Probabilistic_Linear_Regression.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7V9_pKAd1zBI"
   },
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "m4tlqyqh1zBL"
   },
   "source": [
    "Imports and Helper Functions\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "MzXO6CCo8fBB"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive_output\n",
    "import ipywidgets as widgets\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hNTB-sukQBl9"
   },
   "source": [
    "## Data Set Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "lPXeCVINQAnE"
   },
   "outputs": [],
   "source": [
    "N = 100\n",
    "datasets = {}\n",
    "\n",
    "X = 20 * (np.random.rand(100, 1) - 0.5)  # creates random values in [-10, 10) interval.\n",
    "X[10] = 8\n",
    "\n",
    "Y = 0.5 * X - 1.2 + 2*np.random.randn(100, 1)\n",
    "datasets[\"Linear\"] = (X, Y)\n",
    "\n",
    "Y = 0.1 * (X ** 2) + 0.5 * X - 2 + np.random.randn(100, 1)\n",
    "datasets[\"Quadratic\"] = (X, Y)\n",
    "\n",
    "Y = 0.2 * (X ** 3) + 0.6 * (X ** 2) - 0.5 * X - 1 + np.random.randn(100, 1)\n",
    "datasets[\"Cubic\"] = (X, Y)\n",
    "\n",
    "Y = 0.5 * X - 1.2 + np.random.randn(100, 1)\n",
    "Y[10] = -8\n",
    "datasets[\"Outlier\"] = (X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CAtj4OFXQKy8"
   },
   "source": [
    "## Define Prediction, Loss, and Learning Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "oERpoUU-QVWn"
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   "outputs": [],
   "source": [
    "def predict(X, weight, bias):\n",
    "    #Compute Yhat given X and parameters\n",
    "    Yhat = weight * X + bias\n",
    "    return Yhat\n",
    "\n",
    "\n",
    "def squared_loss(Y, Yhat):\n",
    "    #Compute the empirical risk given Y and Yhat\n",
    "    R = np.mean((Y - Yhat) ** 2)\n",
    "    return (R)\n",
    "\n",
    "\n",
    "def fit(X, Y):\n",
    "    #Learn the model parameters\n",
    "    N = X.shape[0]\n",
    "    X = np.hstack((X, np.ones((N, 1))))  #Bias absorbtion!\n",
    "    theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(Y)\n",
    "    weight = theta[0]\n",
    "    bias = theta[1]\n",
    "    sigma = np.sqrt(np.mean((Y.flatten() - (X.dot(theta)).flatten() )**2)) \n",
    "    return weight, bias,sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "C0zQmH4nQlT_"
   },
   "source": [
    "## Interaction Functions and UI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "unR8P_Ij94t3"
   },
   "outputs": [],
   "source": [
    "def plot_model(weight=0, bias=0, sigma=0,dataset=None, N=0, learn=False, show_residuals=False):\n",
    "    plt.figure(figsize=(8, 4))\n",
    "    plt.rcParams.update({'font.size': 12})\n",
    "\n",
    "    if dataset is not None and N > 0:\n",
    "        X, Y = datasets[dataset]\n",
    "        X = X[:N]\n",
    "        Y = Y[:N]\n",
    "\n",
    "        if N >= 2 and learn:\n",
    "            weight, bias, sigma = fit(X, Y)\n",
    "\n",
    "        Yhat = predict(X, weight, bias)\n",
    "        NLL = 0.5*N*np.log(2*np.pi*sigma**2) + N*squared_loss(Y, Yhat)/(2*sigma**2)\n",
    "        \n",
    "        plt.plot(X, Y, 'ko')\n",
    "\n",
    "        if show_residuals:\n",
    "            for n in range(N):\n",
    "                plt.plot([X[n], X[n]], [Y[n], Yhat[n]], 'k-', alpha=0.5)\n",
    "\n",
    "    else:\n",
    "        NLL = np.nan\n",
    "\n",
    "    xs = np.linspace(-10, 10, 200)\n",
    "    ys = xs * weight + bias\n",
    "    plt.plot(xs, ys, '-b')\n",
    "    plt.fill_between(xs, ys-2*sigma, ys+2*sigma,alpha=0.5)\n",
    "\n",
    "    plt.grid(\"True\")\n",
    "    plt.xlim(-10, 10)\n",
    "    plt.ylim(-10, 10)\n",
    "    plt.title(\"NLL: %.4f\" % (NLL))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ww = widgets.FloatSlider(value=0, min=-1, max=1, step=.1, description=\"Weight\", continuous_update=False)\n",
    "wb = widgets.FloatSlider(value=0, min=-10, max=10, step=.1, description=\"Bias\", continuous_update=False)\n",
    "ws = widgets.FloatSlider(value=1, min=0, max=10, step=.1, description=\"Sigma\", continuous_update=False)\n",
    "wd = widgets.Dropdown(options=[\"Linear\", \"Quadratic\",\"Cubic\",\"Outlier\"], description=\"Dataset\")\n",
    "wn = widgets.IntSlider(value=0, min=-1, max=N, step=1, description=\"N\", continuous_update=False)\n",
    "wl = widgets.Checkbox(value=False, description=\"Learn\")\n",
    "wr = widgets.Checkbox(value=False, description=\"Residuals\")\n",
    "\n",
    "out = interactive_output(\n",
    "    plot_model,\n",
    "    {\"weight\": ww, \"bias\": wb, \"sigma\":ws, \"dataset\": wd, \"N\": wn, \"learn\": wl, \"show_residuals\": wr}\n",
    ")\n",
    "#out.layout.height = '400px'\n",
    "box1 = widgets.HBox([ww, wb, ws])\n",
    "box2 = widgets.HBox([wl, wr])\n",
    "box3 = widgets.HBox([wd,wn])\n",
    "ui = widgets.VBox([box1, box2,box3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o-fcWbHQQ7i1"
   },
   "source": [
    "## Linear Regression Demo"
   ]
  },
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    "display(ui,out)"
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