3 6_training_and_validation_v3__M.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
    "    </a>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Linear regression: Training and Validation Data</h1> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Objective</h2><ul><li> How to use learning rate hyperparameter to improve your model result.  .</li></ul> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of Contents</h2>\n",
    "<p>In this lab, you will learn to select the best learning rate by using validation data.</p>\n",
    "\n",
    "<ul>\n",
    "    <li><a href=\"#Makeup_Data\">Make Some Data</a></li>\n",
    "    <li><a href=\"#LR_Loader_Cost\">Create a Linear Regression Object, Data Loader and Criterion Function</a></li>\n",
    "    <li><a href=\"#LR_Hyper\">Different learning rates and Data Structures to Store results for Different Hyperparameters</a></li>\n",
    "    <li><a href=\"#Model\">Train different modules for different Hyperparameters</a></li>\n",
    "    <li><a href=\"#Result\">View Results</a></li>\n",
    "</ul>\n",
    "\n",
    "<p>Estimated Time Needed: <strong>30 min</strong></p>\n",
    "\n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Preparation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll need the following libraries and set the random seed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries we need for this lab, and set the random seed\n",
    "\n",
    "from torch import nn\n",
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from torch import nn,optim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Makeup_Data\">Make Some Data</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we'll create some artificial data in a dataset class. The class will include the option to produce training data or validation data. The training data will include outliers.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create Data class\n",
    "\n",
    "from torch.utils.data import Dataset, DataLoader\n",
    "\n",
    "class Data(Dataset):\n",
    "    \n",
    "    # Constructor\n",
    "    def __init__(self, train = True):\n",
    "            self.x = torch.arange(-3, 3, 0.1).view(-1, 1)\n",
    "            self.f = -3 * self.x + 1\n",
    "            self.y = self.f + 0.1 * torch.randn(self.x.size())\n",
    "            self.len = self.x.shape[0]\n",
    "            \n",
    "            #outliers \n",
    "            if train == True:\n",
    "                self.y[0] = 0\n",
    "                self.y[50:55] = 20\n",
    "            else:\n",
    "                pass\n",
    "      \n",
    "    # Getter\n",
    "    def __getitem__(self, index):    \n",
    "        return self.x[index], self.y[index]\n",
    "    \n",
    "    # Get Length\n",
    "    def __len__(self):\n",
    "        return self.len"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create two objects: one that contains training data and a second that contains validation data. Assume that the training data has the outliers. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create training dataset and validation dataset\n",
    "\n",
    "train_data = Data()\n",
    "val_data = Data(train = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overlay the training points in red over the function that generated the data. Notice the outliers at x=-3 and around x=2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot out training points\n",
    "\n",
    "plt.plot(train_data.x.numpy(), train_data.y.numpy(), 'xr',label=\"training data \")\n",
    "plt.plot(train_data.x.numpy(), train_data.f.numpy(),label=\"true function  \")\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"LR_Loader_Cost\">Create a Linear Regression Object,  Data Loader, and Criterion Function</h2>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create Linear Regression Class\n",
    "\n",
    "from torch import nn\n",
    "\n",
    "class linear_regression(nn.Module):\n",
    "    \n",
    "    # Constructor\n",
    "    def __init__(self, input_size, output_size):\n",
    "        super(linear_regression, self).__init__()\n",
    "        self.linear = nn.Linear(input_size, output_size)\n",
    "    \n",
    "    # Prediction function\n",
    "    def forward(self, x):\n",
    "        yhat = self.linear(x)\n",
    "        return yhat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the criterion function and a <code>DataLoader</code> object: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create MSELoss function and DataLoader\n",
    "\n",
    "criterion = nn.MSELoss()\n",
    "trainloader = DataLoader(dataset = train_data, batch_size = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"LR_Hyper\">Different learning rates and Data Structures to Store results for different Hyperparameters</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a list with different learning rates and a tensor (can be a list) for the training and validating cost/total loss. Include the list MODELS, which stores the training model for every value of the learning rate. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create Learning Rate list, the error lists and the MODELS list\n",
    "\n",
    "learning_rates=[0.0001, 0.001, 0.01, 0.1]\n",
    "\n",
    "train_error=torch.zeros(len(learning_rates))\n",
    "validation_error=torch.zeros(len(learning_rates))\n",
    "\n",
    "MODELS=[]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Model\">Train different models  for different Hyperparameters</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try different values of learning rates, perform stochastic gradient descent, and save the results on the training data and validation data. Finally, save each model in a list.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the train model function and train the model\n",
    "\n",
    "def train_model_with_lr (iter, lr_list):\n",
    "    \n",
    "    # iterate through different learning rates \n",
    "    for i, lr in enumerate(lr_list):\n",
    "        model = linear_regression(1, 1)\n",
    "        optimizer = optim.SGD(model.parameters(), lr = lr)\n",
    "        for epoch in range(iter):\n",
    "            for x, y in trainloader:\n",
    "                yhat = model(x)\n",
    "                loss = criterion(yhat, y)\n",
    "                optimizer.zero_grad()\n",
    "                loss.backward()\n",
    "                optimizer.step()\n",
    "                \n",
    "        # train data\n",
    "        Yhat = model(train_data.x)\n",
    "        train_loss = criterion(Yhat, train_data.y)\n",
    "        train_error[i] = train_loss.item()\n",
    "    \n",
    "        # validation data\n",
    "        Yhat = model(val_data.x)\n",
    "        val_loss = criterion(Yhat, val_data.y)\n",
    "        validation_error[i] = val_loss.item()\n",
    "        MODELS.append(model)\n",
    "\n",
    "train_model_with_lr(10, learning_rates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Result\">View the Results</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the training loss and validation loss for each learning rate:  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the training loss and validation loss\n",
    "\n",
    "plt.semilogx(np.array(learning_rates), train_error.numpy(), label = 'training loss/total Loss')\n",
    "plt.semilogx(np.array(learning_rates), validation_error.numpy(), label = 'validation cost/total Loss')\n",
    "plt.ylabel('Cost\\ Total Loss')\n",
    "plt.xlabel('learning rate')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction by using the validation data for each model:  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 [[3.3840857]\n",
      " [3.2878091]\n",
      " [3.1915324]]\n",
      "1 [[5.7266693]\n",
      " [5.609081 ]\n",
      " [5.4914923]]\n",
      "2 [[6.5074673]\n",
      " [6.375118 ]\n",
      " [6.2427673]]\n",
      "3 [[14.314765]\n",
      " [13.884166]\n",
      " [13.453566]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the predictions\n",
    "\n",
    "i = 0\n",
    "for model, learning_rate in zip(MODELS, learning_rates):\n",
    "    yhat = model(val_data.x)\n",
    "    plt.plot(val_data.x.numpy(), yhat.detach().numpy(), label = 'lr:' + str(learning_rate))\n",
    "    print(i, yhat.detach().numpy()[0:3])\n",
    "    i+=1\n",
    "plt.plot(val_data.x.numpy(), val_data.f.numpy(), 'or', label = 'validation data')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Practice</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object <code>good_model</code> is the best performing model. Use the train loader to get the data samples x and y. Produce an estimate for <code>yhat</code> and print it out for every sample in a for a loop. Compare it to the actual prediction <code>y</code>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yhat=  tensor([[14.3148]], grad_fn=<AddmmBackward>) y tensor([[0.]])\n",
      "yhat=  tensor([[13.8842]], grad_fn=<AddmmBackward>) y tensor([[9.7498]])\n",
      "yhat=  tensor([[13.4536]], grad_fn=<AddmmBackward>) y tensor([[9.4133]])\n",
      "yhat=  tensor([[13.0230]], grad_fn=<AddmmBackward>) y tensor([[8.9958]])\n",
      "yhat=  tensor([[12.5924]], grad_fn=<AddmmBackward>) y tensor([[8.7014]])\n",
      "yhat=  tensor([[12.1618]], grad_fn=<AddmmBackward>) y tensor([[8.5966]])\n",
      "yhat=  tensor([[11.7312]], grad_fn=<AddmmBackward>) y tensor([[8.1052]])\n",
      "yhat=  tensor([[11.3006]], grad_fn=<AddmmBackward>) y tensor([[7.9232]])\n",
      "yhat=  tensor([[10.8700]], grad_fn=<AddmmBackward>) y tensor([[7.4238]])\n",
      "yhat=  tensor([[10.4394]], grad_fn=<AddmmBackward>) y tensor([[7.1771]])\n",
      "yhat=  tensor([[10.0088]], grad_fn=<AddmmBackward>) y tensor([[6.9711]])\n",
      "yhat=  tensor([[9.5782]], grad_fn=<AddmmBackward>) y tensor([[6.7108]])\n",
      "yhat=  tensor([[9.1476]], grad_fn=<AddmmBackward>) y tensor([[6.3922]])\n",
      "yhat=  tensor([[8.7170]], grad_fn=<AddmmBackward>) y tensor([[5.9774]])\n",
      "yhat=  tensor([[8.2864]], grad_fn=<AddmmBackward>) y tensor([[5.7303]])\n",
      "yhat=  tensor([[7.8558]], grad_fn=<AddmmBackward>) y tensor([[5.3712]])\n",
      "yhat=  tensor([[7.4252]], grad_fn=<AddmmBackward>) y tensor([[5.0497]])\n",
      "yhat=  tensor([[6.9946]], grad_fn=<AddmmBackward>) y tensor([[4.8391]])\n",
      "yhat=  tensor([[6.5640]], grad_fn=<AddmmBackward>) y tensor([[4.5672]])\n",
      "yhat=  tensor([[6.1334]], grad_fn=<AddmmBackward>) y tensor([[4.0396]])\n",
      "yhat=  tensor([[5.7028]], grad_fn=<AddmmBackward>) y tensor([[3.7598]])\n",
      "yhat=  tensor([[5.2722]], grad_fn=<AddmmBackward>) y tensor([[3.8694]])\n",
      "yhat=  tensor([[4.8416]], grad_fn=<AddmmBackward>) y tensor([[3.5062]])\n",
      "yhat=  tensor([[4.4110]], grad_fn=<AddmmBackward>) y tensor([[3.0380]])\n",
      "yhat=  tensor([[3.9804]], grad_fn=<AddmmBackward>) y tensor([[2.8072]])\n",
      "yhat=  tensor([[3.5498]], grad_fn=<AddmmBackward>) y tensor([[2.4505]])\n",
      "yhat=  tensor([[3.1192]], grad_fn=<AddmmBackward>) y tensor([[2.3104]])\n",
      "yhat=  tensor([[2.6886]], grad_fn=<AddmmBackward>) y tensor([[1.8163]])\n",
      "yhat=  tensor([[2.2580]], grad_fn=<AddmmBackward>) y tensor([[1.5378]])\n",
      "yhat=  tensor([[1.8274]], grad_fn=<AddmmBackward>) y tensor([[1.2281]])\n",
      "yhat=  tensor([[1.3968]], grad_fn=<AddmmBackward>) y tensor([[1.1158]])\n",
      "yhat=  tensor([[0.9662]], grad_fn=<AddmmBackward>) y tensor([[0.7983]])\n",
      "yhat=  tensor([[0.5356]], grad_fn=<AddmmBackward>) y tensor([[0.3465]])\n",
      "yhat=  tensor([[0.1050]], grad_fn=<AddmmBackward>) y tensor([[-0.0184]])\n",
      "yhat=  tensor([[-0.3256]], grad_fn=<AddmmBackward>) y tensor([[-0.2825]])\n",
      "yhat=  tensor([[-0.7562]], grad_fn=<AddmmBackward>) y tensor([[-0.4495]])\n",
      "yhat=  tensor([[-1.1868]], grad_fn=<AddmmBackward>) y tensor([[-0.9335]])\n",
      "yhat=  tensor([[-1.6174]], grad_fn=<AddmmBackward>) y tensor([[-1.1791]])\n",
      "yhat=  tensor([[-2.0480]], grad_fn=<AddmmBackward>) y tensor([[-1.5740]])\n",
      "yhat=  tensor([[-2.4786]], grad_fn=<AddmmBackward>) y tensor([[-1.7274]])\n",
      "yhat=  tensor([[-2.9092]], grad_fn=<AddmmBackward>) y tensor([[-2.0610]])\n",
      "yhat=  tensor([[-3.3398]], grad_fn=<AddmmBackward>) y tensor([[-2.3208]])\n",
      "yhat=  tensor([[-3.7704]], grad_fn=<AddmmBackward>) y tensor([[-2.6127]])\n",
      "yhat=  tensor([[-4.2010]], grad_fn=<AddmmBackward>) y tensor([[-2.8941]])\n",
      "yhat=  tensor([[-4.6316]], grad_fn=<AddmmBackward>) y tensor([[-3.2506]])\n",
      "yhat=  tensor([[-5.0622]], grad_fn=<AddmmBackward>) y tensor([[-3.3619]])\n",
      "yhat=  tensor([[-5.4928]], grad_fn=<AddmmBackward>) y tensor([[-3.8638]])\n",
      "yhat=  tensor([[-5.9234]], grad_fn=<AddmmBackward>) y tensor([[-4.1536]])\n",
      "yhat=  tensor([[-6.3540]], grad_fn=<AddmmBackward>) y tensor([[-4.5987]])\n",
      "yhat=  tensor([[-6.7846]], grad_fn=<AddmmBackward>) y tensor([[-4.5782]])\n",
      "yhat=  tensor([[-7.2152]], grad_fn=<AddmmBackward>) y tensor([[20.]])\n",
      "yhat=  tensor([[-7.6458]], grad_fn=<AddmmBackward>) y tensor([[20.]])\n",
      "yhat=  tensor([[-8.0764]], grad_fn=<AddmmBackward>) y tensor([[20.]])\n",
      "yhat=  tensor([[-8.5070]], grad_fn=<AddmmBackward>) y tensor([[20.]])\n",
      "yhat=  tensor([[-8.9376]], grad_fn=<AddmmBackward>) y tensor([[20.]])\n",
      "yhat=  tensor([[-9.3682]], grad_fn=<AddmmBackward>) y tensor([[-6.3404]])\n",
      "yhat=  tensor([[-9.7988]], grad_fn=<AddmmBackward>) y tensor([[-6.6899]])\n",
      "yhat=  tensor([[-10.2294]], grad_fn=<AddmmBackward>) y tensor([[-7.1205]])\n",
      "yhat=  tensor([[-10.6600]], grad_fn=<AddmmBackward>) y tensor([[-7.4155]])\n",
      "yhat=  tensor([[-11.0906]], grad_fn=<AddmmBackward>) y tensor([[-7.6921]])\n"
     ]
    }
   ],
   "source": [
    "good_model = MODELS[np.argmin(validation_error)]\n",
    "\n",
    "#Type your code here: \n",
    "\n",
    "for x, y in trainloader:\n",
    "    print(\"yhat= \", model(x),\"y\", y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- \n",
    "for x, y in trainloader:\n",
    "    print(\"yhat= \", model(x),\"y\", y)\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "<a href=\"https://dataplatform.cloud.ibm.com/registration/stepone?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork&context=cpdaas&apps=data_science_experience%2Cwatson_machine_learning\"><img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/Template/module%201/images/Watson_Studio.png\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>About the Authors:</h2> \n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\">Joseph Santarcangelo</a> has a PhD in Electrical Engineering, his research focused on using machine learning, signal processing, and computer vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other contributors: <a href=\"https://www.linkedin.com/in/michelleccarey/\">Michelle Carey</a>, <a href=\"www.linkedin.com/in/jiahui-mavis-zhou-a4537814a\">Mavis Zhou</a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--\n",
    "## Change Log\n",
    "\n",
    "|  Date (YYYY-MM-DD) |  Version | Changed By  |  Change Description |\n",
    "|---|---|---|---|\n",
    "| 2020-09-23  | 2.0  | Shubham  |  Migrated Lab to Markdown and added to course repo in GitLab |\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "## <h3 align=\"center\"> &#169; IBM Corporation. All rights reserved. <h3/>\n"
   ]
  }
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