ee046211_tutorial_02_single_neuron_recap.ipynb

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    "# <img src=\"./assets/course-icon.png\" style=\"height:50px;display:inline\"> ECE 046211- Technion - Deep Learning\n",
    "---\n",
    "\n",
    "#### <a href=\"https://taldatech.github.io\">Tal Daniel</a>\n",
    "\n",
    "## Tutorial 02 - Single Neuron\n",
    "---"
   ]
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    "### <img src=\"https://img.icons8.com/bubbles/50/000000/checklist.png\" style=\"height:50px;display:inline\"> Agenda\n",
    "---\n",
    "\n",
    "* [Discriminative Models](#-Discriminative-Models)\n",
    "* [The Perceptron](#-The-Perceptron)\n",
    "* [Logistic Regression](#-Logistic-Regression)\n",
    "    * [Logistic Regression with PyTorch](#-Logistic-Regression-with-PyTorch)\n",
    "* [Multi-Class (Multinomial) Logistic Regression - Softmax Regression](#-Multi-Class-(Multinomial)-Logistic-Regression---Softmax-Regression)\n",
    "* [Activation Functions](#-Activation-Functions)\n",
    "* [Recommended Videos](#-Recommended-Videos)\n",
    "* [Credits](#-Credits)"
   ]
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    "#### <img src=\"./assets/colab_icon.PNG\" style=\"height:30px;display:inline\"> Additional Packages for Google Colab\n",
    "----\n",
    "If you are using <a href=\"https://colab.research.google.com/\">Google Colab</a>, you have to install additional packages. To do this, simply run the following cell."
   ]
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     "text": [
      "Collecting torchviz\n",
      "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/8f/8e/a9630c7786b846d08b47714dd363a051f5e37b4ea0e534460d8cdfc1644b/torchviz-0.0.1.tar.gz (41kB)\n",
      "\r",
      "\u001b[K     |████████                        | 10kB 15.6MB/s eta 0:00:01\r",
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      "\u001b[K     |████████████████████████████████| 51kB 3.7MB/s \n",
      "\u001b[?25hRequirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from torchviz) (1.7.0+cu101)\n",
      "Requirement already satisfied: graphviz in /usr/local/lib/python3.6/dist-packages (from torchviz) (0.10.1)\n",
      "Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from torch->torchviz) (0.16.0)\n",
      "Requirement already satisfied: dataclasses in /usr/local/lib/python3.6/dist-packages (from torch->torchviz) (0.8)\n",
      "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.6/dist-packages (from torch->torchviz) (3.7.4.3)\n",
      "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from torch->torchviz) (1.19.5)\n",
      "Building wheels for collected packages: torchviz\n",
      "  Building wheel for torchviz (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
      "  Created wheel for torchviz: filename=torchviz-0.0.1-cp36-none-any.whl size=3522 sha256=6a736ad7c5fb8745a0b4912099f190f303604fe6b847bd2e0ab2e6141c6b5828\n",
      "  Stored in directory: /root/.cache/pip/wheels/2a/c2/c5/b8b4d0f7992c735f6db5bfa3c5f354cf36502037ca2b585667\n",
      "Successfully built torchviz\n",
      "Installing collected packages: torchviz\n",
      "Successfully installed torchviz-0.0.1\n"
     ]
    }
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   "source": [
    "# to work locally (win/linux/mac), first install 'graphviz': https://graphviz.org/download/ and restart your machine\n",
    "!pip install torchviz"
   ]
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   "source": [
    "# imports for the tutorial\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torchviz\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import Perceptron, LogisticRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "%matplotlib inline"
   ]
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    "## <img src=\"https://img.icons8.com/nolan/64/000000/categorize.png\" style=\"height:50px;display:inline\"> Discriminative Models\n",
    "---\n",
    "* **Discriminative models** are a class of models used in statistical classification, especially in supervised machine learning. A discriminative classifier tries to build a model just by depending on the observed data while learning how to do the classification from the given statistics.  \n",
    "    * Compared to **generative models**, discriminative models make fewer assumptions on the distributions but depend heavily on the quality of the data.\n",
    "    * For example, given a set of labeled pictures of dog and rabbit, discriminative models will be matching a new, unlabeled picture to a most similar labeled picture and then give out the label class, a dog or a rabbit.\n",
    "* The typical discriminative learning approaches include Logistic Regression (LR), Support Vector Machine (SVM), conditional random fields (CRFs) (specified over an undirected graph), and others."
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    "### <img src=\"https://img.icons8.com/plasticine/100/000000/mind-map.png\" style=\"height:50px;display:inline\"> The Perceptron\n",
    "---\n",
    "* One of the first and simplest linear model.\n",
    "* Based on a *linear threshold unit* (LTU): the input and output are numbers (not binary values), and each connection is associated with a weight.\n",
    "* The LTU computes a weighted sum of its inputs: $z = w_1x_1 + w_2x_2 +....+w_nx_n = w^Tx$, and then it applies a **step function** to that sum and outputs the result: $$ h_w(x) = step(z) = step(w^Tx) $$\n"
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    "* Illustration:\n",
    "<center><img src=\"./assets/perceptron.jpg\" style=\"height:200px\"></center>\n",
    "* The most common step function used is the *Heaviside step function* but sometimes the *sign function* is used (as is the illustration)."
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    "* **Perceptron Training** draws inspiration from biological neurons: the connection weight between two neurons is increased whenever they have **the same output**. Perceptrons are trained by considering the error made.\n",
    "    * At each iteration, the Perceptron is fed with one training instance and makes a prediction for it.\n",
    "    * For every output that produced a wrong prediction, it reinforces the connection weights from the inputs that would have contributed to the correct prediction.\n",
    "    * Criterion: $ E^{perc}(w) = - \\sum_{i \\in D_{miss}}w^T(x^iy^i) $\n",
    "* **Perceptron Learning Rule (weight update)**: $$ w_{t+1} = w_t +\\eta(y_i -sign(w_t^Tx_i))x_i $$\n",
    "    * $\\eta$ is the learing rate (hyper-parameter).\n",
    "* The decision boundary learned is linear, the Perceptron is incapable of learning complex patterns."
   ]
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    "* **Perceptron Convergence Theorem**: If the training instances are **linearly seperable**, the algorithm would converge to a solution.\n",
    "    * **There can be multiple solutions (multiple hyperplanes)**.\n",
    "* Perceptrons do not output a class probability, they just make predicitons based on a **hard threshold**."
   ]
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    "* **Pseudocode**:\n",
    "    * **Require**: Learning rate $\\eta$\n",
    "    * **Require**: Initial parameter $w$\n",
    "    * **While** stopping criterion not met **do**\n",
    "        * For $i=1,...,m$:\n",
    "            * $ w_{t+1} \\leftarrow w_t +\\eta(y_i -sign(w_t^Tx_i))x_i $\n",
    "        * $t \\leftarrow t + 1$\n",
    "    * **end while**"
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       "            id diagnosis  radius_mean  texture_mean  perimeter_mean  \\\n",
       "351     899667         M       15.750         19.22          107.10   \n",
       "27      852781         M       18.610         20.25          122.10   \n",
       "568      92751         B        7.760         24.54           47.92   \n",
       "535     919555         M       20.550         20.86          137.80   \n",
       "497     914580         B       12.470         17.31           80.45   \n",
       "358    9010333         B        8.878         15.49           56.74   \n",
       "75     8610404         M       16.070         19.65          104.10   \n",
       "464  911320502         B       13.170         18.22           84.28   \n",
       "323     895100         M       20.340         21.51          135.90   \n",
       "485     913063         B       12.450         16.41           82.85   \n",
       "\n",
       "     area_mean  smoothness_mean  compactness_mean  concavity_mean  \\\n",
       "351      758.6          0.12430           0.23640         0.29140   \n",
       "27      1094.0          0.09440           0.10660         0.14900   \n",
       "568      181.0          0.05263           0.04362         0.00000   \n",
       "535     1308.0          0.10460           0.17390         0.20850   \n",
       "497      480.1          0.08928           0.07630         0.03609   \n",
       "358      241.0          0.08293           0.07698         0.04721   \n",
       "75       817.7          0.09168           0.08424         0.09769   \n",
       "464      537.3          0.07466           0.05994         0.04859   \n",
       "323     1264.0          0.11700           0.18750         0.25650   \n",
       "485      476.7          0.09514           0.15110         0.15440   \n",
       "\n",
       "     concave points_mean  ...  texture_worst  perimeter_worst  area_worst  \\\n",
       "351              0.12420  ...          24.17           119.40       915.3   \n",
       "27               0.07731  ...          27.26           139.90      1403.0   \n",
       "568              0.00000  ...          30.37            59.16       268.6   \n",
       "535              0.13220  ...          25.48           160.20      1809.0   \n",
       "497              0.02369  ...          24.34            92.82       607.3   \n",
       "358              0.02381  ...          17.70            65.27       302.0   \n",
       "75               0.06638  ...          24.56           128.80      1223.0   \n",
       "464              0.02870  ...          23.89            95.10       687.6   \n",
       "323              0.15040  ...          31.86           171.10      1938.0   \n",
       "485              0.04846  ...          21.03            97.82       580.6   \n",
       "\n",
       "     smoothness_worst  compactness_worst  concavity_worst  \\\n",
       "351           0.15500            0.50460          0.68720   \n",
       "27            0.13380            0.21170          0.34460   \n",
       "568           0.08996            0.06444          0.00000   \n",
       "535           0.12680            0.31350          0.44330   \n",
       "497           0.12760            0.25060          0.20280   \n",
       "358           0.10150            0.12480          0.09441   \n",
       "75            0.15000            0.20450          0.28290   \n",
       "464           0.12820            0.19650          0.18760   \n",
       "323           0.15920            0.44920          0.53440   \n",
       "485           0.11750            0.40610          0.48960   \n",
       "\n",
       "     concave points_worst  symmetry_worst  fractal_dimension_worst  \\\n",
       "351               0.21350          0.4245                  0.10500   \n",
       "27                0.14900          0.2341                  0.07421   \n",
       "568               0.00000          0.2871                  0.07039   \n",
       "535               0.21480          0.3077                  0.07569   \n",
       "497               0.10530          0.3035                  0.07661   \n",
       "358               0.04762          0.2434                  0.07431   \n",
       "75                0.15200          0.2650                  0.06387   \n",
       "464               0.10450          0.2235                  0.06925   \n",
       "323               0.26850          0.5558                  0.10240   \n",
       "485               0.13420          0.3231                  0.10340   \n",
       "\n",
       "     Unnamed: 32  \n",
       "351          NaN  \n",
       "27           NaN  \n",
       "568          NaN  \n",
       "535          NaN  \n",
       "497          NaN  \n",
       "358          NaN  \n",
       "75           NaN  \n",
       "464          NaN  \n",
       "323          NaN  \n",
       "485          NaN  \n",
       "\n",
       "[10 rows x 33 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's load the cancer dataset, shuffle it and  speratre into train and test set\n",
    "dataset = pd.read_csv('./datasets/cancer_dataset.csv')\n",
    "# print the number of rows in the data set\n",
    "number_of_rows = len(dataset)\n",
    "num_train = int(0.8 * number_of_rows)\n",
    "# reminder, the data looks like this\n",
    "dataset.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lZLemcOrTD1h",
    "outputId": "e4a6d0ee-7691-42f4-c526-c9a2c0b2c0c7",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total training samples: 455, total test samples: 114\n"
     ]
    }
   ],
   "source": [
    "# we will take the first 2 features as our data (X) and the diagnosis as labels (y)\n",
    "x = dataset[['radius_mean', 'texture_mean']].values\n",
    "y = dataset['diagnosis'].values == 'M'  # 1 for Malignat, 0 for Benign\n",
    "# shuffle\n",
    "rand_gen = np.random.RandomState(0)\n",
    "shuffled_indices = rand_gen.permutation(np.arange(len(x)))\n",
    "\n",
    "x_train = x[shuffled_indices[:num_train]]\n",
    "y_train = y[shuffled_indices[:num_train]]\n",
    "x_test = x[shuffled_indices[num_train:]]\n",
    "y_test = y[shuffled_indices[num_train:]]\n",
    "\n",
    "print(\"total training samples: {}, total test samples: {}\".format(num_train, number_of_rows - num_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit scaler on training data (not on test data!)\n",
    "scaler = StandardScaler().fit(x_train)\n",
    "\n",
    "# transform training data\n",
    "x_train = scaler.transform(x_train)\n",
    "\n",
    "# transform testing data\n",
    "x_test = scaler.transform(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "FJ63i3NgTD1h",
    "outputId": "e73c7e1c-0e26-40b6-eed4-acde82a254a0",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perceptron accuracy: 85.088 %\n"
     ]
    }
   ],
   "source": [
    "# perceptron using Scikit-Learn\n",
    "per_clf = Perceptron(max_iter=1000)\n",
    "per_clf.fit(x_train, y_train)\n",
    "y_pred = per_clf.predict(x_test)\n",
    "accuracy = np.sum(y_pred == y_test) / len(y_test)\n",
    "print(\"perceptron accuracy: {:.3f} %\".format(accuracy * 100))\n",
    "w = (per_clf.coef_).reshape(-1,)\n",
    "b = (per_clf.intercept_).reshape(-1,)\n",
    "boundary = (-b -w[0] * x_train[:, 0]) / w[1] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "oKqXmJlLTD1h",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_perceptron_result():\n",
    "    fig = plt.figure(figsize=(10, 8))\n",
    "    ax = fig.add_subplot(1,1,1)\n",
    "    ax.scatter(x_train[y_train,0], x_train[y_train, 1], color='r', label=\"M, train\", alpha=0.5)\n",
    "    ax.scatter(x_train[~y_train,0], x_train[~y_train, 1], color='b', label=\"B, train\", alpha=0.5)\n",
    "    ax.scatter(x_test[y_test,0], x_test[y_test, 1], color='r', label=\"M, test\", alpha=1)\n",
    "    ax.scatter(x_test[~y_test,0], x_test[~y_test, 1], color='b', label=\"B, test\", alpha=1)\n",
    "    ax.plot(x_train[:,0], boundary, label=\"decision boundary\", color='g')\n",
    "    ax.legend()\n",
    "    ax.grid()\n",
    "    ax.set_ylim([-5, 5])\n",
    "    ax.set_xlabel(\"radius_mean\")\n",
    "    ax.set_ylabel(\"texture_mean\")\n",
    "    ax.set_title(\"texture_mean vs. radius_mean\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "Axek1oI8TD1i",
    "outputId": "5d5f8c0e-f59c-4f63-8c70-4a65c01ff89c",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plot_perceptron_result()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ho1haAExTD1i",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/dusk/64/000000/cheap-2.png\" style=\"height:50px;display:inline\"> MLE with Bernoulli Assumption\n",
    "---\n",
    "* Recall that there is a connection between maximum likelihood estimation (MLE) and linear regression when we assume that the data can be created as follows: $y=\\theta^Tx + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(0, \\sigma^2) \\to y \\sim \\mathcal{N}(\\theta^Tx, \\sigma^2)$.\n",
    "    * In this case, **minimizing** the negative log-likelihood (NLL): $-\\log P(y|x;\\theta)$ results in the MSE error $(y-\\theta^Tx)^2$, and **minimizing** the NLL is the same as **maximizing** $\\log P(y|x;\\theta)$, which is exactly the MLE!\n",
    "* When we assume that the data is created in a different way, we get different loss functions, as we will now demonstrate. But the idea is the same --\n",
    "\n",
    "  **maximizing the log-likelihood (MLE) = minimizing the negative log-likelihood (NLL)**.\n",
    "  $$ \\log P(y|x;\\theta) = \\log \\left[\\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp{\\left(-\\frac{(y - \\theta^Tx)^2}{2\\sigma^2}\\right)} \\right] $$\n",
    "  $$ = -0.5\\log(2\\pi\\sigma^2) -\\frac{1}{2\\sigma^2}(y -\\theta^Tx)^2$$\n",
    "  $$ \\to \\max_{\\theta}\\log P(y|x;\\theta) = \\min_{\\theta}-\\log P(y|x;\\theta) = \\min_{\\theta}\\frac{1}{2}(y -\\theta^Tx)^2 = \\min_{\\theta} MSE $$\n",
    "* The *Sigmoid* function (also the Logistic Function): $$ \\sigma(x) = \\frac{1}{1+e^{-x}} = \\frac{e^x}{1+e^x} $$\n",
    "    * The output is in $[0,1]$, which is exactly what we need to model a probability distribution.\n",
    "* We assume that: $$ P(y|x,\\theta) = Bern(y|\\sigma(\\theta^Tx)) $$\n",
    "    * Bernoulli Distribution (coin flip): $$ P(y) = p^y(1-p)^{1-y} $$\n",
    "    * $p = \\sigma(\\theta^Tx) \\in [0,1]$\n",
    "* We will use the following notations:\n",
    "\n",
    "$$P(y_i|x_i, w) = \\begin{cases}\n",
    "    \\pi_{i1} = \\sigma(w^Tx) =  \\frac{1}{1+e^{-x}}     & \\quad \\text{if } y_i=1 \\\\\n",
    "    \\pi_{i0} = 1 -  \\sigma(w^Tx) = 1 -  \\frac{1}{1+e^{-x}}    & \\quad \\text{if } y_i = 0  \n",
    "  \\end{cases} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "rB2JSPbiTD1j",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# let's see the sigmoid function\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "x = np.linspace(-5, 5, 1000)\n",
    "sig_x = sigmoid(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "FyelZ9cOTD1j",
    "outputId": "f0f5af02-45ef-4947-b708-ae01d73de8d3",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'sigmoid(x)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(x, sig_x)\n",
    "ax.grid()\n",
    "ax.set_title(\"The Sigmoid Function\")\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_ylabel(\"sigmoid(x)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6JWfaOsRTD1j",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/combo-chart.png\" style=\"height:50px;display:inline\"> Logistic Regression\n",
    "---\n",
    "* Some regression algorithms can be used for **classification** as well.\n",
    "* *Logistic Regression* is commonly used to **estimate the probability** that an instance belongs to a particular class.\n",
    "    * Typically, if the estimated proabibility is greater than 50%, then the model predicts that the instance belongs to that class (called the positive class, labeled \"1\"), or else it predicts that it does not - a binary classifier.\n",
    "* **Estimating Probabilities** - Similarly to *Linear Regression*, a Logistic Regression model computes a weighted sum of the input features (plus a bias term), but unlike Linear Regression, it outputs the **logistic** of the weighted sum - $\\sigma(w^Tx)$, which is a number between 0 and 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MqcWxurYTD1j",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Training and Cost Function\n",
    "---\n",
    "* The objective of training is to set the parameter vector $\\theta$ (or $w$) so that the model estimates high probabilities for positive instances ($y=1$) and low probabilities for negative instances ($y=0$)\n",
    "* Expanding the expression using the negative log-likelihood (NLL): \n",
    "    $$ P(y|x,\\theta) = Bern(y|\\sigma(\\theta^Tx)) \\rightarrow NLL(\\theta) = -\\frac{1}{m}\\sum_{i=1}^m \\log \\sigma(\\theta^Tx_i)^{y_i}(1-\\sigma(\\theta^Tx_i))^{1-y_i} =- \\frac{1}{m} \\sum_{i=1}^m\\log\\pi_{i1}^{y_i}\\pi_{i0}^{1-y_i} $$\n",
    "    $$ =  -\\frac{1}{m} \\sum_{i=1}^m \\left[y_i\\log\\pi_{i1} + (1-y_i)\\log\\pi_{i0} \\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o1UPe7nfTD1k",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* This yields **the Logistic Regression cost function (log loss)**: $$ J(\\theta) = -\\frac{1}{m} \\sum_{i=1}^m \\big[ y_i\\log \\pi_{i1} + (1-y_i)\\log \\pi_{i0} \\big] = -\\frac{1}{m} \\sum_{i=1}^m \\big[ y_i\\log \\pi_{i1} + (1-y_i)\\log (1 - \\pi_{i1}) \\big] $$\n",
    "    * Intuition: $-\\log(t)$ grows very large when $t$ approaches 0, so the cost will be large if the model estimates a probability close to 0 for a **positive instance**, and it will also be very large if the estimated probability is close to 1 for a **negative instance**. On the other hand, $-log(t)$ is close to 0 when $t$ is close to 1, so the cost will be close to 0 if the estimated probability is close to 0 for a **negative instance** or close to 1 for a **positive instance**.\n",
    "    * This expression is also called the **binary cross-entropy (BCE)** loss.\n",
    "    * The cost function in the case of *Logistic Regression* is **convex**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jrukBjrYTD1k",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Logistic cost function derivatives**: $$ \\frac{\\partial}{\\partial \\theta_j}J(\\theta) = \\frac{1}{m}\\sum_{i=1}^m \\big( \\sigma(\\theta^Tx^{i}) - y_i \\big) x_j^{i} $$\n",
    "    * No closed-form solution.\n",
    "    * Thanks to the convexity of the cost function (for the case of Logistic Regression), we can use **Gradient Descent** (or SGD, Mini-Batch GD)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "eZHB4a4yTD1k",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_lr_boundary(x_train, x_test, y_train, y_test, boundary):\n",
    "    fig = plt.figure(figsize=(8, 5))\n",
    "    ax = fig.add_subplot(1,1,1)\n",
    "    ax.scatter(x_train[y_train,0], x_train[y_train, 1], color='r', label=\"M, train\", alpha=0.5)\n",
    "    ax.scatter(x_train[~y_train,0], x_train[~y_train, 1], color='b', label=\"B, train\", alpha=0.5)\n",
    "    ax.scatter(x_test[y_test,0], x_test[y_test, 1], color='r', label=\"M, test\", alpha=1)\n",
    "    ax.scatter(x_test[~y_test,0], x_test[~y_test, 1], color='b', label=\"B, test\", alpha=1)\n",
    "    ax.plot(x_train[:,0], boundary, label=\"decision boundary\", color='g')\n",
    "    ax.legend()\n",
    "    ax.grid()\n",
    "    ax.set_ylim([-5, 5])\n",
    "    ax.set_xlabel(\"radius_mean\")\n",
    "    ax.set_ylabel(\"texture_mean\")\n",
    "    ax.set_title(\"texture_mean vs. radius_mean\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "182fuqu7TD1l",
    "outputId": "a8a004fc-d0f2-466a-b6c3-ad8ec3a49f18",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Regression accuracy: 90.351 %\n"
     ]
    }
   ],
   "source": [
    "# logistic regression with scikit-learn\n",
    "log_reg = LogisticRegression(solver='lbfgs')\n",
    "log_reg.fit(x_train, y_train)\n",
    "y_pred = log_reg.predict(x_test)\n",
    "accuracy = np.sum(y_pred == y_test) / len(y_test)\n",
    "print(\"Logistic Regression accuracy: {:.3f} %\".format(accuracy * 100))\n",
    "w = (log_reg.coef_).reshape(-1,)\n",
    "b = (log_reg.intercept_).reshape(-1,)\n",
    "boundary = (-b -w[0] * x_train[:, 0]) / w[1] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "fqScvG9TTD1l",
    "outputId": "35add6eb-c3b4-4f06-f148-eb18d7732f26",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plot_lr_boundary(x_train, x_test, y_train, y_test, boundary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "u-HhhoBxTD1l",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/color/96/000000/firestorm.png\" style=\"height:50px;display:inline\"> Logistic Regression with PyTorch\n",
    "---\n",
    "* We will now get familiar with building neural networks with PyTorch.\n",
    "* All neural network models inherit from a parent class `nn.Module`. The user must implement the `__init__()` and `__forward()__` methods.\n",
    "* In `__init__()` we initialize the parameters of the neural networks, e.g., number of parameters (such as number of hidden units/layers, type of layers and etc...)\n",
    "* In `__forward()__` we implement the forward pass of the network, i.e., what happens to the input.\n",
    "    * For example, if in `__init__()` you defined a linear layer and a ReLU activation, then in `__forward()__` you will define that the input goes first into the linear layer and then into the activation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "Cfuod-TtTD1l",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# define our simple single neuron network\n",
    "class SingleNeuron(nn.Module):\n",
    "    # notice that we inherit from nn.Module\n",
    "    def __init__(self, input_dim):\n",
    "        super(SingleNeuron, self).__init__()\n",
    "        # here we initialize the building blocks of our network\n",
    "        # single neuron is just one linear (fully-connected) layer\n",
    "        self.fc = nn.Linear(input_dim, 1) \n",
    "        # non-linearity: the sigmoid function for binary classification\n",
    "        self.sigmoid = nn.Sigmoid()\n",
    "\n",
    "    def forward(self, x):\n",
    "        # here we define what happens to the input x in the forward pass\n",
    "        # that is, the order in which x goes through the building blocks\n",
    "        # in our case, x first goes through the signle neuron and then activated with sigmoid\n",
    "        return self.sigmoid(self.fc(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2TG7ywsPTD1n",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Okay, so we have our network, now we need to train it.\n",
    "* We need to define how to optimize the weights and other hyper-parameters, such as number of epochs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "-OS_6OIsTD1n",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# define the device we are going to run calculations on (cpu or gpu)\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "# create an instance of our model and send it to the device\n",
    "input_dim = x_train.shape[1]\n",
    "model = SingleNeuron(input_dim=input_dim).to(device)\n",
    "# define optimizer, and give it the networks weights\n",
    "learning_rate = 0.1\n",
    "# every class that inherits from nn.Module() has the .parameters() method to access the weights\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)\n",
    "# other hyper-parameters\n",
    "num_epochs = 5000\n",
    "# define loss function - BCE for binary classification\n",
    "criterion = nn.BCELoss()\n",
    "# preprocess the data\n",
    "scaler = StandardScaler()\n",
    "x_train_prep = scaler.fit_transform(x_train)\n",
    "x_test_prep = scaler.transform(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Kl2wqmFRTD1n",
    "outputId": "8f6adf9a-a2c0-4167-9886-1c801a1a9d45",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0 loss: 0.6858659386634827\n",
      "epoch: 1000 loss: 0.26053810119628906\n",
      "epoch: 2000 loss: 0.25988084077835083\n",
      "epoch: 3000 loss: 0.25985535979270935\n",
      "epoch: 4000 loss: 0.25985416769981384\n"
     ]
    }
   ],
   "source": [
    "# training loop for the model\n",
    "for epoch in range(num_epochs):\n",
    "    # get data\n",
    "    features = torch.tensor(x_train_prep, dtype=torch.float, device=device)\n",
    "    labels = torch.tensor(y_train, dtype=torch.float, device=device)\n",
    "    # forward pass\n",
    "    logits = model(features)\n",
    "    # loss\n",
    "    loss = criterion(logits.view(-1), labels)\n",
    "    # backward pass\n",
    "    optimizer.zero_grad()  # clean the gradients from previous iteration\n",
    "    loss.backward()  # autograd backward to calculate gradients\n",
    "    optimizer.step()  # apply update to the weights\n",
    "    if epoch % 1000 == 0:\n",
    "        print(f'epoch: {epoch} loss: {loss}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "D0e0JTKUTD1n",
    "outputId": "8f9d18df-933a-41c2-ca9c-0cc66879fa26",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic Regression accuracy: 90.351 %\n"
     ]
    }
   ],
   "source": [
    "# predict and check accuracy\n",
    "test_features = torch.from_numpy(x_test_prep).float().to(device)\n",
    "y_pred_logits = model(test_features).data.cpu().view(-1).numpy()\n",
    "y_pred = (y_pred_logits > 0.5)\n",
    "accuracy = np.sum(y_pred == y_test) / len(y_test)\n",
    "print(\"Logistic Regression accuracy: {:.3f} %\".format(accuracy * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QtWfWb3QTD1o",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Same as Scikit-Learn!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 322
    },
    "id": "PuI11UkBTS_x",
    "outputId": "3c842acb-dac1-4075-82a8-cb3ceee51809",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
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   "source": [
    "# visualize computational graph\n",
    "x = torch.randn(1, input_dim).to(device)\n",
    "torchviz.make_dot(model(x), params=dict(model.named_parameters()))"
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  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cmZUQFrxTD1o",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/cotton/64/000000/network.png\" style=\"height:50px;display:inline\"> Multi-Class (Multinomial) Logistic Regression - Softmax Regression\n",
    "---\n",
    "* The Logistic Regression model can be generalized to support multiple classes.\n",
    "* The idea: when given an instance $x$, the Softmax Regression model first computes a score $s_k(x)$ for each class $k$, then estimates a probability of each class by applying the *softmax function* (normalized exponential) to the scores.\n",
    "* The **Softmax score for class $k$**: $$ s_k(x) = \\big( \\theta^{(k)} \\big)^T \\cdot x $$ \n",
    "    * Each class has its own dedicated parameter vector $\\theta^{(k)}$, which is usually stored in a row of the parameter matrix $\\Theta$."
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   "cell_type": "markdown",
   "metadata": {
    "id": "5Q4BBYwCTD1o",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **The Softmax Function**: $$\\hat{p}_k = p(y=k|x,\\theta) = \\sigma(s(x))_k = \\frac{e^{s_k(x)}}{\\sum_{j=1}^K e^{s_j(x)}} $$\n",
    "    * $K$ is the number of classes.\n",
    "    * $s(x)$ is a *vector* containing the scores of each class for the instance $x$.\n",
    "    * $\\sigma(s(x))_k$ is the estimated probability that the instance $x$ belongs to class $k$ given the scores of each class for that instance.\n",
    "* **The Softmax Regression classifier prediction**: $$\\hat{y} = \\underset{k}{\\mathrm{argmax}} \\sigma(s(x))_k = \\underset{k}{\\mathrm{argmax}} s_k(x) = \\underset{k}{\\mathrm{argmax}} \\big( (\\theta^{(k)})^Tx \\big) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OGBIchXMTD1o",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Cross-Entropy cost function**: $$ J(\\Theta) = -\\frac{1}{m} \\sum_{i=1}^m \\sum_{k=1}^K y_k^{(i)} \\log(\\hat{p}_k^{(i)}) $$\n",
    "    * $y_k^{(i)}$ is equal to 1 if the target class for the $i^{th}$ instance is $k$, otherwise, it is 0.\n",
    "    * When $K=2$ it is the BCE from the previous section.\n",
    "* **Cross-Entropy gradient vector for class $k$**: $$ \\nabla_{\\theta^{(k)}}J(\\Theta) = \\frac{1}{m}\\sum_{i=1}^m (\\hat{p}_k^{(i)} - y_k^{(i)})x^{(i)} $$\n",
    "    * Use Gradient Descent or its variants to solve\n",
    "* In Scikit-Learn: <a href=\"https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html\">`LogisticRegression(multi_class=\"multinomial\", solver=\"lbfgs\", C=10)`</a>\n",
    "    * $C$ is a regularization term: the inverse of regularization strength, smaller values specify stronger regularization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yM_pQ-16TD1o",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/nolan/64/nui2.png\" style=\"height:50px;display:inline\"> Activation Functions\n",
    "---\n",
    "\n",
    "The key change made to the Perceptron that brought upon the era of deep learning is the addition of **activation functions** to the output of each neuron. These allow the learning of **non-linear functions**. We will use three popular activation functions:\n",
    "1. **Logistic function (sigmoid)**: $\\sigma(z) = \\frac{1}{1 + e^{-z}}$. The output is in $[0,1]$ which can be used for binary clssification or as a probability.\n",
    "2. **Hyperbolic tangent function**: $tanh(z) = 2\\sigma(2z) - 1$. The output is in $[-1,1]$ which tends to make each layer's output more or less normalized at the beginning of the training (which may speed up convergence).\n",
    "3. **ReLU (Rectified Linear Unit) function**: $ReLU(z) = max(0,z)$. Continuous but not differentiable at $z=0$. However, it is the most common activation function as it is fast to compute and does not bound the output (which helps with some issues during Gradient Descent)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gZes_GHxTD1o",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**The activation functions derivatives (for the backpropagation)**:\n",
    "1. $\\frac{d\\sigma(z)}{dz} = \\sigma(z)(1-\\sigma(z))$\n",
    "2. $\\frac{d tanh(z)}{dz} = 1 - tanh^2(z)$\n",
    "3. We define the derivative at 0 to be zero: $\\frac{d ReLU(z)}{dz} = 1$ if $x>0$ else $0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "0aWjDI-STD1p",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# activation functions\n",
    "def sigmoid(z, deriv=False):\n",
    "    output = 1 / (1 + np.exp(-1.0 * z))\n",
    "    if deriv:\n",
    "        return output * (1 - output)\n",
    "    return output\n",
    "\n",
    "def tanh(z, deriv=False):\n",
    "    output = np.tanh(z)\n",
    "    if deriv:\n",
    "        return 1 - np.square(output)\n",
    "    return output\n",
    "\n",
    "def relu(z, deriv=False):\n",
    "    output = z if z > 0 else 0\n",
    "    if deriv:\n",
    "        return 1 if z > 0 else 0\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "wSAflgsZTD1p",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_activations():\n",
    "    x = np.linspace(-5, 5, 1000)\n",
    "    y_sig = sigmoid(x)\n",
    "    y_tanh = tanh(x)\n",
    "    y_relu = list(map(lambda z: relu(z), x))\n",
    "    fig = plt.figure(figsize=(8, 5))\n",
    "    ax1 = fig.add_subplot(2,1,1)\n",
    "    ax1.plot(x, y_sig, label='sigmoid')\n",
    "    ax1.plot(x, y_tanh, label='tanh')\n",
    "    ax1.plot(x, y_relu, label='relu')\n",
    "    ax1.grid()\n",
    "    ax1.legend()\n",
    "    ax1.set_xlabel('x')\n",
    "    ax1.set_ylabel('y')\n",
    "    ax1.set_ylim([-2, 2])\n",
    "    ax1.set_title('Activation Functions')\n",
    "\n",
    "    y_sig_derv = sigmoid(x, deriv=True)\n",
    "    y_tanh_derv = tanh(x, deriv=True)\n",
    "    y_relu_derv = list(map(lambda z: relu(z, deriv=True), x))\n",
    "    ax2 = fig.add_subplot(2,1,2)\n",
    "    ax2.plot(x, y_sig_derv, label='sigmoid')\n",
    "    ax2.plot(x, y_tanh_derv, label='tanh')\n",
    "    ax2.plot(x, y_relu_derv, label='relu')\n",
    "    ax2.grid()\n",
    "    ax2.legend()\n",
    "    ax2.set_xlabel('x')\n",
    "    ax2.set_ylabel('y')\n",
    "    # ax2.set_ylim([-2, 2])\n",
    "    ax2.set_title('Activation Functions Derivatives')\n",
    "    plt.tight_layout()"
   ]
  },
  {
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   "execution_count": null,
   "metadata": {
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    "slideshow": {
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plot_activations()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J68kd8QcTD1q",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/bubbles/50/000000/video-playlist.png\" style=\"height:50px;display:inline\"> Recommended Videos\n",
    "---\n",
    "#### <img src=\"https://img.icons8.com/cute-clipart/64/000000/warning-shield.png\" style=\"height:30px;display:inline\"> Warning!\n",
    "* These videos do not replace the lectures and tutorials.\n",
    "* Please use these to get a better understanding of the material, and not as an alternative to the written material.\n",
    "\n",
    "#### Video By Subject\n",
    "\n",
    "* Pereceptron - <a href=\"https://www.youtube.com/watch?v=4Gac5I64LM4\">Pereceptron</a>\n",
    "    * <a href=\"https://www.youtube.com/watch?v=5g0TPrxKK6o\">Perceptron Training</a>\n",
    "* Logistic Regression - <a href=\"https://www.youtube.com/watch?v=HZ4cvaztQEs\">Lecture 3 | Machine Learning (Stanford)</a>\n",
    "    * <a href=\"https://www.youtube.com/watch?v=yIYKR4sgzI8\">StatQuest: Logistic Regression</a>\n",
    "* Softmax Regression - <a href=\"https://www.youtube.com/watch?v=LLux1SW--oM\">Softmax Regression (C2W3L08)</a>\n",
    "* Activation Functions - <a href=\"https://www.youtube.com/watch?v=Xvg00QnyaIY\">Activation Functions (C1W3L06)</a>\n",
    "    * <a href=\"https://www.youtube.com/watch?v=NkOv_k7r6no\">Why Non-linear Activation Functions (C1W3L07)</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ASKEitEBTD1q",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/prize.png\" style=\"height:50px;display:inline\"> Credits\n",
    "---\n",
    "* Icons made by <a href=\"https://www.flaticon.com/authors/becris\" title=\"Becris\">Becris</a> from <a href=\"https://www.flaticon.com/\" title=\"Flaticon\">www.flaticon.com</a>\n",
    "* Icons from <a href=\"https://icons8.com/\">Icons8.com</a> - https://icons8.com\n",
    "* Datasets from <a href=\"https://www.kaggle.com/\">Kaggle</a> - https://www.kaggle.com/\n",
    "* Examples and code snippets were taken from <a href=\"http://shop.oreilly.com/product/0636920052289.do\">\"Hands-On Machine Learning with Scikit-Learn and TensorFlow\"</a>"
   ]
  }
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