notebooks/deep-learning/5.multiclass-classifier-mnist.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-class classifier: MNIST images\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/parrt/msds621/blob/master/notebooks/deep-learning/5.multiclass-classifier-mnist.ipynb)\n",
    "\n",
    "By [Terence Parr](https://explained.ai).\n",
    "\n",
    "To demonstrate $k$ class classification instead of binary ($k=2$) classification, let's use the traditional MNIST digital image recognition problem. We'll again use a random forest model as a baseline classifier. Instead of a sigmoid on a single output neuron, $k$ class classifiers use $k$ neurons in the final layer and then a softmax computation instead of a single-output sigmoid. We see fairly decent recognition results with just 50 neurons. By using 500 neurons, we get slightly better results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import colors \n",
    "\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_loss(history, ax=None, maxy=None, file=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(1,1, figsize=(3.5,3))\n",
    "    ax.set_ylabel(\"Loss\")\n",
    "    ax.set_xlabel(\"Epochs\")\n",
    "    loss = history[:,0]\n",
    "    val_loss = history[:,1]\n",
    "    if maxy:\n",
    "        ax.set_ylim(0,maxy)\n",
    "    else:\n",
    "        ax.set_ylim(0,torch.max(val_loss))\n",
    "    ax.spines['top'].set_visible(False)    # turns off the top \"spine\" completely\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_linewidth(.5)\n",
    "    ax.spines['bottom'].set_linewidth(.5)\n",
    "    ax.plot(loss, label='train_loss')\n",
    "    ax.plot(val_loss, label='val_loss')\n",
    "    ax.legend(loc='upper right')\n",
    "    plt.tight_layout()\n",
    "    if file:\n",
    "        plt.savefig(f\"/Users/{os.environ['USER']}/Desktop/{file}.pdf\")\n",
    "        \n",
    "def plot_accur(history, ax=None, file=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(1,1, figsize=(3.5,3))\n",
    "    ax.set_ylabel(\"Accuracy\")\n",
    "    ax.set_xlabel(\"Epochs\")\n",
    "    accur = history[:,2]\n",
    "    val_accur = history[:,3]\n",
    "    ax.set_ylim(0,1.05)\n",
    "    ax.plot(accur, label='accur')\n",
    "    ax.plot(val_accur, label='val_accur')\n",
    "    ax.spines['top'].set_visible(False)    # turns off the top \"spine\" completely\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_linewidth(.5)\n",
    "    ax.spines['bottom'].set_linewidth(.5)\n",
    "    ax.legend(loc='lower right')\n",
    "    plt.tight_layout()\n",
    "    if file:\n",
    "        plt.savefig(f\"/Users/{os.environ['USER']}/Desktop/{file}.pdf\")\n",
    "        \n",
    "def imgrid(images, digits, dim=(5,5), figsize=(4, 4)):\n",
    "    fig, axes = plt.subplots(*dim, figsize=figsize)\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        img_as_row = images[i]\n",
    "        img28x28 = img_as_row.reshape(28,28)\n",
    "        ax.axis('off') # don't show x, y axes\n",
    "        ax.imshow(img28x28, cmap='Greys')\n",
    "        ax.text(0, 8, digits[i], color='#313695', fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data\n",
    "\n",
    "Let's use a subset of the well-known MNIST handwritten digits data set. This problem is the \"hello world\" of image recognition for deep learning.  The images have 28x28 pixels for a total of 784 features if we flatten them into feature vectors. Each row in the data set will represent an image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_mnist = pd.read_csv(\"https://mlbook.explained.ai/data/mnist-10k-sample.csv.zip\")\n",
    "X = df_mnist.drop('digit', axis=1).values # get just pixels\n",
    "y = df_mnist['digit'].values              # get just digit value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 784)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape # There are 784 pixels per 28x28 image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# shuffle so that images for the digits are not grouped together\n",
    "n = len(X)\n",
    "idx = np.random.randint(0,n,n)\n",
    "X = X[idx,:]\n",
    "y = y[idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the handy function from above, let's display a sample of the images and their true known values. As you can see, there's a great deal of variety in how different people draw Hindu-Arabic numerals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 64 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 288,
       "width": 292
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "imgrid(X,digits=y,dim=(8,8),figsize=(5,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to measure the generality of our model, which is what we really care about, let's split the images 80/20 into training/validation sets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = torch.tensor(X).float()\n",
    "y = torch.tensor(y)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random forest baseline\n",
    "\n",
    "It's also a good idea to get a baseline performance so that we know whether all of this neural network stuff is worth the hassle. In other words, if a random forest, which is easy to use and train, is good enough then we don't need the complexity of a neural network. Let's train a random forest classifier with a lot of trees. (`n_jobs=-1` just tells the scikit-learn library to compute the trees in parallel across multiple core.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(n_estimators=900, n_jobs=-1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf = RandomForestClassifier(n_estimators=900, n_jobs=-1)\n",
    "rf.fit(X_train, y_train) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compute the accuracy of the model on both the training and validation sets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 0.9785)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_accuracy = rf.score(X_train, y_train)\n",
    "y_accuracy = rf.score(X_test, y_test)\n",
    "y_train_accuracy, y_accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The classifier gets 100% accuracy on the 8000 images of the training set and greater than 97% accuracy on the validation set. That's pretty good considering we didn't have to think much to get the classifier to work.\n",
    "\n",
    "To get more detail about how well the model predicts each digit, let's look at the *confusion matrix* whose $(i,j)$ elements represent the count of records (images) known to be class $i$ but predicted to be in class $j$.  In this case, the column and row headers are the digits 0..9. The sklearn function `confusion_matrix` takes the true $y$ and compares it to the predicted $\\hat{y}$ to yield a matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[205   0   1   0   0   0   0   0   0   0]\n",
      " [  0 202   1   0   0   0   0   0   0   1]\n",
      " [  0   0 191   0   0   0   1   2   2   0]\n",
      " [  1   0   0 193   1   1   0   3   2   0]\n",
      " [  0   0   2   0 180   0   1   0   0   0]\n",
      " [  0   0   0   3   1 180   1   0   0   1]\n",
      " [  0   1   0   0   1   1 189   0   0   0]\n",
      " [  0   1   3   0   0   0   0 222   0   2]\n",
      " [  0   0   1   1   0   2   0   0 185   0]\n",
      " [  0   0   0   3   2   0   0   0   0 210]]\n"
     ]
    }
   ],
   "source": [
    "y_pred = rf.predict(X_test)\n",
    "conf = confusion_matrix(y_test, y_pred)\n",
    "print(conf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correct predictions lie on the diagonal when $i=j$ because we have predicted the true value. Without labels that's a little bit harder to interpret so let's thrown into a data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def showmatrix(conf):\n",
    "    df_conf = pd.DataFrame(conf,\n",
    "                       index=[f\"$y$={i}\" for i in range(0,9+1)],\n",
    "                       columns=[\"$\\hat{y}$=\"+str(i) for i in range(0,9+1)])\n",
    "    return df_conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>$\\hat{y}$=0</th>\n",
       "      <th>$\\hat{y}$=1</th>\n",
       "      <th>$\\hat{y}$=2</th>\n",
       "      <th>$\\hat{y}$=3</th>\n",
       "      <th>$\\hat{y}$=4</th>\n",
       "      <th>$\\hat{y}$=5</th>\n",
       "      <th>$\\hat{y}$=6</th>\n",
       "      <th>$\\hat{y}$=7</th>\n",
       "      <th>$\\hat{y}$=8</th>\n",
       "      <th>$\\hat{y}$=9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$y$=0</th>\n",
       "      <td>205</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=1</th>\n",
       "      <td>0</td>\n",
       "      <td>202</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>191</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>193</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>180</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>180</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=6</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>189</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>222</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>185</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>210</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $\\hat{y}$=0  $\\hat{y}$=1  $\\hat{y}$=2  $\\hat{y}$=3  $\\hat{y}$=4  \\\n",
       "$y$=0          205            0            1            0            0   \n",
       "$y$=1            0          202            1            0            0   \n",
       "$y$=2            0            0          191            0            0   \n",
       "$y$=3            1            0            0          193            1   \n",
       "$y$=4            0            0            2            0          180   \n",
       "$y$=5            0            0            0            3            1   \n",
       "$y$=6            0            1            0            0            1   \n",
       "$y$=7            0            1            3            0            0   \n",
       "$y$=8            0            0            1            1            0   \n",
       "$y$=9            0            0            0            3            2   \n",
       "\n",
       "       $\\hat{y}$=5  $\\hat{y}$=6  $\\hat{y}$=7  $\\hat{y}$=8  $\\hat{y}$=9  \n",
       "$y$=0            0            0            0            0            0  \n",
       "$y$=1            0            0            0            0            1  \n",
       "$y$=2            0            1            2            2            0  \n",
       "$y$=3            1            0            3            2            0  \n",
       "$y$=4            0            1            0            0            0  \n",
       "$y$=5          180            1            0            0            1  \n",
       "$y$=6            1          189            0            0            0  \n",
       "$y$=7            0            0          222            0            2  \n",
       "$y$=8            2            0            0          185            0  \n",
       "$y$=9            0            0            0            0          210  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "showmatrix(conf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, now let's see how well a neural network does."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vanilla one hidden layer of 50 neurons, softmax on end\n",
    "\n",
    "Our model has two differences from a binary classification problem. First, we have $k$ neurons in our final layer so that we get $k$ predictions.  Second, we use a softmax rather than a sigmoid, which gives us a likelihood for each target class:\n",
    "\n",
    "<img src=\"images/kclass.png\" width=\"200\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = nn.Sequential(\n",
    "    nn.Linear(784, 50), # 50 neurons\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(50, 10),  # 10 output classes (0-9)\n",
    "    nn.Softmax(dim=1)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the training loop, we just have to change\n",
    "\n",
    "```python\n",
    "loss = F.binary_cross_entropy(y_pred, y)\n",
    "```\n",
    "\n",
    "to\n",
    "\n",
    "```python\n",
    "loss = F.cross_entropy(y_pred, y)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ctrain0(model, X, y, learning_rate = .0001, nepochs=2000):\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)\n",
    "    for epoch in range(nepochs+1):\n",
    "        y_pred = model(X) # dimensions of y_pred are len(X_test) x 10 classes\n",
    "        # Assume model yields softmax probabilities\n",
    "        loss = F.cross_entropy(y_pred, y)\n",
    "        if epoch % (nepochs//10) == 0:\n",
    "            print(f\"Epoch {epoch:5d} cross entropy loss {loss:7.4f}\")\n",
    "\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward() # autograd computes w1.grad, b1.grad, ...\n",
    "        optimizer.step()\n",
    "    print(f\"LAST        cross entropy loss {loss:7.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch     0 cross entropy loss  2.3038\n",
      "Epoch   100 cross entropy loss  1.5642\n",
      "Epoch   200 cross entropy loss  1.5602\n",
      "Epoch   300 cross entropy loss  1.5576\n",
      "Epoch   400 cross entropy loss  1.5565\n",
      "Epoch   500 cross entropy loss  1.5563\n",
      "Epoch   600 cross entropy loss  1.5561\n",
      "Epoch   700 cross entropy loss  1.5646\n",
      "Epoch   800 cross entropy loss  1.5556\n",
      "Epoch   900 cross entropy loss  1.4857\n",
      "Epoch  1000 cross entropy loss  1.4766\n",
      "LAST        cross entropy loss  1.4766\n"
     ]
    }
   ],
   "source": [
    "ctrain0(model, X_train, y_train, learning_rate = .03, nepochs=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to use the model, we can simply pass in a set of feature vectors to get the predictions. Recall that the output of the model is a $k$-vector for each input image, with a probability associated with each possible target class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.02931814e-22, 4.70371223e-36, 6.62555072e-31, 1.98926859e-30,\n",
       "       7.84529218e-30, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00,\n",
       "       2.03743262e-27, 1.02558326e-14], dtype=float32)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba = model(X_train)\n",
    "y_proba[0,:].detach().numpy()  # print probabilities for first image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([8000, 10])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the classification from the probability, we choose the index of the largest probability across the columns, which gives us an index for each input image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([8000])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(7)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = torch.argmax(y_proba, axis=1)\n",
    "print(y_pred.shape)\n",
    "y_pred[0] # what is the predicted digit for the first image?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to compute the overall accuracy for a set of input images, we compare the predicted digit (target class) to the known true values with `y_pred==y_train`. Summing those Boolean values up gives us the number of correct predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy 0.984\n"
     ]
    }
   ],
   "source": [
    "ncorrect = torch.sum(y_pred==y_train)\n",
    "train_accur = ncorrect.float() / len(y_train)\n",
    "print(f\"Training accuracy {train_accur:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAINING CONFUSION MATRIX 98.4%\n"
     ]
    },
    {
     "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>$\\hat{y}$=0</th>\n",
       "      <th>$\\hat{y}$=1</th>\n",
       "      <th>$\\hat{y}$=2</th>\n",
       "      <th>$\\hat{y}$=3</th>\n",
       "      <th>$\\hat{y}$=4</th>\n",
       "      <th>$\\hat{y}$=5</th>\n",
       "      <th>$\\hat{y}$=6</th>\n",
       "      <th>$\\hat{y}$=7</th>\n",
       "      <th>$\\hat{y}$=8</th>\n",
       "      <th>$\\hat{y}$=9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$y$=0</th>\n",
       "      <td>822</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=1</th>\n",
       "      <td>0</td>\n",
       "      <td>786</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>788</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>836</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>741</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=5</th>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>11</td>\n",
       "      <td>4</td>\n",
       "      <td>634</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>763</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>883</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=8</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>825</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=9</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>798</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $\\hat{y}$=0  $\\hat{y}$=1  $\\hat{y}$=2  $\\hat{y}$=3  $\\hat{y}$=4  \\\n",
       "$y$=0          822            0            0            0            0   \n",
       "$y$=1            0          786            2            5            0   \n",
       "$y$=2            0            0          788            0            5   \n",
       "$y$=3            0            0            0          836            0   \n",
       "$y$=4            0            0            0            0          741   \n",
       "$y$=5           11            2            5           11            4   \n",
       "$y$=6            0            0            5            0            0   \n",
       "$y$=7            0            1            1            1            0   \n",
       "$y$=8            0            1            4            0            0   \n",
       "$y$=9            6            1            0            0            2   \n",
       "\n",
       "       $\\hat{y}$=5  $\\hat{y}$=6  $\\hat{y}$=7  $\\hat{y}$=8  $\\hat{y}$=9  \n",
       "$y$=0            0            0            0            0            0  \n",
       "$y$=1            0            0            0            0            0  \n",
       "$y$=2            0            5            3            1            0  \n",
       "$y$=3            1            0            0           10            1  \n",
       "$y$=4            0            0            0            1            4  \n",
       "$y$=5          634           16            0            5            2  \n",
       "$y$=6            0          763            0            0            0  \n",
       "$y$=7            0            0          883            0            0  \n",
       "$y$=8            1            0            0          825            2  \n",
       "$y$=9            0            0            4            1          798  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f\"TRAINING CONFUSION MATRIX {train_accur*100:.1f}%\")\n",
    "conf = confusion_matrix(y_train, y_pred)\n",
    "showmatrix(conf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation accuracy 0.965\n"
     ]
    }
   ],
   "source": [
    "y_test_proba = model(X_test)\n",
    "y_test_pred = torch.argmax(y_test_proba, axis=1)\n",
    "ncorrect = torch.sum(y_test_pred==y_test)\n",
    "test_accur = ncorrect.float() / len(y_test)\n",
    "print(f\"Validation accuracy {test_accur:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VALIDATION CONFUSION MATRIX 96.6%\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>$\\hat{y}$=0</th>\n",
       "      <th>$\\hat{y}$=1</th>\n",
       "      <th>$\\hat{y}$=2</th>\n",
       "      <th>$\\hat{y}$=3</th>\n",
       "      <th>$\\hat{y}$=4</th>\n",
       "      <th>$\\hat{y}$=5</th>\n",
       "      <th>$\\hat{y}$=6</th>\n",
       "      <th>$\\hat{y}$=7</th>\n",
       "      <th>$\\hat{y}$=8</th>\n",
       "      <th>$\\hat{y}$=9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$y$=0</th>\n",
       "      <td>206</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=1</th>\n",
       "      <td>0</td>\n",
       "      <td>203</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>185</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>194</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>177</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=5</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>168</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=6</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>181</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>221</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>184</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=9</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>212</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $\\hat{y}$=0  $\\hat{y}$=1  $\\hat{y}$=2  $\\hat{y}$=3  $\\hat{y}$=4  \\\n",
       "$y$=0          206            0            0            0            0   \n",
       "$y$=1            0          203            0            0            0   \n",
       "$y$=2            0            0          185            3            2   \n",
       "$y$=3            0            0            0          194            0   \n",
       "$y$=4            1            0            0            0          177   \n",
       "$y$=5            0            2            2            4            2   \n",
       "$y$=6            1            1            3            0            1   \n",
       "$y$=7            0            1            0            0            1   \n",
       "$y$=8            0            0            3            0            1   \n",
       "$y$=9            0            1            0            1            0   \n",
       "\n",
       "       $\\hat{y}$=5  $\\hat{y}$=6  $\\hat{y}$=7  $\\hat{y}$=8  $\\hat{y}$=9  \n",
       "$y$=0            0            0            0            0            0  \n",
       "$y$=1            0            0            1            0            0  \n",
       "$y$=2            0            1            2            1            2  \n",
       "$y$=3            1            0            2            4            0  \n",
       "$y$=4            0            2            0            2            1  \n",
       "$y$=5          168            4            0            2            2  \n",
       "$y$=6            0          181            0            5            0  \n",
       "$y$=7            0            0          221            2            3  \n",
       "$y$=8            1            0            0          184            0  \n",
       "$y$=9            0            0            0            1          212  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f\"VALIDATION CONFUSION MATRIX {test_accur*100:.1f}%\")\n",
    "conf = confusion_matrix(y_test, y_test_pred)\n",
    "showmatrix(conf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dang. That's not quite as good as our baseline so let's keep going."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Track validation versus training loss\n",
    "\n",
    "As we did before in a previous notebook, it often helps if we track the validation error has training proceeds so we can see how it diverges from the training error. Here's an improved training method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ctrain1(model, X_train, y_train, X_test, y_test, \n",
    "            learning_rate = .0001, nepochs=2000):\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)\n",
    "    history = []\n",
    "    for epoch in range(nepochs+1):\n",
    "        y_pred = model(X_train)\n",
    "        # Assume model yields softmax probabilities\n",
    "        loss = F.cross_entropy(y_pred, y_train)\n",
    "        y_pred = torch.argmax(y_pred, axis=1)\n",
    "        ncorrect = torch.sum(y_pred==y_train)\n",
    "        accur = ncorrect.float() / len(y_train)\n",
    "\n",
    "        y_test_pred = model(X_test)\n",
    "        loss_test = F.cross_entropy(y_test_pred, y_test)\n",
    "        y_test_pred = torch.argmax(y_test_pred, axis=1)\n",
    "        ncorrect = torch.sum(y_test_pred==y_test)\n",
    "        loss_accur = ncorrect.float() / len(y_test)\n",
    "        \n",
    "        history.append((loss, loss_test, accur, loss_accur))\n",
    "        if epoch % (nepochs//10) == 0:\n",
    "            print(f\"Epoch {epoch:4d} cross entropy loss {loss:7.4f}   test loss {loss_test:7.4f}\")\n",
    "\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward() # autograd computes w1.grad, b1.grad, ...\n",
    "        optimizer.step()\n",
    "    print(f\"LAST       cross entropy loss {loss:7.4f}\")\n",
    "    return torch.tensor(history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make sure to create a new model otherwise it starts from where it left off\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(784, 50),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(50, 10),  # 10 output classes (0-9)\n",
    "    nn.Softmax(dim=1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0 cross entropy loss  2.3026   test loss  2.3024\n",
      "Epoch  100 cross entropy loss  1.4853   test loss  1.5002\n",
      "Epoch  200 cross entropy loss  1.4788   test loss  1.4968\n",
      "Epoch  300 cross entropy loss  1.4775   test loss  1.4950\n",
      "Epoch  400 cross entropy loss  1.4766   test loss  1.4943\n",
      "Epoch  500 cross entropy loss  1.4763   test loss  1.4944\n",
      "Epoch  600 cross entropy loss  1.4758   test loss  1.4942\n",
      "Epoch  700 cross entropy loss  1.4750   test loss  1.4939\n",
      "Epoch  800 cross entropy loss  1.4747   test loss  1.4942\n",
      "Epoch  900 cross entropy loss  1.4747   test loss  1.4940\n",
      "Epoch 1000 cross entropy loss  1.4747   test loss  1.4939\n",
      "LAST       cross entropy loss  1.4747\n"
     ]
    }
   ],
   "source": [
    "history = ctrain1(model, X_train, y_train, X_test, y_test,\n",
    "                  learning_rate = .03, nepochs=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy 0.986\n"
     ]
    }
   ],
   "source": [
    "y_proba = model(X_train)\n",
    "y_pred = torch.argmax(y_proba, axis=1)\n",
    "ncorrect = torch.sum(y_pred==y_train)\n",
    "train_accur = ncorrect.float() / len(y_train)\n",
    "print(f\"Training accuracy {train_accur:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation accuracy 0.967\n"
     ]
    }
   ],
   "source": [
    "y_test_proba = model(X_test)\n",
    "y_test_pred = torch.argmax(y_test_proba, axis=1)\n",
    "ncorrect = torch.sum(y_test_pred==y_test)\n",
    "test_accur = ncorrect.float() / len(y_test)\n",
    "print(f\"Validation accuracy {test_accur:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a complete history, we can plot the error trajectories:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 244
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss(history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 244
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_accur(history)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The good news is that the error curves do not seem to diverge and so our model does not seem to be overfit. On the other hand, our neural network does not perform above the random forest baseline so let's crank up the number of neurons and see what happens."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using more neurons improves accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = nn.Sequential(\n",
    "    nn.Linear(784, 300),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(300, 10),  # 10 output classes (0-9)\n",
    "    nn.Softmax(dim=1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0 cross entropy loss  2.3027   test loss  2.3028\n",
      "Epoch  100 cross entropy loss  1.8546   test loss  1.8608\n",
      "Epoch  200 cross entropy loss  1.6884   test loss  1.6915\n",
      "Epoch  300 cross entropy loss  1.6711   test loss  1.6783\n",
      "Epoch  400 cross entropy loss  1.5685   test loss  1.5825\n",
      "Epoch  500 cross entropy loss  1.4713   test loss  1.4838\n",
      "Epoch  600 cross entropy loss  1.4705   test loss  1.4833\n",
      "Epoch  700 cross entropy loss  1.4704   test loss  1.4834\n",
      "Epoch  800 cross entropy loss  1.4700   test loss  1.4852\n",
      "Epoch  900 cross entropy loss  1.4700   test loss  1.4850\n",
      "Epoch 1000 cross entropy loss  1.4700   test loss  1.4849\n",
      "LAST       cross entropy loss  1.4700\n"
     ]
    }
   ],
   "source": [
    "history = ctrain1(model, X_train, y_train, X_test, y_test,\n",
    "                  learning_rate = 0.02, nepochs=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy 0.991\n"
     ]
    }
   ],
   "source": [
    "y_proba = model(X_train)\n",
    "y_pred = torch.argmax(y_proba, axis=1)\n",
    "ncorrect = torch.sum(y_pred==y_train)\n",
    "train_accur = ncorrect.float() / len(y_train)\n",
    "print(f\"Training accuracy {train_accur:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation accuracy 0.976\n"
     ]
    }
   ],
   "source": [
    "y_test_proba = model(X_test)\n",
    "y_test_pred = torch.argmax(y_test_proba, axis=1)\n",
    "ncorrect = torch.sum(y_test_pred==y_test)\n",
    "test_accur = ncorrect.float() / len(y_test)\n",
    "print(f\"Validation accuracy {test_accur:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VALIDATION CONFUSION MATRIX 97.6%\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\hat{y}$=0</th>\n",
       "      <th>$\\hat{y}$=1</th>\n",
       "      <th>$\\hat{y}$=2</th>\n",
       "      <th>$\\hat{y}$=3</th>\n",
       "      <th>$\\hat{y}$=4</th>\n",
       "      <th>$\\hat{y}$=5</th>\n",
       "      <th>$\\hat{y}$=6</th>\n",
       "      <th>$\\hat{y}$=7</th>\n",
       "      <th>$\\hat{y}$=8</th>\n",
       "      <th>$\\hat{y}$=9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$y$=0</th>\n",
       "      <td>203</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <th>$y$=1</th>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>$y$=2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>190</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>$y$=3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>194</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>$y$=4</th>\n",
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       "      <td>180</td>\n",
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       "    <tr>\n",
       "      <th>$y$=5</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>177</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=6</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>189</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>220</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>186</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$y$=9</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>212</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $\\hat{y}$=0  $\\hat{y}$=1  $\\hat{y}$=2  $\\hat{y}$=3  $\\hat{y}$=4  \\\n",
       "$y$=0          203            0            1            0            0   \n",
       "$y$=1            0          201            1            0            0   \n",
       "$y$=2            0            0          190            2            1   \n",
       "$y$=3            0            0            0          194            0   \n",
       "$y$=4            0            0            1            0          180   \n",
       "$y$=5            0            0            0            2            1   \n",
       "$y$=6            0            1            0            0            1   \n",
       "$y$=7            0            1            3            1            1   \n",
       "$y$=8            0            0            1            0            0   \n",
       "$y$=9            1            0            0            0            0   \n",
       "\n",
       "       $\\hat{y}$=5  $\\hat{y}$=6  $\\hat{y}$=7  $\\hat{y}$=8  $\\hat{y}$=9  \n",
       "$y$=0            0            0            1            0            1  \n",
       "$y$=1            0            0            0            1            1  \n",
       "$y$=2            0            0            1            0            2  \n",
       "$y$=3            1            0            2            3            1  \n",
       "$y$=4            0            1            0            0            1  \n",
       "$y$=5          177            2            0            1            3  \n",
       "$y$=6            0          189            0            1            0  \n",
       "$y$=7            0            0          220            0            2  \n",
       "$y$=8            2            0            0          186            0  \n",
       "$y$=9            0            0            1            1          212  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf = confusion_matrix(y_test, y_test_pred.detach().numpy())\n",
    "print(f\"VALIDATION CONFUSION MATRIX {test_accur*100:.1f}%\")\n",
    "showmatrix(conf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 244
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loss(history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 244
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_accur(history)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Heh, great! We got a tiny bit more accuracy with more neurons (can vary run-to-run, though). When you are this close to 100% accurate, any improvement is very challenging so this is good.\n",
    "\n",
    "In the end, vanilla networks are not the most powerful architecture to process images. For that we need [convolutional networks](https://en.wikipedia.org/wiki/Convolutional_neural_network) or CNNs."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}