Lectures/Lecture22/3dasm_Lecture22.ipynb

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    "<img src=../figures/Brown_logo.svg width=50%>\n",
    "\n",
    "## Data-Driven Design & Analyses of Structures & Materials (3dasm)\n",
    "\n",
    "## Lecture 22\n",
    "\n",
    "### Miguel A. Bessa | <a href = \"mailto: miguel_bessa@brown.edu\">miguel_bessa@brown.edu</a>  | Associate Professor"
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    "**What:** A lecture of the \"3dasm\" course\n",
    "\n",
    "**Where:** This notebook comes from this [repository](https://github.com/bessagroup/3dasm_course)\n",
    "\n",
    "**Reference for entire course:** Murphy, Kevin P. *Probabilistic machine learning: an introduction*. MIT press, 2022. Available online [here](https://probml.github.io/pml-book/book1.html)\n",
    "\n",
    "**How:** We try to follow Murphy's book closely, but the sequence of Chapters and Sections is different. The intention is to use notebooks as an introduction to the topic and Murphy's book as a resource.\n",
    "* If working offline: Go through this notebook and read the book.\n",
    "* If attending class in person: listen to me (!) but also go through the notebook in your laptop at the same time. Read the book.\n",
    "* If attending lectures remotely: listen to me (!) via Zoom and (ideally) use two screens where you have the notebook open in 1 screen and you see the lectures on the other. Read the book."
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    "**Optional reference (the \"bible\" by the \"bishop\"... pun intended 😆) :** Bishop, Christopher M. *Pattern recognition and machine learning*. Springer Verlag, 2006.\n",
    "\n",
    "**References/resources to create this notebook:**\n",
    "* This simple tutorial is still based on a script I created for this article: https://imechanica.org/node/23957\n",
    "* It follows from some examples provided by the scikit-learn user guide, which seem to have originated from Mathieu Blondel, Jake Vanderplas, Vincent Dubourg, and Jan Hendrik Metzen.\n",
    "* Creating a new StandardScaler for Gaussian Processes: https://stats.stackexchange.com/questions/364418/how-to-get-the-prediction-std-using-gaussian-process-in-scikit-learn\n",
    "* The flower to explain the Iris dataset comes from this [source](https://www.ritchieng.com/machine-learning-iris-dataset/)\n",
    "\n",
    "Apologies in advance if I missed some reference used in this notebook. Please contact me if that is the case, and I will gladly include it here."
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    "## **OPTION 1**. Run this notebook **locally in your computer**:\n",
    "1. Confirm that you have the '3dasm' mamba (or conda) environment (see Lecture 1).\n",
    "2. Go to the 3dasm_course folder in your computer and pull the last updates of the [repository](https://github.com/bessagroup/3dasm_course):\n",
    "```\n",
    "git pull\n",
    "```\n",
    "    - Note: if you can't pull the repo due to conflicts (and you can't handle these conflicts), use this command (with **caution**!) and your repo becomes the same as the one online:\n",
    "```\n",
    "git reset --hard origin/main\n",
    "```\n",
    "3. Open command window and load jupyter notebook (it will open in your internet browser):\n",
    "```\n",
    "jupyter notebook\n",
    "```\n",
    "5. Open notebook of this Lecture and choose the '3dasm' kernel."
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    "## **OPTION 2**. Use **Google's Colab** (no installation required, but times out if idle):\n",
    "\n",
    "1. go to https://colab.research.google.com\n",
    "2. login\n",
    "3. File > Open notebook\n",
    "4. click on Github (no need to login or authorize anything)\n",
    "5. paste the git link: https://github.com/bessagroup/3dasm_course\n",
    "6. click search and then click on the notebook for this Lecture."
   ]
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    "# Basic plotting tools needed in Python.\n",
    "\n",
    "import matplotlib.pyplot as plt # import plotting tools to create figures\n",
    "import numpy as np # import numpy to handle a lot of things!\n",
    "from IPython.display import display, Math # to print with Latex math\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\" # render higher resolution images in the notebook\n",
    "plt.rcParams[\"figure.figsize\"] = (8,4) # rescale figure size appropriately for slides"
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    "## Outline for today\n",
    "\n",
    "* Introduction to Supervised Learning for Classification\n",
    "\n",
    "**Reading material**: This notebook + (Sections 1.2.1 + 2.4.2 + 10.1 + 10.2)"
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    "# Logistic regression\n",
    "\n",
    "Last lecture we showed what is classification and how we can make predictions using available packages.\n",
    "\n",
    "* Today we will derive the simplest classification model: Binary Logistic Regression"
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    "It's also very common to convert our target (output) data from strings to integers!\n",
    "\n",
    "In this case we have three discrete target values ('Iris-setosa', 'Iris-versicolor' and 'Iris-virginica') so we can convert to 0, 1 and 2 (respectively):"
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   "source": [
    "import pandas as pd\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures # For Polynomial basis functions\n",
    "from sklearn.pipeline import make_pipeline # to link different objects\n",
    "from matplotlib import cm # to change colors of surface plots\n",
    "\n",
    "# Simple plot of Logistic Regression predictions using only two features\n",
    "def train_and_predict_LogReg_countour(X, y, feature1, feature2, target_names):\n",
    "    # X: features\n",
    "    # y: labels\n",
    "    # feature1: string of the first feature\n",
    "    # feature2: string of the second feature\n",
    "    \n",
    "    n_classes = np.size(target_names)\n",
    "    # WARNING: we did not scale our data because this dataset is really simple, but NEVER do that!!!\n",
    "    C = 1e5  # Logistic Regression regularization parameter.\n",
    "             # It is actually the inverse of regularization strength; must be a positive float.\n",
    "             # Like in support vector machines, smaller values specify stronger regularization.\n",
    "\n",
    "    degree = 1 # Degree of polynomial is usually considered to be 1 (so usually, you don't even make a pipeline).\n",
    "               #    Note: in this dataset, if you consider degree > 2, the 'l-bfgs' optimizer with default\n",
    "               #          parameters does not converge but you can use 'newton-cholesky' in those cases.\n",
    "\n",
    "    LogReg_model = make_pipeline(PolynomialFeatures(degree), LogisticRegression(C=C, solver='lbfgs')) # model\n",
    "\n",
    "    LogReg_model.fit(X, y) # HERE WE ARE USING ONLY 2 FEATURES TO FIT THE MODEL!\n",
    "                           # This is just to assess the predictive power of the SVC even though\n",
    "                           #  it is only using 2 features for training.\n",
    "                           # REMEMBER: WE USUALLY USE ALL FEATURES WHEN TRAINING A MODEL.\n",
    "    if n_classes == 3:\n",
    "        plot_colors = 'ryb' # defining colors for each category\n",
    "    elif n_classes == 2:\n",
    "        plot_colors = 'rb' # defining colors for each category\n",
    "    #\n",
    "    plot_step = 5e-3 # defining the meshgrid step size\n",
    "\n",
    "    # Create grid for plot:\n",
    "    x1_iris_data, x2_iris_data = X[:, 0], X[:, 1]\n",
    "\n",
    "    x1_iris_data_min, x1_iris_data_max = x1_iris_data.min() - 1, x1_iris_data.max() + 1 # define min & max of feature 0\n",
    "    x2_iris_data_min, x2_iris_data_max = x2_iris_data.min() - 1, x2_iris_data.max() + 1 # define min & max of feature 1\n",
    "    X1_iris_data_grid, X2_iris_data_grid = np.meshgrid(np.arange(x1_iris_data_min, x1_iris_data_max, plot_step),\n",
    "                                                       np.arange(x2_iris_data_min, x2_iris_data_max, plot_step))\n",
    "    # Predict for grid points:\n",
    "    y_iris_data_LogReg_pred = LogReg_model.predict(np.c_[X1_iris_data_grid.ravel(), X2_iris_data_grid.ravel()])\n",
    "    Y_iris_data_LogReg_grid = y_iris_data_LogReg_pred.reshape(X1_iris_data_grid.shape)\n",
    "\n",
    "    fig1, ax1 = plt.subplots(tight_layout=True)\n",
    "    plt.subplots_adjust(wspace=0.4, hspace=0.4)\n",
    "\n",
    "    ax1.contourf(X1_iris_data_grid, X2_iris_data_grid, Y_iris_data_LogReg_grid, cmap=cm.RdYlBu, alpha=0.8)\n",
    "\n",
    "    # Plot the training points\n",
    "    for i, color in zip(range(n_classes), plot_colors):\n",
    "        idx = np.where(y_iris_data == i)\n",
    "        ax1.scatter(X[idx, 0], X[idx, 1], c=color,\n",
    "                    label=target_names[i], edgecolor='black', s=15)\n",
    "\n",
    "    ax1.set_xlim(X1_iris_data_grid.min(), X1_iris_data_grid.max())\n",
    "    ax1.set_ylim(X2_iris_data_grid.min(), X2_iris_data_grid.max())\n",
    "    ax1.set_xlabel(feature1, fontsize=20)\n",
    "    ax1.set_ylabel(feature2, fontsize=20)\n",
    "    ax1.legend(loc='lower right', borderpad=0, handletextpad=0, fontsize=15)\n",
    "    ax1.set_title('Logistic regression', fontsize=20)"
   ]
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    "Let's start by recalling the prediction we obtained with Logistic Regression for the Iris dataset"
   ]
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 789
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris_data = pd.read_csv('../data/data_iris.csv')\n",
    "feature1 = 'SepalLengthCm'\n",
    "feature2 = 'SepalWidthCm'\n",
    "X_2d_iris_data = iris_data.loc[:, [feature1,feature2] ].values # just use 2 inputs (features)\n",
    "y_string_iris_data = iris_data.loc[:, 'Species'].values\n",
    "target_names = iris_data.loc[:, 'Species'].unique()\n",
    "y_iris_data = pd.Categorical(pd.factorize(y_string_iris_data)[0])\n",
    "\n",
    "train_and_predict_LogReg_countour(X_2d_iris_data, y_iris_data, feature1, feature2, target_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The simplest classification algorithm: Logistic regression\n",
    "\n",
    "Logistic regression is a simple classification model $p(y|\\mathbf{x}, \\mathbf{z})$, where $\\mathbf{x} \\in \\mathbb{R}^D$ is a fixed-dimensional input vector, $y \\in \\{1, . . . , C\\}$ is the class label, and $\\mathbf{z}$ are the parameters (rvs).\n",
    "\n",
    "* If $C = 2$, this is known as **binary logistic regression**;\n",
    "\n",
    "* If $C > 2$, it is known as **multinomial logistic regression**, or alternatively, multiclass logistic regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Binary Logistic (or sigmoid) regression\n",
    "\n",
    "Let's start by considering **binary logistic regression**, i.e. a case where we only have two classes as output: $C = 2$.\n",
    "\n",
    "Previously when we focused on *regression* we assumed the observation distribution to be a Gaussian probability distribution function (pdf) because we had a continuous output $y$.\n",
    "\n",
    "* However, here we need to use the **Bernoulli distribution**: a **probability mass function** (pmf) because $y$ is a **discrete** rv (e.g. 0 or 1) as we are now focusing on binary classification problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The Bernoulli distribution is one of the simplest distributions that exists!\n",
    "\n",
    "The pmf of the Bernoulli distribution has only **one parameter** $\\rho$ and is simply written as:\n",
    "\n",
    "$$\n",
    "\\text{Ber}(y|\\rho) = \\begin{cases}\n",
    "      \\begin{align} 1- \\rho & \\quad \\text{if } y = 0\\\\\n",
    "      \\rho & \\quad \\text{if }  y = 1\n",
    "      \\end{align}\n",
    "    \\end{cases}\n",
    "$$\n",
    "\n",
    "Or, in a more concise form:\n",
    "\n",
    "$$\n",
    "\\text{Ber}(y|\\rho) = \\rho^y (1-\\rho)^{1-y}\n",
    "$$\n",
    "\n",
    "where $y$ can only be $0$ or $1$.\n",
    "\n",
    "Note that pmf's need to sum to 1, so $\\rho$ is the probability of the event $y$ and it needs to be within $0 \\leq \\rho \\leq 1$.\n",
    "\n",
    "* **Recall**: the integral of pdf's is 1, so the sum of pmf's is 1 (integrals become sums when the integrand is discrete) and the pmf is an actual probability (not a probability density, as in pdf's).\n",
    "\n",
    "For example, the Bernoulli pmf can be used to characterize a binary event like a coin toss where $y=1$ is when it lands heads, and $y=0$ is when it lands tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Bernoulli distribution for mean paramater $\\\\rho = $0.3')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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w29tjsjv/j7jTxYsXjQ4dOtjtT3BwsHHnnXcar732mjFt2jTjo48+Mp577jmjTp06uW5D2bJlbX5pjLz16tXL5nVs3769U3XaO1s6KirKRT32rJiYGJttGTJkiNvaY85vP/DVV1/ZlIWHh6tFixYO1WMYhoYOHarPP/8812XCwsJUo0YNlSlTRunp6Tpz5owOHz5st67hw4crISFBL774okP9uN6ff/6pe+65x+aCCyVKlFC1atVUrlw5xcfH6+TJkzp79qxDdZ86dUrdunVTbGxsjvLIyEhVr15dZcqU0ZUrV3T48GH9/fffdut46aWX1KFDB3Xo0MGhtnfv3q0uXbrowoULdp+3WCyqXr26qlSpovT0dJ08edKmn1k2b96sLl26aPXq1SpfvrxD/YB5LF26VPfff3+uF3DLughJhQoVdOnSJR07dkyXL1+2Pp+WlqZBgwZ5bU74X375RSNGjMj1+dDQUNWsWVOlS5dWaGioEhMTFR8fr+PHjyshIcFzHXWCO8cjZxw6dEh33323EhMTbfpVvXp1lS1bVhcuXNDRo0d15coVm/UNw9CTTz6pyMjIXC+ijMIz63jvzc9AMzLrfjLruJPdkSNHdMcdd+T4TJKkihUrKjo6WhERETp//rz27NmjjIwMm/WXL1+uV155RePGjZMkvfPOO3rzzTdzLBMQEKBatWqpQoUKMgxDx48ft/v6G4ahp556Sp06dXL4uhhmPRbOUrp0aVWqVEklS5ZU8eLFlZCQoLNnz+rYsWN2l4+Pj1ffvn21du1atWrVyun2/XHMyPr8vP6zsaCfn5mZmXrssccUGRmp+++/3yV98vZ+9sSY4+1t9JcxKzfefn1dxaxjstk/l5OSktSzZ09t3LgxR3mxYsX0r3/9S6+++qpKlSpls9748eP11VdfaejQoTbbduHCBX3xxRd5/q2HnLZv325T5uw1lxo3bmxTdvnyZR07dsynrgu3aNEiuxe3HDhwoPsadVusDrtcfeb3b7/9Zvdb0EcffdThusaPH2+3b4GBgcY///lPY9WqVUZKSorNerGxsca4ceOMkiVL2qwbEBBgLFu2rMB9sNf+9fPu9e7d21i2bJndn4ts377dmDZtWoHr7tixY45vg/v372+sWbPGSE9Pz7FuRkaGsXr16ly/Pa1bt26u8xPbk5SUZNx44425fvP+9ttv2503dN++fcbo0aNz/Xlbz549C9wHb5+xeb2ifub3xYsXjYoVK9rdr/Xq1TO+/fZbm59YpqenG//9739tfnpcp04du3W5c1+kpqbaneokKCjIGDZsmLFhwwab/1dZMjMzjSNHjhjff/+9MWjQIKNs2bKGlPuZ37Gxscb69eutN3vbOnfu3BzL5HbLa35ed45Hrj7z+/qx6aabbjLmz59vM2anpKQYP//8s9GmTRu79YSFhRmHDh0qUD8Mw/vjiCfeC86OD2YY7w3DXJ+BhbVr1y6b/WavP/nta3tnLpl5P7lq3HEVe31s166d9X5gYKDx5JNPGtu3b7dZ9+LFi8bbb79thIWF2dQRHBxsHD582Fi+fHmOY9vo6Gjj008/Nc6fP29T386dO+2eWSXJuPXWWx3eNjMcC2c/m7NGjRrG008/bSxYsMA4ceJErutcunTJ+Pbbb3P8n85+q1GjhsNn7PnDmFGQbbp+jG/durUxb948u5+f8+bNM1q1amW3nhIlShjHjh0rcF/MvJ9dNeaYeRv9Yczy1uvrqeNwwzDHmOwLn8vXu++++2z6XLJkyQLPNb1kyRK7U7/VqlXLyMjIcEkfk5OTC/Qe8cTt4MGDLtmm7FJSUuzmdBMmTHCq3k2bNtl9Tzrynva2w4cP2/0FWefOnd3aLuG3h7kq/E5LSzMmT55shIaG2tQVFRVlnD592qH61q9fbwQGBtrUVbt2bePPP/8sUB2nTp0ymjdvblNHdHR0gQ9S7L02WbfixYsb8+fPd2i7Clp3qVKlChRmZGRkGIMGDbJbhyNz/g0fPtxuHa1atSrQxbK2b99uNyCSZHzwwQcF6oO3Q6vrFfXwe8iQIXb358MPP1yguWM//PDDfOendee++O2332zWCQ0NLdT0SykpKcaMGTOMiRMnFmh5Z953eXHneOTq8Dv77eWXX873wDQ9Pd146aWX7K5/yy23FHg7zDaOuOO94Oz4YIbx3jDM9RnoSvb6Uhi+sJ+cHXdcJa8+VqxY0di6dWu+daxatcruMezjjz+e42fXffv2Na5evZpvfY899pjd/uzfv7/A22WWY+EvvvjCuPvuu401a9YUuO/Zffnll3anTxs/frxD9fjjmJHf5+eYMWNy/aI+S3p6uvH888/bXf/2228vcF98YT87O+b4wjb68phlltfXXcfhZhmTfeFzObuZM2fa9DMiIsLYsmWLQ/Xk9h4t6GufnyNHjuQ7JnvqltsJV844ePCg3ba++eYbp+o9efKk3Xq/+OILF/XcfTIyMoyvv/7a7oXkK1as6PYLYxN+e1hu4Xd+30atWrXKWLhwofHxxx8bjzzyiFGuXDm79YSHhzt89diMjAy78+3UrVvX+Pvvvx2qKz4+3m5dBf2GK7cBKSAgwFi6dKlDfSlo3WFhYcZff/1V4HqSk5Ptzoc1YMCAAq1/8OBBu98CNmjQwKHXe//+/Ub58uVt6omMjCzQ1efNFloV5fD7zz//tPvevO+++xz6dn3y5Ml5frC7c1+MGDHCZp1XXnmlwH13hqfDb1eMR+4Kv5999lmH+jFq1Ci79RT0QN5s44jZwm+zjPeGYZ7PQFezt02O8oX95Ipxx1Vy62NERISxb9++Atfz8ssv5zme9erVq8CfgcnJyUbNmjVt6njxxRcLtL6ZjoVdcUb03Llzbdq/4YYb8g12s/PHMSOv99vTTz/tUF1PPfWU3Xp+++23Aq1v9v3sijHH7Nvoy2OWYZjn9XXHsZeZxmRf+FzOcvbsWbtnu3/77bcO17Vjxw672+2qkNXfw+/cfp3o7HsmPT3dbr2OfmnlavZ+nbl69Wpj4cKFxqeffmo89thjRuXKle32vU6dOsbevXvd3kfCbw9z5QUirr/deuutDn2AZ/nxxx9t6goNDTUOHDhQqG3csmWLzRmo1apVK9CHaG7bNnLkyEL1pSB1f/zxxw7XZe8CIzfccEOB1h05cqTdD8/Nmzc73I/vvvvO7jYV5MJ1ZgutinL4be+b9fLlyxuXL192uK6uXbvm+l53577o16+fzTqbNm1yuP+F4enw2xXjkTvC7wYNGhhpaWkO9SMtLc1o0KCBTV0FnarBbOOI2cJvs4z3hmGez0BXs7dNjvKF/eSKccdVcuujoz/rPn/+vFGsWDG7dZUtW9bulAF5mTRpkk09HTt2LNC6ZjoWdpW+ffs6dWzjj2NGbtsUExNjd7qCvKSkpNgN9Xv37u2ezufCXfvZTGOOu7bRl8csV3L29XXHsZeZxmRf+D+Sxd5JLc580WjvS4Mnn3zSJX319/B7wYIFdtsqzLHl9cLDw23qfe6551zQ68IrzEXpS5QoYYwePdq4cuWKR/oYIPi0kJAQPfXUU9q1a5f++9//KiYmxuE6JkyYYFM2fPhw1a5du1B9at68ue68884cZceOHdOyZcsKVV9ISIjLLhR0vapVq+rRRx91eL177rlHAQE5//scP34814tkZUlKStL06dNtyocMGeLwBUol6b777rN7waAPP/zQ4brgHYmJifr6669tyseOHauSJUs6XN/kyZNd0S2HxcfH25RFRkZ6oSfu5c7xyFkTJkxQYKBj17EODAzUO++8Y1O+aNGiXC+KhILxhfHe05+BZuQL+8nM406WatWqafDgwQ6tU7ZsWbVr187uc0888YTKli3rUH29e/e2Kfvzzz9lGEa+65r9WLgw7O2P9evXO1Wnv44Z77zzjoKCghxaJzg4WOPHj7cpX7BggU6dOuWqruXLHfvZbGOOO7bR18csV3LH6+sss4/JZvs/Iknnzp3TJ598kqMsKCjI5kKsjmjYsKFNWW4XM0ZO9i6QLF27KKqzwsPDbcoSExOdrtdTwsPD9fbbbys2NlZvv/223e1xB8JvH5eSkqIPPvhA/fv312effabk5GSH1j927Jg2bNiQo8xisejJJ590ql8PPPCATdnq1asLVVfv3r1VpkwZp/qTm0GDBjkcFklSVFSUatasaVN+4MCBPNfbuHGjzVXFJWno0KEO9yHLY489ZlO2d+9eHT9+vNB1wnPWrl2rhISEHGWhoaH65z//Waj6Gjdu7JWrtEdFRdmUbdq0yeP9cDd3jkfOqFKlinr06FGodXv27KnKlSvnKMvMzNTixYtd0bUiyxfGe09/BpqRL+wns4472Q0aNEjFihVzeL3GjRvbLR8yZIjDddWsWdPmD6j4+HidOXMmz/V84Vi4MOwdC1y/nY7yxzGjQoUKNqFYQfXq1Uvly5fPUZaenq7ff//dFV0rEHfsZ7ONOe56L/vqmOVq7nh9neELY7LZ/o9I0pdffqmrV6/mKBs8eLBq1KhR6DqrV69uU5aWllbo+q6v27g2E4XXbzNmzHDJNmWX2+tUmM/Q69n7sjY1NdXpej0lMTFRY8aMUc+ePfX9998rMzPTI+0SfvuJnTt3atiwYWrUqJFD39SuWrXKpqxNmzaKjo52qj/2znpat25doerq0qWLU33Ji71+FpS9b57j4uLyXMfevqlevbratGlT6H7cfffdKl68eIHagvls3LjRpqxbt26FOus7y3333edMlwrF3pkBL730kmJjYz3eF3dy53jkjL59+9qcVVdQAQEB6tevn025vfcmCs4XxntPfwaakS/sJ7OOO9kV9r1UrVo1m7IqVaoU6o91i8Vit7783pe+cCxcGNeHspJ06NAhp+r0xzGjb9++hQpBpWshRt++fW3KPfnlvzv2s9nGHDO9l80wZrmaO15fZ/jCmGy2/yOS7P6S+MEHH3SqTovFYlOWnp7uVJ1FRUZGht3ywn7e5FeHr+0XwzC0YcMG9e/fXx06dPDImEP4bRIF+UYqMTFRp0+f1po1a/T++++rffv2NvUcPHhQnTp10ty5cwvUrr0Pl5YtWzq9PRUrVlRoaGiOsu3btxeqrsL87LigGjRoUOh17U3pkN/Bir1v0Z35A1uSihcvriZNmtiUE377Bnt/IDl75rY3zvy+4447bMqOHz+uxo0b66233tLZs2c93id3cOd45Axn97m97fLHM/c9yRfGe09/BpqRL+wns4472dWvX79Q60VERNiU1atXr9D9sFdfYcJvsx0LHzx4UB9//LEee+wxtW/fXrVq1VK5cuUUGhoqi8Vi92bv7DJ7v3JwhD+OGe445irs56dZ9rM7xxyzbKMvj1l5Mcvr6wxfGJPN9rm8Z88e/fXXXznKatasmes0PQVl74xcZ07QKkpyO8PbFSG1vTocnbrL1VasWGGTX169elWnTp3SunXr9P7776tjx4521123bp3atm2rHTt2uLWPzp9zD48JCwtTWFiYKlasqPbt2+vpp5/WqlWr9OCDD+rw4cPW5dLS0tS/f3+tXLky3wFv586dNmWBgYEu+alTeHh4jmlYLl26VKh6nP2WNy+lS5cu9Lr2zurKb9oZe3PoNmvWrNB9yF7H9fuMaU98w9GjR23K7IUmjnB2/cJo2bKlunfvbjNVxuXLl/Xiiy/q5ZdfVrt27dStWzd16NBBrVu39tj8Xq7kzvHIGe54zzDnt3N8Ybz39GegGfnCfjLruJNdYd9L1wcRztSVW335vS/NeixsGIZmzZqljz76yGVfRjobaPnjmOGOz8/sf5flx4z72dVjjhm30ZfHrOuZ8fV1hlnH5OzM9rm8dOlSm7LbbrvN6XpPnz5tU2ZvKhTYCgkJsVvuiulJ7NWRW3veVLx4cRUvXlyVKlVS27Zt9fTTT+uvv/7So48+qj/++CPHsufPn1ePHj20c+dOlSpVyi39Ifz2cR07dtSKFSvUtm1bnTx50lqenp6uwYMHa9euXQoODs51fXsXLHjvvff03nvvubyv6enpio+Pd/gieO78dtHV4Vt+Fyix9wFbqVIlp9u9fr7e3NqC+djbT/Z+fuiIqKgoBQcHe3zur+nTp6t169Y5xqIsmZmZWrNmjdasWSPp2s+1mjRpos6dO6tr167q2rWr3T+MzcasZzs4+56xt35CQoIyMjJc8vO8osgXxntPfwaakS/sJ7OOO9mFhYWZsi4p//elGY+F9+/fryFDhrj8V3zOXhDLH8eMihUrunz9+Ph4ZWZm5jsdmVn3syvHHLNuoy+PWdmZ9fV1hhnH5OuZ7XPZ3tzluZ1l6wh7X+QRfheMvV91SLK51ldh2KvD0fewtzRp0kTr1q3TgAEDNGfOnBzPnTp1Ss8884zdC9G7AtOe+IGqVavavSLywYMH9e233+a57sWLF93VLbsK8zMuVx9QeJO9P3xdMVDZ+wAm/PYN9s6scMV7whsfgJUrV9aGDRvUtm3bfJfNyMjQ1q1b9e677+rOO+9UhQoV9OCDD2rr1q0e6GnhmXU8cnZ/2xtDDMPw6pk/vo7x3jf4wn4y67jjL8x2LLxr1y517NiR6es8xNn/7/bWNwzDp/ezq8YcM2+jP/DX19dsY7I9Zvtczjq5KLuC/D2WF8MwdPDgQZvyOnXqOFVvUZHbBVGd/dsqOTlZKSkpBW7PjAIDA/XNN9+oUaNGNs999dVXOnHihHvadUut8Lj+/fvr6aef1oULF3KUT58+XYMHD851PU8HG7lN/F9UJCUl2ZS54mxXe3V48xt7FJy9D6+8fq1RUN766VN0dLTWrl2r2bNna+LEiQUOsxMSEjRjxgzNmDFD/fr108cff+z02cxFibPvmdzeL/benygYxnvfwH6CmY6FExMT1bNnz1yvk1GpUiW1b99eDRo0UNWqVVWhQgWFhoYqNDTU7nyfzoYfRYGz/99zW//q1au5/nS7KOznorCN3uTPr6+ZxmRfcPr0aZ06dSpHWWhoqG644Qan6t29e7fNl/ahoaEumX9duvY3xrZt21xSl7PKlSunWrVqubTO3H5VdObMGafqzW19Z3/F5GlBQUF655131LNnzxzl6enpmjNnjkaMGOHyNgm//URAQIA6dOign376KUf5xo0blZKSkmuwERgY6PMDvi+JjIy0+TbbXT99MdvPsWBfyZIlbX7e54r3RHx8vNN1FJbFYtGAAQM0YMAA7dq1S/Pnz9fy5cu1bt26AoU/P/74o9atW6f//ve/atiwoQd67PsSEhKcmh8tt/dLVFRUoess6hjvfQP7CWY6Fn7zzTcVGxtrU96xY0f9+9//VufOnQtclysuqlUUXLlyxan/m7mNF3nVWRT2c1HYRm/y59fXTGOyL7AXINesWVMWi8Wpeu1dePSmm25y2QlWp0+fNs2XLoMHD9aMGTNcWmflypUVEhJicyKRs9dly239GjVqOFWvN3Tr1k1lypSxyULWrFnjlvCbaU/8iL0LLyQnJ+f5H8zeT/U+/vhjmyu1uupW1OeIshdOuSKktPdzLWcuvlJYaWlpHm/T19kLF525yrt0bX7tK1euOFWHqzRs2FBjxozR4sWLdfnyZW3atEmTJk1Snz598vyp8enTp3XHHXd4NcT3Jc6+Z+ytHxwc7JWfdfrLOOLv472/YD/BLMfC6enpmjJlik35P//5Ty1btsyhMEtiOqSCcvb/u731AwMDVaJECbvLF4X9XBS20Zv8/fU1y5jsK/7880+bMldcu2TRokU2ZV26dHG63qLCYrHYPZt8//79TtV74MABu+W1a9d2ql5vKFasmJo2bWpT7uwXBLkh/PYjuU2qb++iEVmqVq3q0PJwjr0/sh25InxuDh06VKC2sgsMtP3hh7Pf/Ht6jjZ/ULZsWZuy3D7UCurAgQOmuIjU9QIDA9WqVSs988wz+umnn3ThwgUtWrRI9957r92LQh07dkyTJk3yQk99j7PvGXsHYgUJ6hhHcmem8R65Yz/BLMfCq1evtgmhypYtqylTphTqwsPXT4UI+44cOeLy9fP6v14U9nNR2EZv8vfX1yxjsq+wd+a3sxer//vvv7Vw4UKb8rvvvtupeouaZs2a2ZT99ddfTtVpb39HR0fbzRR8Qbly5WzK3PWFHOG3H8ktMMjrpykNGjSwKTt27JjL+oSc7L3erpjryl4d9trKzt6XJc6cLfz3338rOTm50OsXVU2aNLEps/cNviOcXd9TgoKC1L17d33//fdat26d3Q+/r776ygs98z3ueM/Y+yb+eowjuTPTeI/csZ9glmPhLVu22JT16dMn1zOI82P2C0ibhbOfn/aCjLymbCsK+7kobKM3+fvra5Yx2VfYG8OcPQnqq6++svklZps2bexeoBC5a9OmjU3Z7t27nfrFrr0L3Nprx1fYmxLVFdc/s4fw24/kduZfXpPf25tnafny5S7rE3Ky93qvX79eqampha7zzJkz2rt3b4Hays7eXITOXIBh7dq1hV63KLP3YbV06VKn6nR2fW9o06aNPvnkE5vyw4cP21zE5XrOzmnnD5YsWeLU+suWLbMpa926db7rmW0cMdN7wUzjPXLHfoJZjoXtXbiufv36ha5v9erVznSnyHD2dbK3fl6fn0VhPxeFbfQms72+rj72MsuY7AsSEhLs/tLs6NGjha4zKSlJ48ePtyl/9NFHC12nPdWrV3fbVDaO3lw933eWW2+91aYsIyOj0H+3nTt3zu7JFfba8RUnTpywKatQoYJb2iL89hNXrlyxGxqEh4erfPnyua53xx132JQdOnRI27dvd2n/cE27du1syi5dumT3Z0UF9fXXX9tcFMRiseT7DWCFChVsfhJ19uxZnTt3rlD9mD9/fqHWK+rsvSf27dunzZs3F6q+lJQU/fDDD852yyt69+6t0NBQm/L8wlR7v27xl3mjC2rp0qV2/xgqiNOnT9v9wsTee/N6ZhtHzPReMNN4j9yxn2CWY2F7Z4IV9kzOxMREfffdd852qUj49ddfCz3vd1xcnBYsWGBTntf/9aKwn4vCNnqT2V5fVx97mWVM9gV//fWX3bO8jxw5UuhfUk6ePFmnT5/OUVa5cmUNGDCgUPUVZfXr17c773dh/899//33NvvbYrHozjvvLFR93nb27Fm7v55y1y8lCb/9xHvvvWd3gOvRo0eecz5Vq1ZNHTt2tCn/97//7dL+4ZpGjRopJibGpvy9994rVH3Jycn6+OOPbcq7d++e75Xrixcvrnr16tmUL1682OF+nD17Vl9//bXD60GqV6+eWrZsaVNu7xv3gpgyZYouX77sZK+8IzAw0O4FQPO74ru9qTfs/YTKn2VkZGjixImFWnfSpEk2r3GlSpV0yy235Luu2cYRM70XzDTeI3fsJ5jlWNje+yO/Xz7lZurUqT57LOBpycnJ+vzzzwu17tSpU23+/ipZsqR69OiR6zpFYT8XhW30JrO9vq4+9jLLmOwLcpu2KT09vVAnlGzZssXu6/z2228rLCzM4fogDRw40KZs3rx5io2NdagewzD00Ucf2ZR37txZ0dHRhe6fN02dOlWZmZk25Y5etLegCL/9wLJly/T666/bfe6+++7Ld/1Ro0bZlM2dO1fffPON031DThaLRU8++aRN+cqVKzV79myH6xs/frzdC3M9/fTTBVrfXuhamD8Ahg4d6jfz9HrD0KFDbcrmzJnjcIB4+vRpjR071lXd8rj4+HidP3/eprxKlSp5rmfvwlLO/NzPV73//vvatWuXQ+vs2rVL//nPf2zKH374YbsXs7THTOOImd4LZhvvYR/7CZI5joUrV65sU/bbb785XM+BAwf00ksvuaJLRcZrr73m8C+Wzp07Z/fvr4EDB+YZEhWF/VwUttGbzPb6uuPYywxjsi/I6xol9oLSvJw8eVL33XefzbRvrVu3thvgomCGDh1qM4d1Wlqaw//3pk+fbndKPXvHsLk5evSoLBaLzW3IkCEO9cUV9uzZo7feesumvGTJknZ//eE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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 414,
       "width": 735
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import bernoulli\n",
    "fig2, ax2 = plt.subplots(1, 1)\n",
    "\n",
    "rho = 0.3 # mean of Bernoulli distribution\n",
    "\n",
    "y = [0, 1] # rv following a Bernoulli distribution\n",
    "\n",
    "ax2.plot(y, bernoulli.pmf(y, rho), 'bo', ms=8, label='bernoulli pmf')\n",
    "\n",
    "ax2.vlines(y, 0, bernoulli.pmf(y, rho), colors='b', lw=5, alpha=0.5)\n",
    "ax2.set_xlim([-1 ,2])\n",
    "ax2.set_ylim([0, 1])\n",
    "ax2.set_xlabel('$y$', fontsize=20)\n",
    "ax2.set_ylabel('Probability', fontsize=20)\n",
    "ax2.set_title(r'Bernoulli distribution for mean paramater $\\rho = $%1.1f' % rho, fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Understanding classification with **logistic regression** is quite simple after deriving several linear regression models!\n",
    "\n",
    "* **Note: go back to Lecture 11 and see how similar it is to today's lecture!**\n",
    "\n",
    "We will be playing only one small trick: we will use the sigmoid function, as we will see soon!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "But before we play that trick, we start by assuming the observation distribution to be the following Bernoulli pmf:\n",
    "\n",
    "$p(y|\\mathbf{x}, \\mathbf{z}) = \\text{Ber}\\left(y| \\rho = f(\\mathbf{x}, \\mathbf{z}) \\right)$\n",
    "\n",
    "where the function $f(\\mathbf{x}, \\mathbf{z})$ predicts the **mean parameter** $\\rho$ of the Bernoulli distribution.\n",
    "\n",
    "Logistic regression assumes a linear model for the mean, so we write $f(\\mathbf{x}, \\mathbf{z})=\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x})$.\n",
    "\n",
    "* Of course, later we will create nonlinear models for the mean and also use different observation distributions..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Like before, we have:\n",
    "\n",
    "* the vector $\\mathbf{w} = [w_0, w_1, w_2 ..., w_{M-1}]^T$ including the **bias** term $w_0$ and the remaining **weights** $w_m$ with $m=0,..., M-1$.\n",
    "* and the basis functions remain a vector but where each element also acts on a vector $\\mathbf{x}$, where $x_d$ has $D$ features: $\\boldsymbol{\\phi}(\\mathbf{x}) = [\\phi_0(\\mathbf{x}), \\phi_1(\\mathbf{x}), \\phi_2(\\mathbf{x}) ..., \\phi_{M-1}(\\mathbf{x})]^T$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For example, for a 2D input (2 features) $\\mathbf{x}=[x_1, x_2]^T$ the quadratic polynomial basis has $M=6$ leading to: \n",
    "\n",
    "$$\n",
    "\\rho= w_0 + w_1 x_1 + w_2 x_2 + w_3 x_1 x_2 + w_4 x_1^2 + w_5 x_2^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "So, we write the observation distribution for logistic regression as:\n",
    "\n",
    "$p(y|\\mathbf{x}, \\mathbf{z}) = \\text{Ber}(\\; y\\, |\\, \\rho = \\underbrace{\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x})}_{f(\\mathbf{x}, \\mathbf{z})} \\;)$\n",
    "\n",
    "but where we need to explicitly mention that $0 \\leq f(\\mathbf{x}, \\mathbf{z}) \\leq 1$.\n",
    "\n",
    "* For the regression when we used the Gaussian distribution we did not need to include these contraints because it was a continuous distribution!\n",
    "\n",
    "This is **not** a detail. It has profound implications!\n",
    "\n",
    "To avoid writing the Bernoulli distribution and the corresponding constraint on the mean, i.e. $ 0 \\leq f(\\mathbf{x}, \\mathbf{z}) \\leq 1$, we can still consider an **unconstrained function** $f(\\mathbf{x}, \\mathbf{z})$ for describing $\\rho$ if we use the **sigmoid (or logistic) function**:\n",
    "\n",
    "$$\n",
    "\\sigma\\left(f(\\mathbf{x}, \\mathbf{z})\\right) = \\frac{1}{1+e^{-f(\\mathbf{x}, \\mathbf{z})}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$$\n",
    "\\sigma\\left(a\\right) = \\frac{1}{1+e^{-a}}\n",
    "$$\n",
    "\n",
    "where $a = f(\\mathbf{x}, \\mathbf{z})$ is called the **logit function** or pre-activation function.\n",
    "\n",
    "The \"sigmoid\" function is very important in machine learning because:\n",
    "\n",
    "* It maps the whole real line into $[0,1]$\n",
    "\n",
    "* This is necessary for the output to be interpreted as a probability (and hence a valid value for the Bernoulli mean parameter $\\rho$).\n",
    "\n",
    "* Think about the sigmoid (or logistic) function as a **\"soft\" version of the Heaviside** (or step) function:\n",
    "\n",
    "    $H(a)=\\mathbb{1}(a>0)$, where $\\mathbb{1}$ is called the indicator function (it turns to 1 when the argument is true, and zero otherwise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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Sy8s3NG/zUb39/T4lZ+aa9rnhynp6dlArNQwLKOfoAAAAAABAVWIYjmVvAAAA5Y2iNwAAAACoxH6NS9JL/9mjXcfOm16/vF4NvTy4tbo1DS/nyAAAAAAAQFVUuOSN400BAIAVKHoDAAAAgErofHqO3vphn+ZtPiqzB6yDfb301wEtdGe3KHl5epR/gAAAAAAAoEoqnIeg5g0AAFiBojcAAAAAqEQMw9DiHcf1xrK9OpuWbdpnaPv6euH6y1W7hl85RwcAAAAAAKo6o9Bebza2egMAABag6A0AAAAAKom4c+l6fvFurdmfYHq9ee0gvTa0jXo0iyjnyAAAAAAAQHXBTm8AAKAioOgNAAAAACq43Lx8zVx3RJNXxCgjJ8/hur+3px67+jLdfVUT+XhxlCkAAAAAACg/bPQGAACsQNEbAAAAAFRge46f13OLdmv38fOm169rU0cTBrdRgxD/co4MAAAAAABURw47vVH0BgAALEDRGwAAAABUQJk5eXr/x/2auuaQ8vINh+t1a/jp9Zuu0LWt61gQHQAAAAAAwJ9sHHAKAAAsQNEbAAAAAFQw6w8k6LnFuxV7Nt3hms0mje4apacHtlSwn7cF0QEAAAAAgOrMKLzVGwAAgAUoegMAAACACiI1K1dvLNur+ZuPml5vXjtIf7/lSnVuHFbOkQEAAAAAAPzJoeSNjd4AAIAFKHoDAAAAgApg3YEEPf3lLh1PynC45u1p08P9muvBvs3k6+VpQXQAAAAAAAB/KrzRGzVvAADAChS9AQAAAICF0rJy9ffv9mnuxljT6x0bhejNW9vqsjrB5RwZAAAAAACAI6PQXm82G2VvAACg/FH0BgAAAAAW2XDwrJ7+6lfFnXPc3S3Ax1PPDmql0V2j5OFB8hgAAAAAAFQM7PQGAAAqAoreAAAAAKCcpWfn6q3v/9Cs9UdMr3dtEqa3h7VTo/CA8g0MAAAAAADgEgrVvImN3gAAgBUoegMAAACAcrTlyDk99cWvij2b7nDN3/vP3d3u7MbubgAAAAAAoHKwsdcbAACwAEVvAAAAAFAOsnPzNXlFjP79y0GHY0AkqUvjML09vK2iwgPLPzgAAAAAAIAScjjelJo3AABgAYreAAAAAKCMHTiToscX7NRvJ5Idrvl5e+jp61ppbI/G7O4GAAAAAAAqAZOn+QAAAMoZRW8AAAAAUEYMw9DcjbF6Y9leZeXmO1zvFBWqt4e1VdNaQRZEBwAAAAAA4DyHnd6sCQMAAFRzFL0BAAAAQBk4k5Kp//til1bHxDtc8/a06akBLXVPr6byZHc3AAAAAABQiTjs80ZqAwAAWICiNwAAAABwsx9+O6XnFu3WubRsh2uX1Q7S+3e0V5v6NS2IDAAAAAAAoHSMQlu92ah6AwAAFqDoDQAAAADcJC0rV68v/V0LtsSZXh/Xs7GeGdhKft6e5RwZAAAAAACAexTe6c1GzRsAALAARW8AAAAA4AZ7jp/Xo/N36HBCmsO12sG+emd4O/VuUcuCyAAAAAAAANyn0EZv7PMGAAAsQdEbAAAAAJSCYRiavf6IJn67T9l5+Q7XB7apq0m3XKnQQB8LogMAAAAAAChbNrZ6AwAAFvCwOoDqJDY2Vk8++aRatWqlwMBAhYWFKTo6Wm+//bbS09PdssaRI0f0zDPPqFOnTgoJCZG3t7fCwsLUo0cPvfbaazpz5oxb1gEAAAAgJaVn67652/TKN787FLwF+njqrWFt9dHojhS8AQAAAACAKsMotNUbNW8AAMAK7PRWTr755huNHj1aycnJBW3p6enaunWrtm7dqmnTpmnZsmVq3ry5y2vMnTtX999/vzIyMuzaExMTtWHDBm3YsEFTpkzRggULdO2117q8DgAAAABpy5Fzenz+Dp04n+lwrV1kTf1jRAdFhQdaEBkAAAAAAEDZMS7dBQAAoMyx01s52LFjh26//XYlJycrKChIb7zxhtavX6+ffvpJ9957ryQpJiZGN9xwg1JSUlxaY926dRo7dqwyMjLk4eGhcePGacmSJdq8ebO+/PJLDR48WJJ07tw5DR06VIcOHXLb1wcAAABUJ3n5hj78eb/u+GSjacHbfb2b6osHelDwBgAAAAAAqqZCVW9s9AYAAKzATm/l4PHHH1dGRoa8vLy0fPlyde/eveBa//79ddlll+npp59WTEyM3n33Xb3yyitOrzFp0iTl5/95nNIHH3yghx56qOBadHS0br31Vj355JOaPHmyMjIyNHnyZH344Yel/toAAACA6uRMcqb+snCn1h0463AtLNBH797WTv1a1rYgMgAAAAAAgPJReKc3jjcFAABWYKe3MrZ582atWbNGknT33XfbFbxd8OSTT+ryyy+XJE2ZMkU5OTlOr7N+/XpJUnh4uF3B28UmTJhQ8H7Dhg1OrwEAAABUZ2v3J2jQlDWmBW/dm4bru8d7UfAGAAAAAACqPMNwKHuzJA4AAFC9UfRWxpYsWVLwfty4caZ9PDw8dNddd0mSkpKStHLlSqfXyc7OliQ1adKkyD41a9ZURESEXX8AAAAAxcvPN/TBT/t154xNOptm///RHjbpr9e20Kf3dFWdGn4WRQgAAAAAAFB+2OkNAABUBBS9lbG1a9dKkgIDA9WpU6ci+/Xp06fg/bp165xep2XLlpKkw4cPF9knOTlZCQkJdv0BAAAAFC0pPVt3z96id1fEqPBDzPVq+mnBfd312NWXydOD7C4AAAAAAKgeCudIyIoAAAArUPRWxvbu3StJat68uby8vIrs16pVK4cxznjggQckSWfPntXHH39s2uf111936A8AAADA3K5jSbrhH2u18o94h2tXt6qtbx/rpS5NwiyIDAAAlJfY2Fg9+eSTatWqlQIDAxUWFqbo6Gi9/fbbSk9Pd8saR44c0TPPPKNOnTopJCRE3t7eCgsLU48ePfTaa6/pzJkzblkHAACgrNjY6g0AAFig6CoslFpmZmbBzmqRkZHF9g0NDVVgYKDS0tIUFxfn9Frjx4/X2rVrNWfOHD388MPatm2bhgwZonr16uno0aOaO3duwVGrL7zwgq655hqn1zh27Fix10+ePOn0nAAAAEBFYxiGPtt0VK9987uy8/LtrnnYpKeua6kHejeTB7u7AQBQpX3zzTcaPXq0kpOTC9rS09O1detWbd26VdOmTdOyZcvUvHlzl9eYO3eu7r//fmVkZNi1JyYmasOGDdqwYYOmTJmiBQsW6Nprr3V5HQAAAHcyCh1wSoYEAABYgaK3MpSSklLwPigo6JL9LxS9paamOr2Wp6enZs+ercGDB2vixImaNm2apk2bZtenX79+ev75510qeJOkhg0bujQOAAAAqCzSs3P1wuI9WrzjuMO1iCAf/WNEB/VoFmFBZAAAoDzt2LFDt99+uzIyMhQUFKTnnntO/fr1U0ZGhhYsWKCpU6cqJiZGN9xwg7Zu3arg4GCn11i3bp3Gjh2r/Px8eXh4aMyYMRo6dKjq16+vo0ePavbs2frmm2907tw5DR06VHv27FHTpk3L4KsFAABwTuHjTQEAAKzA8aZlKDMzs+C9j4/PJfv7+vpKksOTnSW1d+9ezZkzR7t37za9vmHDBk2fPl3Hjzv+BR4AAABQ3R2MT9VN/1xnWvAW3ThUyx7rRcEbAADVxOOPP66MjAx5eXlp+fLlev7559W9e3f1799fn3zyid566y1JUkxMjN59912X1pg0aZLy8//cVfaDDz7QjBkzNHToUEVHR+vWW2/V119/rb/+9a+S/swXTp482T1fHAAAQCkVrnnjdFMAAGAFit7KkJ+fX8H77OzsS/bPysqSJPn7+zu91po1a9S9e3d98803atCggebOnatTp04pOztbcXFx+uc//6mAgAAtWLBAXbp00W+//eb0GnFxccW+Nm/e7PScAAAAQEWw4vfTGvrhOsWcdtx1+d5eTTTv3m6qU8PPZCQAAKhqNm/erDVr1kiS7r77bnXv3t2hz5NPPqnLL79ckjRlyhTl5OQ4vc769eslSeHh4XrooYdM+0yYMKHg/YYNG5xeAwAAoEwUqnqzccApAACwAMeblqGLjzUoyZGlaWlpkkp2FOrFsrKyNGLECJ0/f15169bVxo0bVbdu3YLrkZGReuihh9SnTx917txZJ06c0JgxY7R161an1omMjHSqPwAAAFDR5ecb+sfP+/X+j/sdrgX7eunt4W018Ip6FkQGAACssmTJkoL348aNM+3j4eGhu+66S88995ySkpK0cuVKDRgwwKl1Ljwk26RJkyL71KxZUxEREUpISCjRQ7UAAADlwShU9cZObwAAwArs9FaG/Pz8FB4eLkk6duxYsX0TExMLit4aNmzo1Drff/99wZGljz76qF3B28XatGmj0aNHS5K2bdumX3/91al1AAAAgKokJTNH93+6zbTgrVXdYH396FUUvAEAUA2tXbtWkhQYGKhOnToV2a9Pnz4F79etW+f0Oi1btpQkHT58uMg+ycnJSkhIsOsPAABgNaPw+aYAAAAWoOitjLVu3VqSdODAAeXm5hbZb9++fQXvLxyNUFJ79+4teN+xY8di+16cqLt4TQAAAKA6ORSfqpv+uU4rfj/tcO2m9vW1+KGeahIRaEFkAADAahdybc2bN5eXV9EHZbRq1cphjDMeeOABSdLZs2f18ccfm/Z5/fXXHfo749ixY8W+Tp486fScAAAAhWve2OkNAABYgeNNy9hVV12lNWvWKC0tTdu2bVPXrl1N+61evbrgfc+ePZ1a4+LkW3GFdZKUk5NjOg4AAACoLn7ed1qPz9+plCz7/3f29LDpuUGtdPdVTWQjWwsAQLWUmZlZsLNaZGRksX1DQ0MVGBiotLQ0xcXFOb3W+PHjtXbtWs2ZM0cPP/ywtm3bpiFDhqhevXo6evSo5s6dW3DU6gsvvKBrrrnG6TWcPVECAADAFTaRRwEAAOWPnd7K2E033VTwfubMmaZ98vPzNWfOHElSSEiI+vXr59QaTZo0KXi/Zs2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      "text/plain": [
       "<Figure size 1500x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 1246
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "# Plot sigmoid function\n",
    "a = np.linspace(-4, 4, 1001) # using many points to plot the heaviside properly\n",
    "sigmoid = 1/(1+np.exp(-a))\n",
    "fig3, (ax3_1, ax3_2) = plt.subplots(1, 2) # create a plot with 2 subplots side-by-side\n",
    "ax3_1.plot(a, sigmoid)\n",
    "ax3_1.set_title(\"sigmoid function\",fontsize=20)\n",
    "ax3_1.set_xlabel(\"a\",fontsize=20)\n",
    "ax3_1.set_ylabel(r\"$\\sigma(a)$\",fontsize=20)\n",
    "# Plot Heaviside function\n",
    "heaviside = np.heaviside(a,0.5)\n",
    "ax3_2.plot(a, heaviside)\n",
    "ax3_2.set_title(\"Heaviside function\",fontsize=20)\n",
    "ax3_2.set_xlabel(\"a\",fontsize=20)\n",
    "ax3_2.set_ylabel(r\"$H(a)$\",fontsize=20)\n",
    "fig3.set_size_inches(15, 4) # scale figure to be wider (since there are 2 subplots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The great advantage of the sigmoid function compared to the Heaviside function is that it is easily differentiable, plus it has some very interesting mathematical properties:\n",
    "\n",
    "$\\begin{align}\n",
    "\\sigma(a) = \\frac{1}{1+e^{-a}}=\\frac{e^{a}}{1+e^{a}}\\\\\n",
    "\\frac{d}{d a}\\sigma(a) = \\sigma(a)\\left(1-\\sigma(a)\\right)\\\\\n",
    "1-\\sigma(a) = \\sigma(-a)\\\\\n",
    "\\sigma^{-1}(p) = \\log{\\frac{p}{1-p}}=\\text{logit}(p)\\\\\n",
    "\\sigma_+(a) = \\log{(1+e^a)} = \\text{softplus}(a)\\\\\n",
    "\\frac{d}{d a}\\sigma_+(a)=\\sigma(a)\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Binary Logistic Regression model\n",
    "\n",
    "We are now ready to define the logistic regression model.\n",
    "\n",
    "1. Bernoulli observation distribution: $p(y|\\mathbf{x}, \\mathbf{z}) = \\text{Ber}\\left(y| \\rho = \\sigma\\left(\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x})\\right) \\right)$\n",
    "\n",
    "    where $\\mathbf{z} = \\mathbf{w}$ are all the unknown model parameters (hidden rv's).\n",
    "\n",
    "2. Uniform prior distribution for each hidden rv $\\mathbf{z}$: $p(\\mathbf{z}) \\propto 1$\n",
    "    * Note: we can also use a Gaussian prior.\n",
    "\n",
    "3. MLE point estimate for posterior: $\\hat{\\mathbf{z}}_{\\text{mle}} = \\underset{z}{\\mathrm{argmin}}\\left[-\\sum_{i=1}^{N}\\log{ p(y=y_i|\\mathbf{x}=\\mathbf{x}_i, \\mathbf{z})}\\right]$\n",
    "    * Note: if we use a Gaussian prior, then it becomes the MAP estimate.\n",
    "\n",
    "Finally, the <font color='orange'>PPD</font>: $\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathbf{x}^*, \\mathcal{D})} = \\int p(y^*|\\mathbf{x}^*,\\mathbf{z}) \\delta(\\mathbf{z}-\\hat{\\mathbf{z}}) d\\mathbf{z} = p(y^*|\\mathbf{x}^*, \\mathbf{z}=\\hat{\\mathbf{z}})$\n",
    "\n",
    "And the final class prediction is given by the **mode** of the PPD: $y^* = \\underset{y}{\\mathrm{argmax}}\\left[ p(y|\\mathbf{x}^*, \\mathbf{z}=\\hat{\\mathbf{z}}) \\right]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now is a good time to stop and think about the differences between a regression model and a classification model.\n",
    "\n",
    "Let's play a game!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# Define the function y = x * sin(x)\n",
    "def f(x):\n",
    "    return x * np.sin(x)\n",
    "\n",
    "\n",
    "def Gaussian_PPD_riding_mean_prediction(point_x=1.0):\n",
    "    xmin = 0.0\n",
    "    xmax = 8.0\n",
    "    npoints = 100\n",
    "\n",
    "    # Generate x values for the ground truth function and calculate y values\n",
    "    x_func = np.linspace(xmin, xmax, npoints)\n",
    "    y_func = f(x_func)\n",
    "\n",
    "    # Specify the point where we want to overlay the Gaussian distribution\n",
    "    #point_x = 1.5\n",
    "    point_y = f(point_x)\n",
    "\n",
    "    # Parameters for the Gaussian distribution\n",
    "    mean = point_y  # Mean of the distribution\n",
    "    std_dev = 1.0  # Standard deviation\n",
    "    \n",
    "    ymin = np.min(y_func)-2*std_dev # just to define y-axis plot limits\n",
    "    ymax = np.max(y_func)+2*std_dev # just to define y-axis plot limits\n",
    "\n",
    "    # Generate data for the Gaussian distribution\n",
    "    y_values_from_pdf = np.linspace(mean - 1.96 * std_dev,\n",
    "                                    mean + 1.96 * std_dev, 100) # samples of y to calculate respective pdf\n",
    "    pdf_values = norm.pdf(y_values_from_pdf, mean, std_dev) # probablility densities of Gaussian that\n",
    "                                                            # will be displayed in the x-axis\n",
    "    pdf_values_scaled = pdf_values/(np.max(pdf_values))*(xmax-xmin)/20 # scaled so that they are visible\n",
    "\n",
    "    fig, ax = plt.subplots(1, 1)\n",
    "    # Plot the a schematic of a PPD (Gaussian distribution to be shown vertically):\n",
    "    ax.plot(pdf_values_scaled+point_x,y_values_from_pdf, color='orange',\n",
    "             label=r'PPD: $\\mathcal{N}(y*|x*=%2.2f, \\mathcal{D})$' %point_x)  \n",
    "    ax.fill_betweenx(y_values_from_pdf,pdf_values_scaled+point_x, point_x, color='orange', alpha=0.25)\n",
    "\n",
    "    # Plot a curve that should illustrate the predicted mean:\n",
    "    ax.plot(x_func, y_func, label=r'Predicted mean: $\\mu^*(x)$', color='black')\n",
    "\n",
    "    # Highlight the point where the Gaussian is centered\n",
    "    ax.scatter([point_x], [point_y], color='orange', marker=\"*\", label=r'$\\mu^*(x=%2.2f)$' %point_x)\n",
    "    ax.axhline(0, color='black', linewidth=0.5, linestyle='--')  # X-axis\n",
    "    ax.axvline(0, color='black', linewidth=0.5, linestyle='--')  # Y-axis\n",
    "\n",
    "    # Adding labels and title\n",
    "    ax.set_title('Schematic of Regression model and its PPD at a point')\n",
    "    ax.set_xlabel('X-axis')\n",
    "    ax.set_ylabel('Y-axis')\n",
    "    ax.axis([xmin, xmax, ymin, ymax])\n",
    "    ax.legend()\n",
    "    ax.grid()\n",
    "    plt.figure(figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dff7578429a44833b1bb7d4f0f77a1e9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='point_x', max=8.0), Output()), _dom_classes=('widget…"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Showing posteriors and Dirac delta with interactive plot. Code is hidden in presentation.\n",
    "from ipywidgets import interactive # so that we can interact with the plot\n",
    "interactive_plot = interactive(Gaussian_PPD_riding_mean_prediction,\n",
    "                       point_x=(0.0, 8.0))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import bernoulli\n",
    "\n",
    "# Define a function that outputs a categorical variable\n",
    "def true_function(x,jump_location): # The Heaviside function creates the simplest classification example\n",
    "    return np.heaviside(x-jump_location, 0.5)\n",
    "\n",
    "# Define the sigmoid function:\n",
    "def sigmoid(a): \n",
    "    return 1/(1+np.exp(-a))\n",
    "\n",
    "# let's simply define a linear basis function with corresponding weights:\n",
    "def f_x_comma_z(x, z):\n",
    "    w_0 = z[0]\n",
    "    w_1 = z[1]\n",
    "    return w_0 + x*w_1\n",
    "\n",
    "def Gaussian_PPD_riding_mean_prediction(point_x=1.5,\n",
    "                                        w_0 = 0.0, w_1 = 1.0):\n",
    "    xmin = 0.0\n",
    "    xmax = 8.0\n",
    "    npoints = 1000\n",
    "    \n",
    "    jump_location = 4.0 # in case we want to change where the Heaviside function jumps\n",
    "\n",
    "    # Generate x values for the ground truth function and calculate y values\n",
    "    x_func = np.linspace(xmin, xmax, npoints)\n",
    "    y_func = true_function(x_func,jump_location)\n",
    "    \n",
    "    # Specify the point where we want to overlay the Gaussian distribution\n",
    "    #point_x = 1.5\n",
    "    point_y = true_function(point_x,jump_location)\n",
    "\n",
    "    # Parameter for the Bernoulli distribution\n",
    "    mean = point_y  # Mean is the rho parameter\n",
    "    \n",
    "    ymin = -2.0 # just to define y-axis plot limits\n",
    "    ymax = 2.0 # just to define y-axis plot limits\n",
    "\n",
    "    # Now calculate the sigmoid of that linear model:\n",
    "    z = [w_0, w_1] # collect weights into z vector\n",
    "    sigmoid_at_point_x = sigmoid( f_x_comma_z(point_x,z) ) # calculate sigmoid of linear model\n",
    "    \n",
    "    PPD_mean_at_point_x = sigmoid_at_point_x # mean of Bernoulli distribution is the result of the sigmoid\n",
    "    \n",
    "    PPD_mean = sigmoid( f_x_comma_z(x_func,z) )\n",
    "    \n",
    "    # Generate data for the Gaussian distribution\n",
    "    y_values_from_pmf = [0, 1] # the output of a Bernoulli distribution can only be 0 or 1\n",
    "    pmf_values = bernoulli.pmf(y_values_from_pmf, PPD_mean_at_point_x) # output the probability of y=0 and of y=1\n",
    "                                                            # this will be shown in the x-axis\n",
    "    # In this case, there is no need to scale the probabilities to make them visible...\n",
    "    #pmf_values_scaled = pmf_values/1*(xmax-xmin)/10 # scaled so that they are visible\n",
    "\n",
    "    fig, ax = plt.subplots(1, 1)\n",
    "    \n",
    "    ax.plot(x_func, y_func, label=r'Ground truth', color='black', linewidth=2.0)\n",
    "    \n",
    "    # Plot the a schematic of a PPD (Gaussian distribution to be shown vertically):\n",
    "    ax.plot(bernoulli.pmf(y_values_from_pmf, PPD_mean_at_point_x)+point_x,y_values_from_pmf, 'bo', ms=8,\n",
    "            label='PPD: Bernoulli distribution')\n",
    "    ax.hlines(y_values_from_pmf,pmf_values+point_x, point_x, colors='b', lw=5, alpha=0.5)\n",
    "    ax.vlines(point_x,0.0,1.0, color='black', linewidth=2.5, linestyle='--')  # to show the support domain\n",
    "    \n",
    "    ax.plot(x_func, f_x_comma_z(x_func,z),\n",
    "            label=r'$f(x,\\mathbf{z})$ with $\\mathbf{z}=[w_0=%2.1f, w_1=%2.1f]^T$' %(w_0,w_1),\n",
    "            color='red', linewidth=1.0, linestyle='--' )\n",
    "\n",
    "    # Plot a curve that should illustrate the predicted mean:\n",
    "    \n",
    "    ax.plot(x_func, PPD_mean, label=r'PPD mean: $\\rho^*(x)=\\sigma[f(x^*,\\mathbf{z})]$',\n",
    "            color='orange', linewidth=2.0, linestyle='--')\n",
    "    \n",
    "    # Highlight the point where the mean of the Bernoulli PPD is located:\n",
    "    ax.scatter([point_x], [PPD_mean_at_point_x], color='orange', marker=\"o\", s=50,\n",
    "               label=r'Mean of PPD at point_x: $\\rho^*(x=%2.2f)$' %point_x)\n",
    "    \n",
    "    if PPD_mean_at_point_x>= 0.5:\n",
    "        PPD_mode_at_point_x = 1.0\n",
    "    else:\n",
    "        PPD_mode_at_point_x = 0.0\n",
    "    #\n",
    "    ax.scatter([point_x], [PPD_mode_at_point_x], color='blue', marker=\"*\", s=200,\n",
    "               label=r'Mode of PPD at point_x: $y^*(x=%2.2f)$' %point_x)\n",
    "    \n",
    "    ax.axhline(0, color='black', linewidth=0.5, linestyle='--')  # X-axis\n",
    "\n",
    "    # Adding labels and title\n",
    "    ax.set_title('Schematic of Classification model and its PPD at a point')\n",
    "    ax.set_xlabel('X-axis')\n",
    "    ax.set_ylabel('Y-axis')\n",
    "    ax.axis([xmin, xmax, ymin, ymax])\n",
    "    ax.legend(loc='lower right')\n",
    "    ax.grid()\n",
    "    plt.figure(figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 392,
       "width": 707
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 600x300 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Gaussian_PPD_riding_mean_prediction(point_x=3.0, w_0=-4.0, w_1 = 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a65c39f6acfc43fc889c55de694b6f5a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.5, description='point_x', max=8.0), FloatSlider(value=0.0, descripti…"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Showing posteriors and Dirac delta with interactive plot. Code is hidden in presentation.\n",
    "from ipywidgets import interactive # so that we can interact with the plot\n",
    "interactive_plot = interactive(Gaussian_PPD_riding_mean_prediction,\n",
    "                       point_x=(0.0, 8.0), w_0=(-4.0, 0.0), w_1 = (-1.0, 1.0))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Like we did before for other models, let's determine the PPD from the MLE point estimate:\n",
    "\n",
    "$\\begin{align}\n",
    "\\text{NLL}(\\mathbf{w}) =& -\\log \\prod_{n=1}^N \\text{Ber}(y_n|\\rho_n)\\\\\n",
    "=& -\\sum_{n=1}^N \\log [\\rho_n^{y_n}\\times(1-\\rho_n)^{1-y_n}]\\\\\n",
    "=& -\\sum_{n=1}^N [y_n\\log \\rho_n + (1-y_n)\\log(1-\\rho_n)]\\\\\n",
    "=& \\sum_{n=1}^N \\mathbb{H}(y_n,\\rho_n)\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "where $\\rho_n = \\sigma(a_n)$ is the probability of class 1, $a_n = \\mathbf{w}^T\\boldsymbol{\\phi}(\\mathbf{x}_n)$ is the log odds (or pre-activation, as mentioned above), and $\\mathbb{H}(y_n,\\rho_n)$ is called the **binary cross entropy** loss in deterministic ML (recall that in a deterministic view of ML, we think about loss functions, instead of posterior and PPD).\n",
    "\n",
    "The binary cross entropy loss is then defined as:\n",
    "\n",
    "$$\n",
    "\\mathbb{H}(p,q) = -[p\\log q + (1-p)\\log(1-q)]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* As usual, how do we find the MLE point estimate?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Minimize the negative log likelihood by computing the gradient wrt the unknowns $\\mathbf{z}$ (in this case $\\mathbf{z}=\\mathbf{w})$:\n",
    "\n",
    "$\\begin{align}\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})=&\\mathbf{0}\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$\\require{color}\\begin{align}\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})=& -\\sum_{n=1}^N [y_n{\\color{blue}\\nabla_{\\mathbf{w}}\\log \\rho_n} + (1-y_n){\\color{green}\\nabla_{\\mathbf{w}}\\log(1-\\rho_n)}]\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "where the colored terms, ${\\color{blue}\\nabla_{\\mathbf{w}}\\log \\rho_n} = \\frac{1}{\\rho_n}{\\color{red}\\nabla_{\\mathbf{w}}\\rho_n}$ and ${\\color{green}\\nabla_{\\mathbf{w}}\\log(1-\\rho_n)} = -\\frac{1}{1-\\rho_n}{\\color{red}\\nabla_{\\mathbf{w}}\\rho_n}$, depend on the same term highlighted in red (using index notation):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$\n",
    "{\\color{red}\\frac{\\partial}{\\partial w_d}\\rho_n} = \\frac{\\partial}{\\partial w_d}\\sigma\\left(\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x})\\right) = \\frac{\\partial}{\\partial a_n}\\sigma(a_n) \\frac{\\partial a_n}{\\partial w_d} = \\rho_n(1-\\rho_n)\\phi_{d}(\\mathbf{x}_n) \\quad \\Rightarrow \\quad {\\color{red}\\nabla_{\\mathbf{w}}\\rho_n} = \\rho_n(1-\\rho_n)\\boldsymbol{\\phi}({\\mathbf{x}_n})\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$\\begin{align}\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})=& -\\sum_{n=1}^N [y_n{\\color{blue}(1-\\rho_n)\\boldsymbol{\\phi}({\\mathbf{x}_n})} - (1-y_n){\\color{green}\\rho_n\\boldsymbol{\\phi}({\\mathbf{x}_n})}]\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "**Note**: Some people may find the above derivative calculation too short, so here I include all intermediate steps.\n",
    "\n",
    "$\\begin{align}\n",
    "{\\color{red}\\frac{\\partial}{\\partial w_d}\\rho_n} =& \\frac{\\partial}{\\partial w_d}\\sigma\\left(\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x}_n)\\right)\\\\\n",
    "        =& \\frac{\\partial}{\\partial w_d}\\sigma\\left(w_m \\phi_m(\\mathbf{x}_n)\\right) \\quad \\text{where we put everything in index notation and use Einstein's notation: } \\sum_{m=0}^{M-1}w_m \\phi_m(\\mathbf{x}_n)=w_m \\phi_m(\\mathbf{x}_n)\\\\\n",
    "=& \\frac{\\partial}{\\partial w_d}\\sigma(a_n) \\quad \\text{where for brevity we just used: } a_n = \\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x}) = w_m \\phi_m(\\mathbf{x}) \\\\\n",
    "=& {\\color{violet}\\frac{\\partial}{\\partial a_n}\\sigma(a_n)} \\frac{\\partial a_n}{\\partial w_d} \\quad \\text{where we used the chain rule (and colored one of the terms for clarity)}\\\\\n",
    "=& {\\color{violet}\\sigma(a_n)(1-\\sigma(a_n))}\\frac{\\partial a_n}{\\partial w_d} \\quad \\text{where we calculate the derivative of the sigmoid (see previous Lecture)}\\\\\n",
    "=& {\\color{violet}\\sigma(a_n)(1-\\sigma(a_n))}\\phi_{d}(\\mathbf{x}_n) \\quad \\text{where the derivative of the second term is simply: } \\frac{\\partial a_n}{\\partial w_d} = \\frac{\\partial}{\\partial w_d}\\left( w_m \\phi_m(\\mathbf{x}) \\right) = \\delta_{md}\\phi_m(\\mathbf{x}) = \\phi_d(\\mathbf{x}) \\\\\n",
    "=& \\rho_n(1-\\rho_n)\\phi_{d}(\\mathbf{x}_n)\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "From where we can go back to matrix notation:\n",
    "\n",
    "${\\color{red}\\nabla_{\\mathbf{w}}\\rho_n}= \\rho_n(1-\\rho_n)\\boldsymbol{\\phi}({x_n})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The gradient of the NLL wrt to the unknowns can then be simplified as follows:\n",
    "\n",
    "$\\begin{align}\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})=& -\\sum_{n=1}^N [y_n(1-\\rho_n)\\boldsymbol{\\phi}(\\mathbf{x}_n)- (1-y_n)\\rho_n\\boldsymbol{\\phi}(\\mathbf{x}_n)]\\\\\n",
    "=& -\\sum_{n=1}^N [y_n\\boldsymbol{\\phi}(\\mathbf{x}_n)-y_n\\boldsymbol{\\phi}(\\mathbf{x}_n)\\rho_n - \\boldsymbol{\\phi}(\\mathbf{x}_n)\\rho_n + y_n\\boldsymbol{\\phi}(\\mathbf{x}_n)\\rho_n]\\\\\n",
    "=& \\sum_{n=1}^N \\boldsymbol{\\phi}(\\mathbf{x}_n)(\\rho_n-y_n)\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "where recall that $\\rho_n = \\sigma\\left(\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x}_n)\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This result has a nice intuitive interpretation: it is the sum of the differences between the observed target (output or label) and the prediction $\\rho_n$, weighted by the input basis vectors $\\boldsymbol{\\phi}(x_n)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Note**: We can also write the gradient of the NLL as a product of the matrix of basis functions and the vector with all the training point measurements $\\rho_n$ and $y_n$:\n",
    "\n",
    "$\\begin{align}\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})=& \\sum_{n=1}^N \\boldsymbol{\\phi}(\\mathbf{x}_n)(\\rho_n-y_n)\\\\\n",
    "=& \\boldsymbol{\\Phi}^T\\left(\\boldsymbol{\\rho}-\\mathbf{y}\\right)\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "where we group all output measurements $y_n$ into a $N\\times 1$ vector $\\mathbf{y}$, likewise for $\\boldsymbol{\\rho}$, and where we group all $N$ evaluations of the basis functions into the $N\\times M$ matrix of basis functions:\n",
    "\n",
    "$$\n",
    "\\boldsymbol{\\Phi} = \\begin{bmatrix} \\phi_0(\\mathbf{x}_1) & \\phi_1(\\mathbf{x}_1) & \\cdots & \\phi_{M-1}(\\mathbf{x}_1) \\\\\n",
    "\\phi_0(\\mathbf{x}_2) & \\phi_1(\\mathbf{x}_2) & \\cdots & \\phi_{M-1}(\\mathbf{x}_2) \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "\\phi_0(\\mathbf{x}_N) & \\phi_1(\\mathbf{x}_N) & \\cdots & \\phi_{M-1}(\\mathbf{x}_N) \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "just like we did for Linear Regression in Lecture 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Unfortunately, the expression we obtained to try to find the MLE (by equalling the gradient of the NLL to zero):\n",
    "\n",
    "$\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})= 0 \\quad \\Rightarrow \\quad \\sum_{n=1}^N \\boldsymbol{\\phi}(\\mathbf{x}_n)(\\rho_n-y_n) =0 \\quad \\Rightarrow \\quad \\sum_{n=1}^N \\boldsymbol{\\phi}(\\mathbf{x}_n)\\left[\\sigma\\left(\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x}_n)\\right)-y_n\\right] =0\n",
    "$\n",
    "\n",
    "has a small problem...\n",
    "\n",
    "- Can you see it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We cannot explicitly obtain an expression for the unknowns $\\mathbf{w}$ because we have a nonlinear expression on the weights due to the sigmoid function.\n",
    "\n",
    "This did not happen in Linear Regression! See Lecture 11, where we found the actual MLE value for the weights."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- What do we do now? Any ideas??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Point estimate for binary logistic regression\n",
    "\n",
    "Since we at least found an expression for the $\\text{NLL}$ and its gradient wrt the unknowns:\n",
    "\n",
    "$\n",
    "\\text{NLL}(\\mathbf{w}) = -\\sum_{n=1}^N [y_n\\log \\rho_n + (1-y_n)\\log(1-\\rho_n)]\n",
    "$\n",
    "\n",
    "$\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})= \\boldsymbol{\\Phi}^T\\left(\\boldsymbol{\\rho}-\\mathbf{y}\\right)\n",
    "$\n",
    "\n",
    "we can use a **gradient-based optimization algorithm** to find the minimum of the NLL, i.e. the MLE point estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Note**: It can also be shown that the point of zero gradient is actually a global optimum (just like in linear regression), by calculating the second derivative of the NLL wrt the unknowns (called the **Hessian**) and noting that it is positive semi-definite. (See the notes below, if you are curious)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "#### Note on the Hessian of NLL for logistic regression\n",
    "\n",
    "$\n",
    "\\mathbf{H}(\\mathbf{w}) = \\nabla_{\\mathbf{w}}\\nabla_{\\mathbf{w}}^T \\text{NLL}(\\mathbf{w}) = \\sum_{n=1}^N (\\rho_n (1-\\rho_n)\\boldsymbol{\\phi}({x_n}))\\boldsymbol{\\phi}({x_n})^T = \\boldsymbol{\\Phi}^T\\mathbf{S}\\boldsymbol{\\Phi}\n",
    "$\n",
    "\n",
    "where $\\mathbf{S} = \\text{diag}\\left( \\rho_1 (1-\\rho_1), \\ldots, \\rho_N (1-\\rho_N) \\right)$.\n",
    "\n",
    "This result implies $\\mathbf{H}$ is positive definite, since for any nonzero vector $\\mathbf{v}$, we have:\n",
    "\n",
    "$\n",
    "\\mathbf{v}^T\\boldsymbol{\\Phi}^T \\mathbf{S}\\boldsymbol{\\Phi}\\mathbf{v} = (\\mathbf{v}^T\\boldsymbol{\\Phi}^T\\mathbf{S}^{1/2})(\\mathbf{S}^{1/2}\\boldsymbol{\\Phi}\\mathbf{v}) = || \\mathbf{v}^T\\boldsymbol{\\Phi}^T\\mathbf{S}^{1/2} ||_2^2 > 0\n",
    "$\n",
    "\n",
    "which follows from $\\rho_n>0$ for all $n$, because of the use of the sigmoid function. Consequently the NLL is strictly convex. However, in practice, values of $\\rho_n$ which are close to 0 or 1 might cause the Hessian to be close to singular. As we learned in linear regression when introducing ridge regression, we can avoid this by considering a Gaussian prior (i.e. $\\ell_2$ regularization). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The usual optimizer of choice for finding the point estimate of Logistic Regression is the same we used for Gaussian processes! Do you still remember which one?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* **L-BFGS**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "But there are many others that also work (it's a concave loss landscape, as the Hessian shows!), for example: *SAGA* (fast convergence but important to standardize dataset), and *Newton's method* (requires the calculation of the Hessian)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Some practical notes**:\n",
    "\n",
    "1. It can be useful to use a Gaussian prior on the weights (regularization), as in Linear Regression.\n",
    "    * This is useful when the problem is **perfectly separable**, e.g. it is possible to draw a decision boundary that is a straight line that perfectly separates the data such that every $y=1$ is on one side of the line, and $y=0$ is on the other. In that case, the slope of the line is infinite, and the sigmoid has a sharp transition. By including a Gaussian prior, you are introducing a bit of aleatoric uncertainty (remember Lecture 12: Ridge regression)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. Perfectly separating classes becomes more likely as your model for the mean becomes more complex. (Go back to Lecture 21 and remembere what happened when we considered a higher-order polynomial). As you increased the degree of the basis function, the decision boundary becomes more \"wavy\" and starts separating more points.\n",
    "    * Also remember the lessons you learned from Gaussian process regression: if instead of a finite basis function, you use the kernel trick (recall: kernel is the inner product of two basis function vectors), then you will be able to create more general approximations in the kernel space, with the hope of making it easier to separate classes...\n",
    "        * One of the simplest (and popular) classification algorithms that uses kernels is called **Support Vector Machine**. You can read about it in Section 17.3 of the book."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Anyway... Going back to predicting the point estimate from using an optimizer...\n",
    "\n",
    "Once the optimizer provides us with the point estimate $\\hat{\\mathbf{z}} = {\\color{red}\\hat{\\mathbf{w}}}$, we can get our prediction via the PPD:\n",
    "\n",
    "Final prediction is given by the <font color='orange'>PPD</font>: $\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathbf{x}^*, \\mathcal{D})} = \\int p(y^*|\\mathbf{x}^*,\\mathbf{z}) \\delta(\\mathbf{z}-\\hat{\\mathbf{z}}) d\\mathbf{z} = p(y^*|\\mathbf{x}^*, \\mathbf{z}=\\hat{\\mathbf{z}}) = \\text{Ber}\\left(y^*| \\rho = \\sigma\\left({\\color{red}\\hat{\\mathbf{w}}}^T \\boldsymbol{\\phi}(\\mathbf{x}^*)\\right) \\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Although we already saw the predictions in the previous lecture, let's see a few more predictions for simplified cases.\n",
    "\n",
    "For example, if we consider the Iris dataset but considering only two classes: Iris-Virginica and Iris-Versicolor.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 789
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feature1 = 'PetalWidthCm'\n",
    "feature2 = 'PetalLengthCm'\n",
    "# Let's only retrieve the samples for Iris-versicolor and Iris-virginica\n",
    "X_2d_iris_data = iris_data.loc[50:, [feature1,feature2] ].values # just use 2 inputs (features)\n",
    "y_string_iris_data = iris_data.loc[50:, 'Species'].values\n",
    "target_names = iris_data.loc[50:, 'Species'].unique()\n",
    "y_iris_data = pd.Categorical(pd.factorize(y_string_iris_data)[0])\n",
    "\n",
    "train_and_predict_LogReg_countour(X_2d_iris_data, y_iris_data, feature1, feature2, target_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's now make a prediction using only **one feature** (Petal width) and using only 2 classes (Iris-versicolor and Iris-virginica)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'C': 100000.0, 'class_weight': None, 'dual': False, 'fit_intercept': True, 'intercept_scaling': 1, 'l1_ratio': None, 'max_iter': 100, 'multi_class': 'deprecated', 'n_jobs': None, 'penalty': 'l2', 'random_state': None, 'solver': 'lbfgs', 'tol': 0.0001, 'verbose': 0, 'warm_start': False}\n"
     ]
    }
   ],
   "source": [
    "feature1 = 'PetalWidthCm'\n",
    "# Let's only retrieve the samples for 2 classes (sample 51 onwards): Iris-versicolor and Iris-virginica\n",
    "x = iris_data.loc[50:, feature1 ].values # just use 2 inputs (features)\n",
    "y_strings = iris_data.loc[50:, 'Species'].values\n",
    "target_names = iris_data.loc[50:, 'Species'].unique()\n",
    "y = pd.Categorical(pd.factorize(y_strings)[0])\n",
    "\n",
    "n_classes = np.size(target_names)\n",
    "# WARNING: we did not scale our data because this dataset is really simple, but NEVER do that!!!\n",
    "C = 1e5  # Logistic Regression regularization parameter.\n",
    "         # It is actually the inverse of regularization strength; must be a positive float.\n",
    "         # Like in support vector machines, smaller values specify stronger regularization.\n",
    "\n",
    "LogReg_model = LogisticRegression(C=C, solver='lbfgs') # model\n",
    "\n",
    "LogReg_model.fit(x.reshape(-1,1), y) # HERE WE ARE USING ONLY 2 FEATURES TO FIT THE MODEL!\n",
    "                       # This is just to assess the predictive power of the SVC even though\n",
    "                       #  it is only using 2 features for training.\n",
    "                       # REMEMBER: WE USUALLY USE ALL FEATURES WHEN TRAINING A MODEL.\n",
    "\n",
    "parameters = LogReg_model.get_params()\n",
    "print(parameters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "plot_colors = 'ry' # defining colors for the 2 classes\n",
    "plot_step = 5e-3 # defining the meshgrid step size\n",
    "\n",
    "#parameters = lr.fit(x, y, lambd=1)\n",
    "\n",
    "x_plot = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "rho = LogReg_model.predict_proba(x_plot) # outputs the rho and 1-rho parameters (class probabilities)\n",
    "decision_boundary = x_plot[rho[:,0] < 0.5][0] # locate the decision boundary (point where rho = 0.5)\n",
    "\n",
    "fig4, ax4 = plt.subplots(1, 1)\n",
    "ax4.scatter(x[y == 0], y[y == 0], s=15, c=\"r\", marker=\"s\")\n",
    "ax4.scatter(x[y == 1], y[y == 1], s=15, c=\"b\", marker=\"^\")\n",
    "ax4.plot(\n",
    "    [decision_boundary, decision_boundary],\n",
    "    [-1, 2],\n",
    "    color=\"black\",\n",
    "    linestyle=\":\",\n",
    "    label=\"Decision boundary\",\n",
    "    linewidth = 4.0\n",
    ")\n",
    "ax4.plot(x_plot, rho[:,0], \"r-\", label=target_names[0])\n",
    "ax4.plot(x_plot, rho[:,1], \"b--\", label=target_names[1])\n",
    "\n",
    "ax4.arrow(decision_boundary[0], 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc=\"r\", ec=\"r\")\n",
    "ax4.arrow(decision_boundary[0], 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc=\"b\", ec=\"b\")\n",
    "\n",
    "ax4.set_xlabel(feature1,fontsize=20)\n",
    "ax4.set_ylabel(\"Probabilities\", fontsize=20)\n",
    "ax4.set_title(r\"Decision boundary but also showing $\\rho$ and $(1-\\rho)$ probabilities\", fontsize=20)\n",
    "ax4.legend(bbox_to_anchor=(1, 1),fontsize=15)\n",
    "ax4.axis([0, 3, -0.02, 1.02])\n",
    "fig4.set_size_inches(8, 6) # scale figure to be larger\n",
    "plt.close(fig4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "image/png": {
       "height": 568,
       "width": 1044
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Logistic Regression only for 1 feature (Petal Width) and 2 classes (Iris-versicolor and Iris-virginica)\n",
    "fig4 # Plot rho and rho-1 probabilities, as well as the corresponding decision boundary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note: you don't see 50 samples of each class because multiple points become on top of each other (they have the same Petal Width, although they have different values for the other features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Multinomial Logistic Regression model\n",
    "\n",
    "We saw in the last lecture and the beginning of this one that we can also do classification for more than 2 classes.\n",
    "\n",
    "**Multinomial** logistic regression is a trivial generalization of binary logistic regression:\n",
    "\n",
    "1. Instead of the Bernoulli distribution (which is binary), we need to use the **Categorical distribution**.\n",
    "\n",
    "2. Instead of using the sigmoid function, we need to use the **softmax** function.\n",
    "\n",
    "Of course, the Categorical distribution when we have two classes reduces to the Bernoulli distribution, and the softmax reduces to the sigmoid..."
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    "Summary of **Multinomial Logistic Regression** model:\n",
    "\n",
    "1. Categorical observation distribution: $p(y|\\mathbf{x}, \\mathbf{z}) = \\text{Cat}\\left(y| \\boldsymbol{\\rho} = \\text{softmax}\\left(\\mathbf{W}^T \\boldsymbol{\\phi}(\\mathbf{x})\\right) \\right)$\n",
    "\n",
    "    where $\\mathbf{z} \\equiv \\mathbf{W}$ is now a **matrix** containing all the unknown model parameters (hidden rv's).\n",
    "\n",
    "\n",
    "2. Uniform prior distribution for each hidden rv $\\mathbf{z}$: $p(\\mathbf{z}) \\propto 1$\n",
    "\n",
    "\n",
    "3. MLE point estimate for posterior: $\\hat{\\mathbf{z}}_{\\text{mle}} = \\underset{z}{\\mathrm{argmin}}\\left[-\\sum_{i=1}^{N}\\log{ p(y=y_i|\\mathbf{x}=\\mathbf{x}_i, \\mathbf{z})}\\right]$\n",
    "\n",
    "\n",
    "The <font color='orange'>PPD</font>: $\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathbf{x}^*, \\mathcal{D})} = \\int p(y^*|\\mathbf{x}^*,\\mathbf{z}) \\delta(\\mathbf{z}-\\hat{\\mathbf{z}}) d\\mathbf{z} = p(y^*|\\mathbf{x}^*, \\mathbf{z}=\\hat{\\mathbf{z}})$\n",
    "\n",
    "And the final class $c^*$ prediction is given by the mode of the PPD: $c^* = \\underset{y^*}{\\mathrm{argmax}}\\left[ p(y^*|\\mathbf{x}^*, \\mathbf{z}=\\hat{\\mathbf{z}}) \\right]$"
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    "#### Categorical distribution\n",
    "\n",
    "The Categorical distribution is also a discrete probability distribution (pmf) but has one parameter $\\rho_c$ per class $c$:\n",
    "\n",
    "$$\n",
    "\\text{Cat}(y|\\boldsymbol{\\rho}) = \\prod_{c=1}^C \\rho_c^{\\mathbb{1}(y=c)}\n",
    "$$\n",
    "\n",
    "where $\\mathbb{1}$ is the indicator function (in this case, it becomes 1 when $y=c$, and zero otherwise).\n",
    "\n",
    "As before, the $\\rho_c$ parameter is a probability for that class:\n",
    "\n",
    "$$\n",
    "p(y=c|\\boldsymbol{\\rho})=\\rho_c\n",
    "$$\n",
    "\n",
    "where $0 \\leq \\rho_c \\leq 1$ and $\\sum_{c=1}^C \\rho_c = 1$, which means that there are only $C-1$ independent parameters."
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   "source": [
    "#### Note on one-hot encoding\n",
    "\n",
    "It's also possible to write the Categorical distribution in a simpler way by converting the discrete variable $y$ into a **one-hot vector** with $C$ elements, all of which are 0 except for the entry corresponding to the class label.\n",
    "\n",
    "For example, if $C=3$, we encode classes 1, 2 and 3 as $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$. More generally, we can encode classes using unit vectors, where $\\mathbf{e}_c$ is all 0s except the dimension $c$.\n",
    "\n",
    "Using one-hot encodings, the Categorical distribution becomes:\n",
    "\n",
    "$$\n",
    "\\text{Cat}(\\mathbf{y}|\\boldsymbol{\\rho}) = \\prod_{c=1}^C \\rho_c^{y_c}\n",
    "$$"
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    "#### Softmax function\n",
    "\n",
    "As we did in binary logistic regression, we define the observation distribution as:\n",
    "\n",
    "$$\n",
    "p(y|\\mathbf{x}, \\mathbf{z}) = \\text{Cat}\\left(y|\\boldsymbol{\\rho}= \\mathbf{f}(\\mathbf{x},\\mathbf{z}) \\right)\n",
    "$$\n",
    "\n",
    "where we require that $0 \\leq f_c(\\mathbf{x},\\mathbf{z}) \\leq 1$ and $\\sum_{c=1}^C f_c(\\mathbf{x},\\mathbf{z})=1$.\n",
    "\n",
    "The softmax function does the same as the sigmoid, but now for multiple classes:\n",
    "\n",
    "$$\n",
    "\\text{softmax}(\\mathbf{a}) = \\left[ \\frac{e^{a_1}}{\\sum_{c'=1}^C e^{a_{c'}}}, \\ldots, \\frac{e^{a_C}}{\\sum_{c'=1}^C e^{a_{c'}}} \\right]\n",
    "$$\n",
    "\n",
    "which maps $\\mathbb{R}^C$ to $[0,1]^C$ and satisfies the constraints that $0 \\leq \\text{softmax} \\leq 1$ and $\\sum_{c=1}^C \\text{softmax}(\\mathbf{a}_c)=1$."
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    "Calculating the $\\text{NLL}$ and its gradient is done very similarly to what was done for binary logistic regression. See Section 10.3.2 of the book.\n",
    "\n",
    "It leads to:\n",
    "\n",
    "$\n",
    "\\text{NLL}(\\mathbf{w}) = -\\sum_{n=1}^N \\sum_{c=1}^C y_{nc}\\log \\rho_{nc}\n",
    "$\n",
    "\n",
    "where $\\rho_{nc} = \\text{softmax}\\left(\\mathbf{w}^T \\boldsymbol{\\phi}(\\mathbf{x}_n)\\right)$, and $\\mathbf{y}_n$ is the one-hot encoding of the label, i.e. $y_{nc}=\\mathbb{1}(y=c)$ which means that it is one for $y=c$ and zero otherwise.\n",
    "\n",
    "The gradient of the NLL is easier to understand in index notation:\n",
    "\n",
    "$\n",
    "\\nabla_{w_m}\\text{NLL}(\\mathbf{w})= \\frac{\\partial}{\\partial w_m} \\left[ \\text{NLL}(\\mathbf{w}) \\right] = \\phi_m(\\mathbf{x}_n)\\left(\\rho_{nm}-y_{nm}\\right)\n",
    "$\n",
    "\n",
    "or equivalently in matrix notation: $\n",
    "\\nabla_{\\mathbf{w}}\\text{NLL}(\\mathbf{w})= \\boldsymbol{\\phi}(\\mathbf{x}_n)\\left(\\boldsymbol{\\rho}_{n}-\\mathbf{y}_{n}\\right)^T \\quad \\text{(summation in $n$)}\n",
    "$\n",
    "\n",
    "Recall that $\\boldsymbol{\\phi}(\\mathbf{x}_n)$ is an $M\\times 1$ vector of basis functions, but that in the case of multidimensional outputs, $\\boldsymbol{\\rho}_{n}$ and $\\mathbf{y}_n$ are $C\\times 1$ vectors, leading to a gradient of the NLL that is a $M\\times C$ matrix. (In binary logistic regression the gradient is $M\\times 1$)"
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    "## What about going Bayesian??\n",
    "\n",
    "Similarly to what we did in linear regression, we can also go Bayesian with logistic regression to capture uncertainty:\n",
    "\n",
    "* Bayesian logistic regression\n",
    "\n",
    "However, unlike Bayesian linear regression, it is not possible to compute the posterior exactly for a logistic regression model...\n",
    "\n",
    "Study Section 10.5, if you are curious about this!"
   ]
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   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  }
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