{
 "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 - 2026"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f75bc56-1806-4248-a195-1bbad6509fe2",
   "metadata": {},
   "source": [
    "    cd ~/SE_data\n",
    "    git pull\n",
    "    rsync -hvrPt --ignore-existing ~/SE_data/* /media/sf_LVM_shared/my_SE_data\n",
    "    cd  /media/sf_LVM_shared/my_SE_data/exercise\n",
    "    jupyter-lab Tree_Height_05Perceptron_intro_2026.ipynb "
   ]
  },
  {
   "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": 1,
   "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": 3,
   "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": 4,
   "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": 4,
     "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": 5,
   "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": 6,
   "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": 7,
   "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 4667.2607421875\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'slope: -24.213, r_value: -0.325')"
      ]
     },
     "execution_count": 7,
     "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": 8,
   "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": 9,
   "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 0x7fa33fee7ed0>]"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "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": 11,
   "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": 12,
   "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": 13,
   "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": 14,
   "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": 15,
   "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": 16,
   "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": 17,
   "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 0x7fa330506490>]"
      ]
     },
     "execution_count": 17,
     "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": 18,
   "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 0.013135942630469799\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": 20,
   "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",
      "608285  7.768016  49.695662   9.7400\n",
      "948893  8.971471  49.693502  18.6975\n",
      "235611  6.821825  49.669922  16.6500\n",
      "247893  6.855443  49.533505   2.3075\n",
      "850112  8.716271  49.602624  32.3450\n"
     ]
    }
   ],
   "source": [
    "### Try the the tree height with Perceptron\n",
    "predictors = pd.read_csv(\"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": 21,
   "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": 22,
   "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([3.443e+03, 3.693e+03, 2.374e+03, 2.205e+03, 2.233e+03, 2.323e+03,\n",
       "        2.762e+03, 3.044e+03, 3.329e+03, 3.856e+03, 4.237e+03, 4.604e+03,\n",
       "        4.973e+03, 5.145e+03, 5.369e+03, 5.536e+03, 6.062e+03, 6.078e+03,\n",
       "        5.694e+03, 5.131e+03, 4.460e+03, 3.597e+03, 2.847e+03, 2.093e+03,\n",
       "        1.532e+03, 1.077e+03, 7.040e+02, 5.070e+02, 3.230e+02, 2.130e+02,\n",
       "        1.470e+02, 9.900e+01, 6.700e+01, 3.900e+01, 3.300e+01, 2.100e+01,\n",
       "        2.000e+01, 2.100e+01, 1.000e+01, 1.600e+01, 1.100e+01, 1.100e+01,\n",
       "        1.300e+01, 6.000e+00, 5.000e+00, 6.000e+00, 9.000e+00, 6.000e+00,\n",
       "        6.000e+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": 22,
     "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": 23,
   "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": 24,
   "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": 25,
   "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": 26,
   "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 0x7fa32b080e10>]"
      ]
     },
     "execution_count": 26,
     "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": 27,
   "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 0.019174350425601006\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
}