VGfOnNHy5cu1\nYcMGbdiwIcdxFxcXTZ482aJbTCWpRYsWmjx5st5++21FRUVp0KBBuc7p06ePhg4dalH7sE/nz5/X\nxo0bjZ9nzZpl3HmYn40bN+aaJFKQzMxMHTx40FijPy9OTk4aNmyYRo0aVeR2UT6kpaXlmbOy8/Ly\n0pQpU/Tggw9aFIP8Ben/rg2dnZ3VtWtXq7RJ/qr4JkyYoD179uR57PZrtKlTp6pnz545nps+fbqG\nDBmiw4cPa+7cuZo7d26O4zVq1NBnn32W5wTMoirtMaC9oVgNm3J1ddW8efP03Xff6dtvv1VUVJRu\n3LihWrVq6eGHH9bAgQOLNRDOzz//+U8FBwdr6dKlOnDggBITE1WtWjU1b95c/fr1U3BwsBXeDcpa\nRkaG1q5dK0kKDAy06pqroaGh8vX11cGDBxUdHa2kpCQlJyfLw8ND/v7+atGihXr16qV7773XajFh\nH8aNG6fffvtNhw4d0rlz55SYmKhbt27pjjvuUMOGDdW2bVuFhobKz8+vxLHat2+v1atXa9GiRdq2\nbZvi4+Pl4eGhu+++Wz179izTNdhRsZDDKq4JEyaoY8eO+uqrr3TkyBFduXJFNWrUUJs2bTRgwADd\nfffdJWq/R48eatKkiRYvXqxdu3bp4sWL8vLyUtOmTdW3b98ca8MCRTVs2DA1btxYhw4d0unTp5WU\nlKSUlBRVrVpV9erVU8uWLdW7d2/deeedtu4qSsHUqVO1b98+HT58WPHx8UpKSlJqaqq8vLzUqFEj\ntW/fXs8++2yJN5Mmf1VuycnJxhJrDz30kEXLiOaF/IXC/O1vf9OyZcu0fPlyrVmzRtHR0UpNTZW/\nv786d+6sgQMHWuX3sbTHgPbEIfP2xU4AAAAAAAAAAChjbLAIAAAAAAAAALA5itUAAAAAAAAAAJuj\nWA0AAAAAAAAAsDmK1QAAAAAAAAAAm6NYDQAAAAAAAACwOYrVAAAAAAAAAACbo1gNAAAAAAAAALA5\nitUAAAAAAAAAAJujWA0AAAAAAAAAsDmK1QAAAAAAAAAAm6NYDQAAAAAAAACwOYrVAAAAAAAAAACb\no1gNAAAAAAAAALA5itUAAAAAAAAAAJujWA0AAAAAAAAAsDmK1QAAAAAAAAAAm6NYDQAAAAAAAACw\nOYrVAAAAAAAAAACbo1gNAAAAAAAAALC5/wdDOIk1Ibs5lAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 725,
              "height": 476
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hj_KFvzl3SsA",
        "colab_type": "text"
      },
      "source": [
        "## Training\n",
        "\n",
        "With the model in place, we need to find parameters that predict will it rain tomorrow. First, we need something to tell us how good we're currently doing:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MhL1DT_MQIIf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "criterion = nn.BCELoss()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "byOLim3xSElu",
        "colab_type": "text"
      },
      "source": [
        "The [BCELoss](https://pytorch.org/docs/stable/nn.html#bceloss) is a loss function that measures the difference between the two binary vectors. In our case, the predictions of our model and the real values. It expects the values to be outputed by the sigmoid function. The closer this value gets to 0, the better your model should be.\n",
        "\n",
        "But how do we find parameters that minimize the loss function?\n",
        "\n",
        "### Optimization\n",
        "\n",
        "Imagine that each parameter of our NN is a knob. The optimizer's job is to find the perfect positions for each knob so that the loss gets close to 0. \n",
        "\n",
        "Real-world models can contain millions or even billions of parameters. With so many knobs to turn, it would be nice to have an efficient optimizer that quickly finds solutions.\n",
        "\n",
        "Contrary to what you might believe, optimization in Deep Learning is just satisfying. In practice, you're content with good enough parameter values.\n",
        "\n",
        "While there are tons of optimizers you can choose from, [Adam](https://pytorch.org/docs/stable/optim.html#torch.optim.Adam) is a safe first choice. PyTorch has a well-debugged implementation you can use:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q2rXijYXUEjJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "optimizer = optim.Adam(net.parameters(), lr=0.001)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S5eNPERFXEC-",
        "colab_type": "text"
      },
      "source": [
        "Naturally, the optimizer requires the parameters. The second argument `lr` is *learning rate*. It is a tradeoff between how good parameters you're going to find and how fast you'll get there. Finding good values for this can be black magic and a lot of brute-force \"experimentation\".\n",
        "\n",
        "### Doing it on the GPU\n",
        "\n",
        "Doing massively parallel computations on GPUs is one of the enablers for modern Deep Learning. You'll need nVIDIA GPU for that.\n",
        "\n",
        "PyTorch makes it really easy to transfer all the computation to your GPU:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OHX2pDdkuzvo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6fHaY9Owvb6s",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_train = X_train.to(device)\n",
        "y_train = y_train.to(device)\n",
        "\n",
        "X_test = X_test.to(device)\n",
        "y_test = y_test.to(device)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "32SucCs6vXCp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "net = net.to(device)\n",
        "\n",
        "criterion = criterion.to(device)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UbSU2TBkYfO2",
        "colab_type": "text"
      },
      "source": [
        "We start by checking whether or not a CUDA device is available. Then, we transfer all training and test data to that device. Finally, we move our model and loss function.\n",
        "\n",
        "### Finding Good Parameters\n",
        "\n",
        "Having a loss function is great, but tracking the accuracy of our model is something easier to understand, for us mere mortals. Here's the definition for our accuracy:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4AWiqHzlt59W",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def calculate_accuracy(y_true, y_pred):\n",
        "  predicted = y_pred.ge(.5).view(-1)\n",
        "  return (y_true == predicted).sum().float() / len(y_true)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LwyrFDedbU-B",
        "colab_type": "text"
      },
      "source": [
        "We convert every value below 0.5 to 0. Otherwise, we set it to 1. Finally, we calculate the percentage of correct values.\n",
        "\n",
        "With all the pieces of the puzzle in place, we can start training our model:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D6hnlmt1ciGo",
        "colab_type": "code",
        "outputId": "563a7506-d51c-4b76-960f-da47e36745dc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 697
        }
      },
      "source": [
        "def round_tensor(t, decimal_places=3):\n",
        "  return round(t.item(), decimal_places)\n",
        "\n",
        "for epoch in range(1000):\n",
        "    \n",
        "    y_pred = net(X_train)\n",
        "    \n",
        "    y_pred = torch.squeeze(y_pred)\n",
        "    train_loss = criterion(y_pred, y_train)\n",
        "    \n",
        "    if epoch % 100 == 0:\n",
        "      train_acc = calculate_accuracy(y_train, y_pred)\n",
        "\n",
        "      y_test_pred = net(X_test)\n",
        "      y_test_pred = torch.squeeze(y_test_pred)\n",
        "\n",
        "      test_loss = criterion(y_test_pred, y_test)\n",
        "\n",
        "      test_acc = calculate_accuracy(y_test, y_test_pred)\n",
        "      print(\n",
        "f'''epoch {epoch}\n",
        "Train set - loss: {round_tensor(train_loss)}, accuracy: {round_tensor(train_acc)}\n",
        "Test  set - loss: {round_tensor(test_loss)}, accuracy: {round_tensor(test_acc)}\n",
        "''')\n",
        "    \n",
        "    optimizer.zero_grad()\n",
        "    \n",
        "    train_loss.backward()\n",
        "    \n",
        "    optimizer.step()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch 0\n",
            "Train set - loss: 2.513, accuracy: 0.779\n",
            "Test  set - loss: 2.517, accuracy: 0.778\n",
            "\n",
            "epoch 100\n",
            "Train set - loss: 0.457, accuracy: 0.792\n",
            "Test  set - loss: 0.458, accuracy: 0.793\n",
            "\n",
            "epoch 200\n",
            "Train set - loss: 0.435, accuracy: 0.801\n",
            "Test  set - loss: 0.436, accuracy: 0.8\n",
            "\n",
            "epoch 300\n",
            "Train set - loss: 0.421, accuracy: 0.814\n",
            "Test  set - loss: 0.421, accuracy: 0.815\n",
            "\n",
            "epoch 400\n",
            "Train set - loss: 0.412, accuracy: 0.826\n",
            "Test  set - loss: 0.413, accuracy: 0.827\n",
            "\n",
            "epoch 500\n",
            "Train set - loss: 0.408, accuracy: 0.831\n",
            "Test  set - loss: 0.408, accuracy: 0.832\n",
            "\n",
            "epoch 600\n",
            "Train set - loss: 0.406, accuracy: 0.833\n",
            "Test  set - loss: 0.406, accuracy: 0.835\n",
            "\n",
            "epoch 700\n",
            "Train set - loss: 0.405, accuracy: 0.834\n",
            "Test  set - loss: 0.405, accuracy: 0.835\n",
            "\n",
            "epoch 800\n",
            "Train set - loss: 0.404, accuracy: 0.834\n",
            "Test  set - loss: 0.404, accuracy: 0.835\n",
            "\n",
            "epoch 900\n",
            "Train set - loss: 0.404, accuracy: 0.834\n",
            "Test  set - loss: 0.404, accuracy: 0.836\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fb4WPtLjfn7m",
        "colab_type": "text"
      },
      "source": [
        "During the training, we show our model the data for `10,000` times. Each time we measure the loss, propagate the errors trough our model and asking the optimizer to find better parameters.\n",
        "\n",
        "The `zero_grad()` method clears up the accumulated gradients, which the optimizer uses to find better parameters.\n",
        "\n",
        "What about that accuracy? 83.6% accuracy on the test set sounds reasonable, right? Well, I am about to disappoint you. But first, let's learn how to save and load our trained models."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KIRPLYNnu3my",
        "colab_type": "text"
      },
      "source": [
        "## Saving the model\n",
        "\n",
        "Training a good model can take a lot of time. And I mean weeks, months or even years. So, let's make sure that you know how you can save your precious work. Saving is easy:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EKVMkwgMxGZB",
        "colab_type": "code",
        "outputId": "a7c21c43-72f0-4980-c0ad-1847bb7b7fcf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "MODEL_PATH = 'model.pth'\n",
        "\n",
        "torch.save(net, MODEL_PATH)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/torch/serialization.py:360: UserWarning: Couldn't retrieve source code for container of type Net. It won't be checked for correctness upon loading.\n",
            "  \"type \" + obj.__name__ + \". It won't be checked \"\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-61Wk5E0gqWY",
        "colab_type": "text"
      },
      "source": [
        "Restoring your model is easy too:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9ckrjxYPxZ4w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "net = torch.load(MODEL_PATH)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5CobNIWq3OQc",
        "colab_type": "text"
      },
      "source": [
        "## Evaluation\n",
        "\n",
        "Wouldn't it be perfect to know what kinds of errors your model makes? Of course, that's impossible. But you can get an estimate.\n",
        "\n",
        "Using just accuracy wouldn't be a good way to do it. Recall that our data contains mostly no rain examples.\n",
        "\n",
        "One way to delve a bit deeper into your model performance is to assess the precision and recall for each class. In our case, that will be *no rain* and *rain*:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kvaK-sVE1Xmy",
        "colab_type": "code",
        "outputId": "031e2faf-1d2b-47da-8bfa-ad9df02c899c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        }
      },
      "source": [
        "classes = ['No rain', 'Raining']\n",
        "\n",
        "y_pred = net(X_test)\n",
        "\n",
        "y_pred = y_pred.ge(.5).view(-1).cpu()\n",
        "y_test = y_test.cpu()\n",
        "\n",
        "print(classification_report(y_test, y_pred, target_names=classes))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "     No rain       0.85      0.96      0.90     19413\n",
            "     Raining       0.74      0.40      0.52      5525\n",
            "\n",
            "    accuracy                           0.84     24938\n",
            "   macro avg       0.80      0.68      0.71     24938\n",
            "weighted avg       0.83      0.84      0.82     24938\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RGHvrs7CkNOe",
        "colab_type": "text"
      },
      "source": [
        " A maximum precision of 1 indicates that the model is perfect at identifying only relevant examples. A maximum recall of 1 indicates that our model can find all relevant examples in the dataset for this class.\n",
        "\n",
        " You can see that our model is doing good when it comes to the *No rain* class. We have so many examples. Unfortunately, we can't really trust predictions of the *Raining* class.\n",
        "\n",
        " One of the best things about binary classification is that you can have a good look at a simple confusion matrix:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d6g_WirP1iMz",
        "colab_type": "code",
        "outputId": "556adc5f-8da3-482a-ab56-99fa1163be5a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 529
        }
      },
      "source": [
        "cm = confusion_matrix(y_test, y_pred)\n",
        "df_cm = pd.DataFrame(cm, index=classes, columns=classes)\n",
        "\n",
        "hmap = sns.heatmap(df_cm, annot=True, fmt=\"d\")\n",
        "hmap.yaxis.set_ticklabels(hmap.yaxis.get_ticklabels(), rotation=0, ha='right')\n",
        "hmap.xaxis.set_ticklabels(hmap.xaxis.get_ticklabels(), rotation=30, ha='right')\n",
        "plt.ylabel('True label')\n",
        "plt.xlabel('Predicted label');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
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AAAAAANCBlLXYfeyxx+bMM8/M66+/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\nKHYDAAAAAGVRNMaECjLGBAAAAACAqqfYDQAAAABA1TPGBAAAAAAoi2Z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rtOn376qRwOh0JDQ/Xcc8/pnnvuUXR0tAwGg4qLi/W7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\nPqmEhAR3LB0AAOCSIuwGgDbS2I87KChIdXV12r17tzIyMtSzZ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            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "image/png": {
              "width": 733,
              "height": 512
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "781wID8HlD5u",
        "colab_type": "text"
      },
      "source": [
        "You can clearly see that our model shouldn't be trusted when it says it's going to rain."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HogiB9ZomRJ0",
        "colab_type": "text"
      },
      "source": [
        "## Conclusion\n",
        "\n",
        "Well done! You now have a Neural Network that can predict the weather. Well, sort of. Building well-performing models is hard, really hard. But there are tricks you'll pick up along the way and (hopefully) get better at your craft!\n",
        "\n",
        "- [Run the complete notebook in your browser (Google Colab)](https://colab.research.google.com/drive/1lDXVkdt7GC8jK_nGmOMKeDywXse-DY-u)\n",
        "- [Read the Getting Things Done with Pytorch book](https://github.com/curiousily/Getting-Things-Done-with-Pytorch)\n",
        "\n",
        "You learned how to:\n",
        "\n",
        "- Preprocess CSV files and convert the data to Tensors\n",
        "- Build your own Neural Network model with PyTorch\n",
        "- Use a loss function and an optimizer to train your model\n",
        "- Evaluate your model and learn about the perils of imbalanced classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SY47i7y_lFXE",
        "colab_type": "text"
      },
      "source": [
        "## References\n",
        "\n",
        "- [Precision and Recall](https://en.wikipedia.org/wiki/Precision_and_recall)\n",
        "- [Beyond Accuracy: Precision and Recall](https://towardsdatascience.com/beyond-accuracy-precision-and-recall-3da06bea9f6c)"
      ]
    }
  ]
}