{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d7732643-d6e3-4652-9a4f-61f60d647f72",
   "metadata": {
    "id": "d7732643-d6e3-4652-9a4f-61f60d647f72"
   },
   "source": [
    "# Estimation of tree height using GEDI dataset - Perceptron - 2025"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "347e6c11",
   "metadata": {
    "id": "347e6c11"
   },
   "source": [
    "Packages that you will need to install to this tutorial\n",
    "\n",
    "`conda install pytorch torchvision torchaudio cudatoolkit=10.2 -c pytorch`\n",
    "\n",
    "We will use these other packages that as well, but you already should have them installed ( <span style=\"color: red;\">NO NEED TO INSTALL THESE PACKAGES AGAIN</span> if you already went through this for the SVM tutorial):\n",
    "\n",
    "`conda install -c anaconda scikit-learn pandas scipy matplotlib numpy`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58b12f60-2a68-458c-a85a-5c3127d7d9fc",
   "metadata": {
    "id": "58b12f60-2a68-458c-a85a-5c3127d7d9fc",
    "tags": []
   },
   "outputs": [],
   "source": [
    "'''\n",
    "Packages that you will need to install\n",
    "conda install pytorch torchvision torchaudio cudatoolkit=10.2 -c pytorch\n",
    "\n",
    "We will use these other packages that as well, but you already should have them installed:\n",
    "conda install -c anaconda scikit-learn\n",
    "conda install pandas scipy matplotlib numpy\n",
    "'''\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import pandas as pd\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f3f045f-bf11-478c-bf5a-8e0da1c09511",
   "metadata": {
    "id": "8f3f045f-bf11-478c-bf5a-8e0da1c09511"
   },
   "source": [
    "Single-layer perceptron takes data as input and its weights are summed up then an activation function is applied before sent to the output layer. Here is an example for a data with 3 features (ie, predictors):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "51ab91de-746a-46c4-afa8-ccd0694d3b34",
   "metadata": {
    "id": "8ca92439-d084-41ad-98b7-bdd66e3c19b5"
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "image/jpeg": {
       "height": 400,
       "width": 800
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(\"../images/perceptron.jpeg\" , width = 800, height = 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2210a8f-ce68-465c-8cb7-1cf735a37ab5",
   "metadata": {
    "id": "c2210a8f-ce68-465c-8cb7-1cf735a37ab5"
   },
   "source": [
    "The use of an activation function depends on the expected output range or ditribution, which we will discuss in more details later. There are several options for activation function. To learn more about activation functions, checkout this great [blogpost](https://www.analyticsvidhya.com/blog/2020/01/fundamentals-deep-learning-activation-functions-when-to-use-them/)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c76382c-97fe-4301-8e65-424aefe8e1c4",
   "metadata": {
    "id": "7c76382c-97fe-4301-8e65-424aefe8e1c4"
   },
   "source": [
    "<span style=\"color:red\">**Question 1**</span>: what is the difference between the Perceptron shown above an a simple linear regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "032b4914-c8fb-48ef-944a-41263fe70a12",
   "metadata": {
    "id": "032b4914-c8fb-48ef-944a-41263fe70a12"
   },
   "source": [
    "Now let's see how we can implement a Perceptron:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b88a28fb-e0a2-486b-9e36-ab446370f810",
   "metadata": {
    "id": "b88a28fb-e0a2-486b-9e36-ab446370f810",
    "tags": []
   },
   "outputs": [],
   "source": [
    "class Perceptron(torch.nn.Module):\n",
    "    def __init__(self,input_size, output_size, use_activation_fn=False):\n",
    "        super(Perceptron, self).__init__()\n",
    "        self.fc = nn.Linear(input_size,output_size) # Initializes weights with uniform distribution centered in zero\n",
    "        self.activation_fn = nn.ReLU() # instead of Heaviside step fn\n",
    "        self.use_activation_fn = use_activation_fn # If we want to use an activation function\n",
    "    def forward(self, x):\n",
    "        output = self.fc(x)\n",
    "        if self.use_activation_fn:\n",
    "            output = self.activation_fn(output) # To add the non-linearity. Try training you Perceptron with and without the non-linearity\n",
    "        return output"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a62a3727-f3e5-493c-a3b4-0a0a2da80f4f",
   "metadata": {
    "id": "a62a3727-f3e5-493c-a3b4-0a0a2da80f4f"
   },
   "source": [
    "The building blocks of the Perceptron code:\n",
    "- nn.Linear: Applies a linear transformation to the incoming data: y = xA^T + b\n",
    "- nn.ReLU: Applies the rectified linear unit function element-wise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "127b95e2-d4b3-42dc-825b-eb60fdcba81c",
   "metadata": {
    "id": "127b95e2-d4b3-42dc-825b-eb60fdcba81c"
   },
   "source": [
    "Before we try to solve a real-world problem let's see how it works on a simpler data. For data, I will create a simple 2D regression problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62f4e1f2-929e-4829-812a-c1deae2e3562",
   "metadata": {
    "id": "62f4e1f2-929e-4829-812a-c1deae2e3562",
    "outputId": "9941d9aa-8764-490a-c598-f9c4394d6ffb",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Test data')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CREATE RANDOM DATA POINTS\n",
    "# from sklearn.datasets import make_blobs\n",
    "from sklearn.datasets import make_regression\n",
    "\n",
    "x_train, y_train = make_regression(n_samples=100, n_features=2, random_state=0)\n",
    "x_train = torch.FloatTensor(x_train)\n",
    "y_train = torch.FloatTensor(y_train)\n",
    "\n",
    "x_test, y_test = make_regression(n_samples=50, n_features=2, random_state=1)\n",
    "x_test = torch.FloatTensor(x_test)\n",
    "y_test = torch.FloatTensor(y_test)\n",
    "\n",
    "\n",
    "#Visualize the data\n",
    "fig,ax=plt.subplots(1,2,figsize=(10,5), sharey=True)\n",
    "ax[0].scatter(x_train[:,0],x_train[:,1],c=y_train)\n",
    "ax[0].set_xlabel('X')\n",
    "ax[0].set_ylabel('Y')\n",
    "ax[0].set_title('Training data')\n",
    "\n",
    "ax[1].scatter(x_test[:,0],x_test[:,1],c=y_test)\n",
    "ax[1].set_xlabel('X')\n",
    "ax[1].set_title('Test data')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "395243cd-b329-45e5-b839-50248d2df9e1",
   "metadata": {
    "id": "395243cd-b329-45e5-b839-50248d2df9e1"
   },
   "source": [
    "Let's have a quick look at the distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "448d903d-d091-4bc8-ba38-729ec1e234a8",
   "metadata": {
    "id": "448d903d-d091-4bc8-ba38-729ec1e234a8",
    "outputId": "140b2d59-951d-471b-96af-644beb0f442f",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_train = np.concatenate([x_train, y_train[:,None]],axis=1)\n",
    "n_plots_x = int(np.ceil(np.sqrt(data_train.shape[1])))\n",
    "n_plots_y = int(np.floor(np.sqrt(data_train.shape[1])))\n",
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5), dpi=100, facecolor='w', edgecolor='k')\n",
    "ax=ax.ravel()\n",
    "for idx in range(data_train.shape[1]):\n",
    "    ax[idx].hist(data_train[:,idx].flatten())\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "033b5902-c7df-4dfc-9c6a-4e175a4a4c6a",
   "metadata": {
    "id": "033b5902-c7df-4dfc-9c6a-4e175a4a4c6a"
   },
   "source": [
    "Now let's initialize our Perceptron model, define the type of optimizer and loss we want to use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcd27df5-fe85-40e7-b6b5-29a06e290c8a",
   "metadata": {
    "id": "dcd27df5-fe85-40e7-b6b5-29a06e290c8a",
    "tags": []
   },
   "outputs": [],
   "source": [
    "model = Perceptron(input_size=2, output_size=1)\n",
    "criterion = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.01) #Check slides for a review on SGD"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fefbca67-3623-4a34-8dd0-7c6f7e333adb",
   "metadata": {
    "id": "fefbca67-3623-4a34-8dd0-7c6f7e333adb"
   },
   "source": [
    "Just for curiosity, let's se how bad a naive model would perform in this task"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3ae3a9f1-8bc2-4a25-9a51-66685c565a82",
   "metadata": {
    "id": "3ae3a9f1-8bc2-4a25-9a51-66685c565a82",
    "outputId": "123f5824-32ef-46eb-9371-d1024e24086f",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_test.shape:  torch.Size([50, 2])\n",
      "y_pred.shape:  torch.Size([50, 1])\n",
      "y_test.shape:  torch.Size([50])\n",
      "Test loss before training 4622.46923828125\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'slope: 157.640, r_value: 0.532')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.eval()\n",
    "y_pred = model(x_test)\n",
    "print('x_test.shape: ',x_test.shape)\n",
    "print('y_pred.shape: ',y_pred.shape)\n",
    "print('y_test.shape: ',y_test.shape)\n",
    "before_train = criterion(y_pred.squeeze(), y_test)\n",
    "print('Test loss before training' , before_train.item())\n",
    "\n",
    "y_pred = y_pred.detach().numpy().squeeze()\n",
    "slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(y_pred, y_test)\n",
    "\n",
    "# # Fit line\n",
    "# x = np.arange(-150,150)\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "ax.scatter(y_pred, y_test)\n",
    "# ax.plot(x, intercept + slope*x, 'r', label='fitted line')\n",
    "ax.set_xlabel('Prediction')\n",
    "ax.set_ylabel('True')\n",
    "ax.set_title('slope: {:.3f}, r_value: {:.3f}'.format(slope, r_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "854869aa-777b-4e55-804c-20abcad6d815",
   "metadata": {
    "id": "854869aa-777b-4e55-804c-20abcad6d815"
   },
   "source": [
    "<span style=\"color:red\">**Question 1.1**</span>: Can you make sense of this model's output range?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0edd1a7e-8911-43c7-97d1-f9862d776bae",
   "metadata": {
    "id": "0edd1a7e-8911-43c7-97d1-f9862d776bae"
   },
   "source": [
    "Now let's train our Perceptron to model this data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21cdb3da-ca7d-42c8-bdbe-c542ac69ff70",
   "metadata": {
    "id": "21cdb3da-ca7d-42c8-bdbe-c542ac69ff70",
    "tags": []
   },
   "outputs": [],
   "source": [
    "model.train()\n",
    "epoch = 1000\n",
    "all_loss=[]\n",
    "for epoch in range(epoch):\n",
    "    optimizer.zero_grad()\n",
    "    # Forward pass\n",
    "    y_pred = model(x_train)\n",
    "    # Compute Loss\n",
    "    loss = criterion(y_pred.squeeze(), y_train)\n",
    "\n",
    "    # Backward pass\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    all_loss.append(loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9d48f19-513c-4628-bb70-1e727f57d28e",
   "metadata": {
    "id": "e9d48f19-513c-4628-bb70-1e727f57d28e",
    "outputId": "d69126bd-7025-4eeb-98d3-bce2c9d414f2",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1487b6593d30>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(all_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "576ba478-b5c6-42cc-a811-88a4b3ef4915",
   "metadata": {
    "id": "576ba478-b5c6-42cc-a811-88a4b3ef4915",
    "outputId": "215a28a3-75ea-4b71-804e-e7e980b0d9bd",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss after Training 298.5340576171875\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(x_test)\n",
    "    after_train = criterion(y_pred.squeeze(), y_test)\n",
    "    print('Test loss after Training' , after_train.item())\n",
    "\n",
    "    y_pred = y_pred.detach().numpy().squeeze()\n",
    "    slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(y_pred, y_test)\n",
    "\n",
    "    # Fit line\n",
    "    x = np.arange(-150,150)\n",
    "\n",
    "    fig,ax=plt.subplots()\n",
    "    ax.scatter(y_pred, y_test)\n",
    "    ax.plot(x, intercept + slope*x, 'r', label='fitted line')\n",
    "    ax.set_xlabel('Prediction')\n",
    "    ax.set_ylabel('True')\n",
    "    ax.set_title('slope: {:.3f}, r_value: {:.3f}'.format(slope, r_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77ae39c9-c5ca-443f-bd16-a8e57bfa34eb",
   "metadata": {
    "id": "77ae39c9-c5ca-443f-bd16-a8e57bfa34eb"
   },
   "source": [
    "This results is not bad, but note that we didn't use any activation function. Now let's see what happens when we add an activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "406723ed-892d-446b-afb9-25c09aaf50fe",
   "metadata": {
    "id": "406723ed-892d-446b-afb9-25c09aaf50fe",
    "outputId": "3786d886-83ef-45a5-9ecc-09515833cc4d",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss after Training 1798.1878662109375\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Add activation and retrain the model\n",
    "del model, optimizer\n",
    "model = Perceptron(input_size=2, output_size=1, use_activation_fn=True)\n",
    "criterion = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.01)\n",
    "\n",
    "model.train()\n",
    "epoch = 1000\n",
    "all_loss=[]\n",
    "for epoch in range(epoch):\n",
    "    optimizer.zero_grad()\n",
    "    # Forward pass\n",
    "    y_pred = model(x_train)\n",
    "    # Compute Loss\n",
    "    loss = criterion(y_pred.squeeze(), y_train)\n",
    "\n",
    "    # Backward pass\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    all_loss.append(loss.item())\n",
    "\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(x_test)\n",
    "    after_train = criterion(y_pred.squeeze(), y_test)\n",
    "    print('Test loss after Training' , after_train.item())\n",
    "\n",
    "    y_pred = y_pred.detach().numpy().squeeze()\n",
    "    slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(y_pred, y_test)\n",
    "\n",
    "    # Fit line\n",
    "    x = np.arange(-150,150)\n",
    "\n",
    "    fig,ax=plt.subplots()\n",
    "    ax.scatter(y_pred, y_test)\n",
    "    ax.plot(x, intercept + slope*x, 'r', label='fitted line')\n",
    "    ax.set_xlabel('Prediction')\n",
    "    ax.set_ylabel('True')\n",
    "    ax.set_title('slope: {:.3f}, r_value: {:.3f}'.format(slope, r_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31566549-7a6f-4c39-ac04-c2f797cbb503",
   "metadata": {
    "id": "31566549-7a6f-4c39-ac04-c2f797cbb503"
   },
   "source": [
    "<span style=\"color:red\">**Question 2**</span>: what is happenng to this model? Why do we have so many predicted outputs with 'zeros'?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a5559d1-41bc-4a2c-8013-a842364fac68",
   "metadata": {
    "id": "8a5559d1-41bc-4a2c-8013-a842364fac68"
   },
   "source": [
    "Let's see what happens when the data and target are normalized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f294e85c-d49a-4d4a-a2c7-b3ee8cea230a",
   "metadata": {
    "id": "f294e85c-d49a-4d4a-a2c7-b3ee8cea230a",
    "tags": []
   },
   "outputs": [],
   "source": [
    "#Now normalize the data\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler()\n",
    "\n",
    "data_train = np.concatenate([x_train, y_train[:,None]],axis=1)\n",
    "data_train = scaler.fit_transform(data_train)\n",
    "data_test = np.concatenate([x_test, y_test[:,None]],axis=1)\n",
    "data_test = scaler.transform(data_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bcd65c51-535b-4ddd-ad15-58a7d31e802b",
   "metadata": {
    "id": "bcd65c51-535b-4ddd-ad15-58a7d31e802b",
    "outputId": "03103022-b5b3-473b-bd11-dd0007d14b2d",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_plots_x = int(np.ceil(np.sqrt(data_train.shape[1])))\n",
    "n_plots_y = int(np.floor(np.sqrt(data_train.shape[1])))\n",
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5), dpi=100, facecolor='w', edgecolor='k')\n",
    "ax=ax.ravel()\n",
    "for idx in range(data_train.shape[1]):\n",
    "    ax[idx].hist(data_train[:,idx].flatten())\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4cd0f06c-76a8-4f27-a23a-1bc7b85df2bf",
   "metadata": {
    "id": "4cd0f06c-76a8-4f27-a23a-1bc7b85df2bf",
    "tags": []
   },
   "outputs": [],
   "source": [
    "x_train,y_train = data_train[:,:2],data_train[:,2]\n",
    "x_test,y_test = data_test[:,:2],data_test[:,2]\n",
    "\n",
    "x_train = torch.FloatTensor(x_train)\n",
    "y_train = torch.FloatTensor(y_train)\n",
    "\n",
    "x_test = torch.FloatTensor(x_test)\n",
    "y_test = torch.FloatTensor(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63a2405b-a272-4751-a6d0-a4e365cbb544",
   "metadata": {
    "id": "63a2405b-a272-4751-a6d0-a4e365cbb544",
    "tags": []
   },
   "outputs": [],
   "source": [
    "del model, optimizer\n",
    "model = Perceptron(input_size=2, output_size=1, use_activation_fn=True)\n",
    "criterion = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8da01d5c-e312-4b6a-8909-98a1f2957e35",
   "metadata": {
    "id": "8da01d5c-e312-4b6a-8909-98a1f2957e35",
    "tags": []
   },
   "outputs": [],
   "source": [
    "model.train()\n",
    "epoch = 1000\n",
    "all_loss=[]\n",
    "for epoch in range(epoch):\n",
    "    optimizer.zero_grad()\n",
    "    # Forward pass\n",
    "    y_pred = model(x_train)\n",
    "    # Compute Loss\n",
    "    loss = criterion(y_pred.squeeze(), y_train)\n",
    "\n",
    "    # Backward pass\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    all_loss.append(loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7ddb9006-fdd8-4732-bc42-851991445d47",
   "metadata": {
    "id": "7ddb9006-fdd8-4732-bc42-851991445d47",
    "outputId": "c2fcfa2d-07a7-4302-c589-2851a453bef3",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x147704cc5fd0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(all_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c74713da-ea8c-4069-aba0-009d7d812bb4",
   "metadata": {
    "id": "c74713da-ea8c-4069-aba0-009d7d812bb4",
    "outputId": "0dfe5bd7-d28a-4ba0-9ae0-2e25a58cc64a",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss after Training 0.0005619959556497633\n",
      "0.18696567 0.80532324\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(x_test)\n",
    "    after_train = criterion(y_pred.squeeze(), y_test)\n",
    "    print('Test loss after Training' , after_train.item())\n",
    "\n",
    "    y_pred = y_pred.detach().numpy().squeeze()\n",
    "    slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(y_pred, y_test)\n",
    "\n",
    "    # Fit line\n",
    "    print(y_test.numpy().min(),y_test.numpy().max())\n",
    "    x = np.linspace(y_test.numpy().min(),y_test.numpy().max(),len(y_test))\n",
    "\n",
    "    fig,ax=plt.subplots()\n",
    "    ax.scatter(y_pred, y_test)\n",
    "    ax.plot(x, intercept + slope*x, 'r', label='fitted line')\n",
    "    ax.set_xlabel('Prediction')\n",
    "    ax.set_ylabel('True')\n",
    "    ax.set_title('slope: {:.3f}, r_value: {:.3f}'.format(slope, r_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ab32742-1b39-40ec-b7f2-474f5459665a",
   "metadata": {
    "id": "8ab32742-1b39-40ec-b7f2-474f5459665a"
   },
   "source": [
    "Now that we know how to implement a Perceptron and how it works on a toy data, let's see a more interesting dataset. For that, we will use the tree height dataset. For simplicity, let's start with just few variables: latitude (x) and longitude (y)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4baf219-69cf-43cb-931c-cfdfef792bdb",
   "metadata": {
    "id": "d4baf219-69cf-43cb-931c-cfdfef792bdb",
    "outputId": "e7b85147-4136-4848-ded5-516ea36b47a5",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100000, 3)\n",
      "                X          Y       hm\n",
      "95985    6.391195  49.846923  33.8525\n",
      "266461   6.904085  49.553928  26.2275\n",
      "1101817  9.344710  49.898716  21.7225\n",
      "580826   7.693388  48.701113  22.7675\n",
      "265428   6.901073  49.505759  30.0575\n"
     ]
    }
   ],
   "source": [
    "### Try the the tree height with Perceptron\n",
    "predictors = pd.read_csv(\"/home/ahf38/Documents/geo_comp_offline/tree_height/txt/eu_x_y_height_predictors_select.txt\", sep=\" \",  index_col=False)\n",
    "predictors_sel = predictors.loc[(predictors['h'] < 7000)  ].sample(100000)\n",
    "predictors_sel.insert ( 4, 'hm' ,  predictors_sel['h']/100 ) # add a col of heigh in meters\n",
    "data  = predictors_sel[['X','Y','hm']]\n",
    "print(data.shape)\n",
    "print(data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28b39994-e920-4aad-a50f-61adabce41f7",
   "metadata": {
    "id": "28b39994-e920-4aad-a50f-61adabce41f7",
    "tags": []
   },
   "outputs": [],
   "source": [
    "#Normalize the data\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler()\n",
    "data = scaler.fit_transform(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2529ed9-00a6-4391-a072-00f68280a634",
   "metadata": {
    "id": "a2529ed9-00a6-4391-a072-00f68280a634",
    "outputId": "6a86db00-e0e0-49c8-f4e3-d1233c14b632",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.470e+03, 3.461e+03, 2.313e+03, 2.165e+03, 2.293e+03, 2.365e+03,\n",
       "        2.610e+03, 3.022e+03, 3.404e+03, 3.909e+03, 4.219e+03, 4.669e+03,\n",
       "        4.947e+03, 5.322e+03, 5.390e+03, 5.532e+03, 5.906e+03, 5.988e+03,\n",
       "        5.652e+03, 5.206e+03, 4.494e+03, 3.792e+03, 2.926e+03, 2.094e+03,\n",
       "        1.475e+03, 1.040e+03, 7.270e+02, 5.060e+02, 3.280e+02, 2.250e+02,\n",
       "        1.330e+02, 1.170e+02, 5.700e+01, 3.500e+01, 3.400e+01, 3.000e+01,\n",
       "        2.000e+01, 2.000e+01, 1.300e+01, 8.000e+00, 7.000e+00, 7.000e+00,\n",
       "        1.600e+01, 9.000e+00, 9.000e+00, 7.000e+00, 5.000e+00, 9.000e+00,\n",
       "        4.000e+00, 1.000e+01]),\n",
       " array([0.  , 0.02, 0.04, 0.06, 0.08, 0.1 , 0.12, 0.14, 0.16, 0.18, 0.2 ,\n",
       "        0.22, 0.24, 0.26, 0.28, 0.3 , 0.32, 0.34, 0.36, 0.38, 0.4 , 0.42,\n",
       "        0.44, 0.46, 0.48, 0.5 , 0.52, 0.54, 0.56, 0.58, 0.6 , 0.62, 0.64,\n",
       "        0.66, 0.68, 0.7 , 0.72, 0.74, 0.76, 0.78, 0.8 , 0.82, 0.84, 0.86,\n",
       "        0.88, 0.9 , 0.92, 0.94, 0.96, 0.98, 1.  ]),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Inspect the ranges\n",
    "fig,ax = plt.subplots(1,3,figsize=(15,5))\n",
    "ax[0].hist(data[:,0],50)\n",
    "ax[1].hist(data[:,1],50)\n",
    "ax[2].hist(data[:,2],50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c21aafd-7367-4172-9f9a-6cf04eef0f20",
   "metadata": {
    "id": "0c21aafd-7367-4172-9f9a-6cf04eef0f20",
    "outputId": "295d0729-0956-4b2a-e00a-1c37ad029fc2",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train.shape: torch.Size([70000, 2]), X_test.shape: torch.Size([30000, 2]), y_train.shape: torch.Size([70000]), y_test.shape: torch.Size([30000])\n"
     ]
    }
   ],
   "source": [
    "#Split the data\n",
    "X_train, X_test, y_train, y_test = train_test_split(data[:,:2], data[:,2], test_size=0.30, random_state=0)\n",
    "X_train = torch.FloatTensor(X_train)\n",
    "y_train = torch.FloatTensor(y_train)\n",
    "X_test = torch.FloatTensor(X_test)\n",
    "y_test = torch.FloatTensor(y_test)\n",
    "print('X_train.shape: {}, X_test.shape: {}, y_train.shape: {}, y_test.shape: {}'.format(X_train.shape, X_test.shape, y_train.shape, y_test.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f4608af6-afc4-4201-90df-196f7dec7b7f",
   "metadata": {
    "id": "f4608af6-afc4-4201-90df-196f7dec7b7f",
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Create percetron\n",
    "model = Perceptron(input_size=2, output_size=1)\n",
    "criterion = torch.nn.MSELoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4751f542-6105-459f-8de0-1386860c6dcc",
   "metadata": {
    "id": "4751f542-6105-459f-8de0-1386860c6dcc",
    "tags": []
   },
   "outputs": [],
   "source": [
    "model.train()\n",
    "epoch = 2000\n",
    "all_loss=[]\n",
    "for epoch in range(epoch):\n",
    "    optimizer.zero_grad()\n",
    "    # Forward pass\n",
    "    y_pred = model(X_train)\n",
    "    # Compute Loss\n",
    "    loss = criterion(y_pred.squeeze(), y_train)\n",
    "\n",
    "    # Backward pass\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    all_loss.append(loss.item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "681f2273-6361-4aff-9837-4a84f921cee6",
   "metadata": {
    "id": "681f2273-6361-4aff-9837-4a84f921cee6",
    "outputId": "e656539e-b230-4f92-d1db-af7b5351c7a6",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1487b455f070>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(all_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43652372-29f9-4e83-bd5f-cde9aff3a5bd",
   "metadata": {
    "id": "43652372-29f9-4e83-bd5f-cde9aff3a5bd",
    "outputId": "5d909792-e6cd-41a5-8d4c-191587ac4bda",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss after Training 0.018815793097019196\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_pred = model(X_test)\n",
    "    after_train = criterion(y_pred.squeeze(), y_test)\n",
    "    print('Test loss after Training' , after_train.item())\n",
    "\n",
    "    y_pred = y_pred.detach().numpy().squeeze()\n",
    "    slope, intercept, r_value, p_value, std_err = scipy.stats.linregress(y_pred, y_test)\n",
    "\n",
    "    fig,ax=plt.subplots()\n",
    "    ax.scatter(y_pred, y_test)\n",
    "    ax.set_xlabel('Prediction')\n",
    "    ax.set_ylabel('True')\n",
    "    ax.set_title('slope: {:.3f}, r_value: {:.3f}'.format(slope, r_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00aa6061-6b38-4f96-9ad8-018135d57a90",
   "metadata": {
    "id": "00aa6061-6b38-4f96-9ad8-018135d57a90"
   },
   "source": [
    "<span style=\"color:red\">**Question 3**</span>: As we can see, the Perceptron didn't perform well with the setup described above. Based on what we have discussed so far, what is wrong with our setup (model and data) and how can we make it better?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3e44342f",
   "metadata": {
    "id": "3e44342f"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}