slides.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Machine Learning: A Primer for Radiologists"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Contents\n",
    "\n",
    "* Machine Learning Basics\n",
    "* Machine Learning Workflow\n",
    "* Commonly Used Models\n",
    "* Applications in Radiology\n",
    "* Notes and Tips\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Machine Learning Basics\n",
    "* Supervised and Unsupervised Learning\n",
    "* Supervised Learning Through Gradient Descent\n",
    "* Model Specification, Training, and Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Unsupervised and Supervised Learning\n",
    "\n",
    "| Unsupervised | Supervised |\n",
    "| :-------------: | :-------------:|\n",
    "| Aims to \"summarize\" data  | Aims to \"learn\" a function or parameters of a function as a map between input data and output/prediction |\n",
    "| Methods to reduce dimensionality of data | Methods to train a system for prediction |\n",
    "| Clustering, Compression, Association Rules | Regression |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning - Example\n",
    "\n",
    "<table>\n",
    "  <tr>\n",
    "    <td> Classification by nearest neighbor voting - this models \"learns\" from a set of labeled data, based on how close a particular point in space is to other labeled points. </td>\n",
    "    <th rowspan=\"2\" style=\"width:40%\"><img src=\"assets/images/knn_regression.png\" alt='knn_regression'></th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td> A function of 2-dimensional input space is \"learned\" based on the majority voting of the 15 nearest neighbors in the dataset. <p> $$F(x_{1}, x_{2}) = \\frac{1}{k} \\sum_{x_{i} \\in N_{k}(k)} y_{i}$$ </p> </td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning, Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013. Chapter 2, Page 7</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "x1 = np.random.normal(loc=1.0, scale=0.5, size=(1000,))\n",
    "x2 =  x1  + np.random.normal(loc=3.0, scale=0.7, size=(1000,))\n",
    "\n",
    "X_pca = pd.DataFrame([x1,\n",
    "                      x2]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "X_pca = X_pca.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "pca = PCA()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(X_pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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AmvmlUUUppddHavsAH4JrlIO1mMUrv/+Y6AkYDQwe27JU1r6//uAK+PzB6GdK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5f498e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure()\n",
    "plt.scatter(x1- pca.mean_[0],x2-pca.mean_[1])\n",
    "X, Y = zip(*pca.components_.transpose())\n",
    "# X = np.array(X)\n",
    "# Y = np.array(Y)\n",
    "# X += pca.mean_\n",
    "# Y += pca.mean_\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.quiver([0,0], [0,0], X,Y, scale=1, scale_units='xy')\n",
    "plt.xlabel(r'$x_{1}$')\n",
    "plt.ylabel(r'$x_{2}$')\n",
    "\n",
    "plt.show()\n",
    "fig.savefig('assets/images/pca.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Unsupervised Learning - Example\n",
    "\n",
    "<table>\n",
    "  <tr>\n",
    "    <td> Principal Component Analysis (PCA) - a technique that finds a linearly independent set of features that best describe the variance of the input dataset </td>\n",
    "    <th rowspan=\"2\" style=\"width:60%\"><img src=\"assets/images/pca.png\" alt='pca' style=\"width:600px;\"></th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td> Often used to reduce the dimensionality of a dataset to a small number of features with the best \"signal\", as the new features found by PCA will best explain the variance within the dataset. </td>\n",
    "  </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Unsupervised and Supervised Learning\n",
    "<table>\n",
    "  <tr>\n",
    "    <td>These methods are not exclusive of each other and can compliment each other!</td>\n",
    "    <th rowspan=\"2\" style=\"width:55%\"><img src=\"assets/images/gene_expression_regression.jpg\" alt='gene_express'></th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>Example: reducing the dimensionality of gene expression data to summarize the most important gene expression patterns of a dataset (unsupervised), which is then used to estimate survival (supervised).</td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning, Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013. Chapter 16 Page 29</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/matt/anaconda2/envs/py35/lib/python3.5/site-packages/ipykernel/__main__.py:10: RankWarning: Polyfit may be poorly conditioned\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "x = np.linspace(0, 500.0, num=50)\n",
    "x += abs(x.min()) + 1.0\n",
    "y = np.log(x) + np.random.normal(scale=0.25,size=(x.size,))\n",
    "\n",
    "p_lin = np.polyfit(x, y, 1)\n",
    "p_high = np.polyfit(x, y, 32)\n",
    "p_lin_y = np.polyval(p_lin, x)\n",
    "p_high_y = np.polyval(p_high, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gxz/GnXCC7yibN6/y5aFehPVhXEQSXZX9W/Fuf93dvNkP8Xr/fVi40H/duBEA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\nClhERERERCRuKWAREREREZG49f+1RJcKSAkvhwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa65cac05f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(14,4))\n",
    "plt.subplot(121)\n",
    "plt.scatter(x, y, s=5)\n",
    "plt.text(0.05, 6.0, 'Linear Function')\n",
    "plt.plot(x, p_lin_y, color='r')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.scatter(x, y, s=5)\n",
    "plt.plot(x, p_high_y, color='r')\n",
    "plt.text(0.05, 6.0 , '$32^{ nd }$ degree polynomial')\n",
    "fig.savefig(os.path.join('assets', 'images', 'bias_var.png'), bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def cost(predictions, ground_truth):\n",
    "    total_cost = 0.0\n",
    "    for i in range(len(predictions)):\n",
    "        total_cost += (1.0 / 2.0) * (predictions[i] - ground_truth[i])**2.0\n",
    "    \n",
    "    total_cost /= float(len(predictions))\n",
    "    return total_cost\n",
    "    \n",
    "\n",
    "def hypothesis_function(m, x, b):\n",
    "    h = m * x + b\n",
    "    return h\n",
    "\n",
    "def gradients(m, b, x, ground_truth):\n",
    "    m_gradient = 0.0\n",
    "    b_gradient = 0.0\n",
    "    \n",
    "    predictions = []\n",
    "    \n",
    "    for i in range(len(x)):\n",
    "        predictions.append(hypothesis_function(m, x[i], b))\n",
    "    \n",
    "    for i in range(len(x)):\n",
    "        error = predictions[i] - ground_truth[i]\n",
    "        m_gradient += error * x[i]\n",
    "        b_gradient += error * 1.0\n",
    "        \n",
    "    m_gradient /= float(len(x))\n",
    "    b_gradient /= float(len(x))\n",
    "    \n",
    "    return m_gradient, b_gradient\n",
    "\n",
    "def update_parameters(m, b, m_gradient, b_gradient, alpha):\n",
    "    m_updated = m - (m_gradient * alpha)\n",
    "    b_updated = b - (b_gradient * alpha)\n",
    "    \n",
    "    return m_updated, b_updated\n",
    "\n",
    "\n",
    "def run_gradient_descent(x, y, m_init, b_init, alpha=0.01, num_iteration=1500, tol=1e-4):\n",
    "    \n",
    "    m = m_init\n",
    "    b = b_init\n",
    "    \n",
    "    m_vals = []\n",
    "    b_vals = []\n",
    "    costs = []\n",
    "    \n",
    "    for iteration_num in range(num_iteration):\n",
    "        #save the current values of m and b\n",
    "        m_vals.append(m)\n",
    "        b_vals.append(b)\n",
    "        \n",
    "        #make our predictions\n",
    "        predictions = []\n",
    "        for i in range(len(x)):\n",
    "            predictions.append(hypothesis_function(m, x[i], b))\n",
    "        \n",
    "        #compute the cost and save it\n",
    "        current_cost = cost(predictions, y)\n",
    "        costs.append(current_cost)\n",
    "        \n",
    "        if current_cost < tol: #check if we are done\n",
    "            break\n",
    "        else: \n",
    "            #compute the gradients\n",
    "            m_grad, b_grad = gradients(m, b, x, y)\n",
    "        \n",
    "            #update parameters m and b\n",
    "            m_new, b_new = update_parameters(m, b, m_grad, b_grad, alpha)\n",
    " \n",
    "            #reset m and b\n",
    "            m = m_new\n",
    "            b = b_new\n",
    "            \n",
    "    return m_vals, b_vals, costs\n",
    "        \n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "\n",
    "* Core concept in ML\n",
    "* Main idea:\n",
    "    1. Specify a model\n",
    "    2. Make an initial guess at the model parameters\n",
    "    3. Measure the error associated with the current model parameters\n",
    "    4. Adjust model parameters to reduce error on the next round of prediction\n",
    "    5. Repeat steps 1-4 until the error is minimized over a model and datas set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "* Pieces of machinery that are needed:\n",
    "    1. A method for measuring the error associated with our guesses\n",
    "    2. A method to adjust the model parameters so that future predictions are better"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* A few definitions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "X := \\text{input data, which is a set of examples such that } x^{(i)} \\in X \\text{ for } i=1 .. N\n",
    "\\\\\n",
    "Y := \\text{output data, or what we are trying to predict such that } y^{(i)} \\in Y \\text{ for } i=1..N\n",
    "\\\\\n",
    "\\Theta := \\text{model parameters (unspecified before training)}\n",
    "\\\\\n",
    "M(X, \\Theta) := \\text{the model, which takes } X \\text{ and } \\Theta \\text{ as input to attempt to predict the output }Y\n",
    "\\\\\n",
    "J(M(X, \\Theta), Y) := \\text{the error or \"cost\" function, which compares model prediction to desired output}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "A common choice for the cost function is the squared difference function\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\\\\n",
    "J(M(X, \\Theta), Y) & =  \\frac{1}{2N} \\sum_{i=1}^{N} (M(x^{(i)}, \\Theta) - y^{(i)})^{2} &\n",
    "\\\\\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "One reason is because this function, when taking the derivative with respect to $\\Theta$ has a simple form:\n",
    "\n",
    "$$\\frac{\\partial J}{\\partial \\Theta} = \\frac{1}{N}\\sum_{i=1}^{N} (M(x^{(i)}, \\Theta) - y^{(i)})^{2} \\frac{\\partial M}{\\partial \\Theta} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "* We still need a method for updating the model parameters to reduce the error on future iterations\n",
    "* The crux of the idea of Gradient Descent is to use the derivative of the cost function to \"nudge\" the parameters $\\Theta$ in the right direction\n",
    "* This is typically done by measuring the gradient and then multiplying the gradient by some small value $\\alpha$, and subtracting it from the current value of $\\Theta$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\Theta_{j+1} = \\Theta_{j} - \\alpha \\frac{\\partial J}{\\partial \\Theta}$$\n",
    "<center>where $\\Theta_{j}$ is the value of $\\Theta$ on the $j^{\\text{th}}$ iteration of the algorithm</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "* Let's walk through a concrete example\n",
    "* Let's use gradient descent with a linear model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "* One of the most well known cases - linear regression\n",
    "* Task is to \"learn\" the values of a linear model that best fits the data\n",
    "\n",
    "<br>\n",
    "<br>\n",
    " <center> $$ Y = mx + b $$ </center>\n",
    "<br>\n",
    "<br>\n",
    "\n",
    "* Our goal here is to estimate what values of $m$ and $b$ best fit the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Therefore the model function looks like this\n",
    "$$M(X, m, b) = mX + b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* And the cost function has this form:\n",
    "$$J(M(X,m,b), Y) = \\frac{1}{2N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\frac{\\partial J}{\\partial m} = \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2} x^{(i)} $$\n",
    "\n",
    "and\n",
    "\n",
    "\n",
    "$$\\\\ \\frac{\\partial J}{\\partial b} = \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "So the update rules for our parameters becomes:\n",
    "\n",
    "$$m_{j+1} = m_{j} - \\alpha \\frac{1}{N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2} x^{(i)}$$\n",
    "\n",
    "\n",
    "and\n",
    "\n",
    "\n",
    "$$b_{j+1+} = b_{j} - \\alpha \\frac{1}{N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "\n",
    "Cost function equation:\n",
    "\n",
    "$$J(M(X,m,b), Y) = \\frac{1}{2N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Cost function code:\n",
    "\n",
    "```python\n",
    "    def cost(predictions, ground_truth):\n",
    "        total_cost = 0.0\n",
    "        for i in range(len(predictions)):\n",
    "            total_cost += (1.0 / 2.0) * (predictions[i] - ground_truth[i])**2.0\n",
    "\n",
    "        total_cost /= float(len(predictions))\n",
    "        return total_cost\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "\n",
    "Model Equation:\n",
    "\n",
    "$$M(X, m, b) = mX + b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Model Code:\n",
    "\n",
    "```python\n",
    "def hypothesis_function(m, x, b):\n",
    "    h = m * x + b\n",
    "    return h\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "\n",
    "Gradient Equation:\n",
    "\n",
    "$$J(M(X,m,b), Y) = \\frac{1}{2N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Gradient Code:\n",
    "\n",
    "```python\n",
    "def gradients(m, b, x, ground_truth):\n",
    "    m_gradient = 0.0\n",
    "    b_gradient = 0.0\n",
    "    predictions = []\n",
    "    for i in range(len(x)):\n",
    "        predictions.append(hypothesis_function(m, x[i], b))\n",
    "    \n",
    "    for i in range(len(x)):\n",
    "        error = predictions[i] - ground_truth[i]\n",
    "        m_gradient += error * x[i]\n",
    "        b_gradient += error * 1.0\n",
    "        \n",
    "    m_gradient /= float(len(x))\n",
    "    b_gradient /= float(len(x))\n",
    "    return m_gradient, b_gradient\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "Parameter update equations:\n",
    "\n",
    "$$m_{j+1} = m_{j} - \\alpha \\frac{1}{N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2} x^{(i)}$$\n",
    "\n",
    "\n",
    "and\n",
    "\n",
    "\n",
    "$$b_{j+1+} = b_{j} - \\alpha \\frac{1}{N} \\sum_{i=1}^{N} ((mx^{(i)}+b) - y^{(i)})^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Parameter update code:\n",
    "\n",
    "```python\n",
    "def update_parameters(m, b, m_gradient, b_gradient, alpha):\n",
    "    m_updated = m - (m_gradient * alpha)\n",
    "    b_updated = b - (b_gradient * alpha)\n",
    "    \n",
    "    return m_updated, b_updated\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "```python\n",
    "def run_gradient_descent(x, y, m_init, b_init, alpha=0.01, num_iteration=1500, tol=1e-4):\n",
    "    m = m_init\n",
    "    b = b_init\n",
    "    m_vals = []\n",
    "    b_vals = []\n",
    "    costs = []\n",
    "    \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "```python\n",
    "    for iteration_num in range(num_iteration):\n",
    "        #save the current values of m and b\n",
    "        m_vals.append(m)\n",
    "        b_vals.append(b)\n",
    "        #make our predictions\n",
    "        predictions = []\n",
    "        for i in range(len(x)):\n",
    "            predictions.append(hypothesis_function(m, x[i], b))\n",
    "        #compute the cost and save it\n",
    "        current_cost = cost(predictions, y)\n",
    "        costs.append(current_cost)\n",
    "        if current_cost < tol: #check if we are done\n",
    "            break\n",
    "        else: \n",
    "            #compute the gradients\n",
    "            m_grad, b_grad = gradients(m, b, x, y)\n",
    "            #update parameters m and b\n",
    "            m_new, b_new = update_parameters(m, b, m_grad, b_grad, alpha)\n",
    "            #reset m and b\n",
    "            m = m_new\n",
    "            b = b_new\n",
    "    return m_vals, b_vals, costs\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "* Lets see it in action!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4DgD5EKYAxQPEqA0y8xzV8uiZF3TsyfPLQlOe5vC6j31J0GMFAPkQpgBl37AyrYKVdn0S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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa658d497b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m_true = 3.5\n",
    "b_true = 4.0\n",
    "x = np.linspace(0, 10.0, num=250)\n",
    "y = x * m_true + b_true + np.random.normal(scale=1.3,size=(x.size,))\n",
    "fig = plt.figure(figsize=(10, 3))\n",
    "plt.scatter(x, y,s=1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "mv, bv, c = run_gradient_descent(x, y, -2.0, 30.0, num_iteration=5000) #initalizes m=-2.0 and b=30.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "import plotly\n",
    "\n",
    "idxs = range(0,len(mv), 500)\n",
    "\n",
    "# make figure\n",
    "figure = {\n",
    "    'data': [],\n",
    "    'layout': {},\n",
    "    'frames': []\n",
    "}\n",
    "\n",
    "# fill in most of layout\n",
    "figure['layout']['xaxis'] = {'range': [0, 10], 'title': 'X'}\n",
    "figure['layout']['yaxis'] = {'range':[0,45], 'title': 'Y'}\n",
    "figure['layout']['hovermode'] = 'closest'\n",
    "figure['layout']['sliders'] = {\n",
    "    'args': [\n",
    "        'transition', {\n",
    "            'duration': 800\n",
    "        }\n",
    "    ],\n",
    "    'plotlycommand': 'animate',\n",
    "    'values': idxs,\n",
    "    'visible': True\n",
    "}\n",
    "figure['layout']['width'] = '700'\n",
    "\n",
    "figure['layout']['updatemenus'] = [\n",
    "    {\n",
    "        'buttons': [\n",
    "            {\n",
    "                'args': [None, {'frame': {'duration': 800, 'redraw': False},\n",
    "                         'fromcurrent': True, 'transition': {'duration': 800}}],\n",
    "                'label': 'Play',\n",
    "                'method': 'animate'\n",
    "            },\n",
    "            {\n",
    "                'args': [[None], {'frame': {'duration': 0, 'redraw': False}, 'mode': 'immediate',\n",
    "                'transition': {'duration': 0}}],\n",
    "                'label': 'Pause',\n",
    "                'method': 'animate'\n",
    "            }\n",
    "        ],\n",
    "        'direction': 'left',\n",
    "        'pad': {'r': 10, 't': 87},\n",
    "        'showactive': False,\n",
    "        'type': 'buttons',\n",
    "        'x': 0.1,\n",
    "        'xanchor': 'right',\n",
    "        'y': 0,\n",
    "        'yanchor': 'top'\n",
    "    }\n",
    "]\n",
    "\n",
    "sliders_dict = {\n",
    "    'active': -1,\n",
    "    'yanchor': 'top',\n",
    "    'xanchor': 'left',\n",
    "    'currentvalue': {\n",
    "        'font': {'size': 20},\n",
    "        'prefix': '',\n",
    "        'visible': True,\n",
    "        'xanchor': 'right'\n",
    "    },\n",
    "    'transition': {'duration': 800},\n",
    "    'pad': {'b': 10, 't': 50},\n",
    "    'len': 0.9,\n",
    "    'x': 0.1,\n",
    "    'y': 0,\n",
    "    'steps': []\n",
    "}\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "for idx in [idxs[0]]:\n",
    "    y_hat = mv[idx] * x + bv[idx]\n",
    "    \n",
    "    data_dict = {'x':x,\n",
    "                 'y':y_hat,\n",
    "                 'name':'Model',\n",
    "                 'line':dict(width=4)}\n",
    "    \n",
    "    figure['data'].append(data_dict)\n",
    "    \n",
    "figure['data'].append({'x':x, 'y':y,'mode':'markers','name':\"Data\",'marker':dict(color='green')})\n",
    "\n",
    "    \n",
    "#make frames\n",
    "for idx in idxs:\n",
    "    frame = {'data': [], 'name': str(idx)}\n",
    "    \n",
    "    y_hat = mv[idx] * x + bv[idx]\n",
    "    \n",
    "    data_dict = {'x':x,\n",
    "                 'y':y_hat}\n",
    "    \n",
    "    frame['data'].append(data_dict)\n",
    "\n",
    "    figure['frames'].append(frame)\n",
    "    slider_step = {'args': [\n",
    "        [idx],\n",
    "        {'frame': {'redraw': False},\n",
    "         'mode': 'immediate',\n",
    "       'transition': {'duration': 800}}\n",
    "     ],\n",
    "     'label': 'Iteration: {i} | {cmv:.2f}x + {cbv:.2f}'.format(cmv=mv[idx], cbv=bv[idx], i=idx),\n",
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    "    sliders_dict['steps'].append(slider_step)\n",
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       "        });</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotly.offline.iplot(figure, show_link=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "m_final = mv[-1]\n",
    "b_final = bv[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Supervised Learning Through Gradient Descent\n",
    "* Based on the code, it looks like we got $m=3.50$ and $b=3.94$\n",
    "* Not too shabby!\n",
    "* This idea can be applied to any model function $M$ (as long as it has a continuous, well defined derivative)\n",
    "* We used a linear function here, but it could be anything"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Machine Learning Workflow\n",
    "* Typical approach to using machine learning\n",
    "    1. Identify problem, data source\n",
    "    2. Feature extraction and dataset compilation\n",
    "    3. Model selection and training\n",
    "    4. Model testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Problem Identification\n",
    "* Sounds simple, often most challenging\n",
    "* A few questions to ask:\n",
    "    1. What is my goal? \n",
    "    2. What \"output\" do I want the system to produce?\n",
    "    3. What do I want to predict? \n",
    "    4. What data do I have to make such a prediction? Is it logical to use the data I have to make the prediction?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Feature Extraction\n",
    "* Raw data typically not suitable for prediction\n",
    "* All models require a fixed number of input parameters (some exceptions to this using kernels)\n",
    "* Intermediate processing steps to reliably measure features from raw data\n",
    "    * Manual extraction of features\n",
    "    * SIFT features from images\n",
    "    * Term Frequency - Document Inverse Frequency (TF-IDF) vectors from text data\n",
    "    \n",
    "    \n",
    "* Features from each sample are compiled into a table\n",
    "* Automation is ideal but **not** necessary!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Feature Extraction\n",
    "\n",
    "Example from our recent [AHA poster](https://aha.apprisor.org/epsView.cfm?y4IQEr57sqsVQGWpLxb9XXbq6itE%2FzVu6GolXdn34Ln8nE%2FYsSsz9A%3D%3D)\n",
    "\n",
    "![simp_man](assets/images/simplified_extraction.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Feature Extraction\n",
    "SIFT Features from images - used to construct a \"fingerprint\" for objects in images. See [this github repository for some examples](https://github.com/themantalope/bag-of-visual-words-example)\n",
    "<p float=\"left\">\n",
    "    <img src=\"assets/images/owl.jpg\" width=\"50%\" align=\"left\"/>\n",
    "    <img src=\"assets/images/toad.jpg\" width=\"50%\" align=\"left\"/>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "\n",
    "categories = ['alt.atheism', 'soc.religion.christian','comp.graphics', 'sci.med']\n",
    "twenty_train = fetch_20newsgroups(subset='train', categories=categories, shuffle=True, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction.text import TfidfTransformer\n",
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "\n",
    "count_vect = CountVectorizer()\n",
    "X_train_counts = count_vect.fit_transform(twenty_train.data)\n",
    "tf_transformer = TfidfTransformer(use_idf=False).fit(X_train_counts)\n",
    "X_train_tf = tf_transformer.transform(X_train_counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.matrixlib.defmatrix.matrix"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X_train_tf.todense())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "X_pd = pd.DataFrame(X_train_tf.todense())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "desc = X_pd.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
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       "      <td>0.000040</td>\n",
       "      <td>0.000038</td>\n",
       "      <td>0.000031</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>9.015170e-07</td>\n",
       "      <td>0.000002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.009588</td>\n",
       "      <td>0.014123</td>\n",
       "      <td>0.000086</td>\n",
       "      <td>0.001918</td>\n",
       "      <td>4.024102e-05</td>\n",
       "      <td>0.001156</td>\n",
       "      <td>0.001792</td>\n",
       "      <td>0.001459</td>\n",
       "      <td>0.000773</td>\n",
       "      <td>4.282917e-05</td>\n",
       "      <td>0.000080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.146211</td>\n",
       "      <td>0.505964</td>\n",
       "      <td>0.004075</td>\n",
       "      <td>0.065233</td>\n",
       "      <td>1.911766e-03</td>\n",
       "      <td>0.043073</td>\n",
       "      <td>0.085126</td>\n",
       "      <td>0.069338</td>\n",
       "      <td>0.036711</td>\n",
       "      <td>2.034724e-03</td>\n",
       "      <td>0.003824</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0            1            2            3             4   \\\n",
       "count  2257.000000  2257.000000  2257.000000  2257.000000  2.257000e+03   \n",
       "mean      0.001606     0.001003     0.000002     0.000057  8.470387e-07   \n",
       "std       0.009588     0.014123     0.000086     0.001918  4.024102e-05   \n",
       "min       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "25%       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "50%       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "75%       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "max       0.146211     0.505964     0.004075     0.065233  1.911766e-03   \n",
       "\n",
       "                5            6            7            8             9   \\\n",
       "count  2257.000000  2257.000000  2257.000000  2257.000000  2.257000e+03   \n",
       "mean      0.000040     0.000038     0.000031     0.000016  9.015170e-07   \n",
       "std       0.001156     0.001792     0.001459     0.000773  4.282917e-05   \n",
       "min       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "25%       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "50%       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "75%       0.000000     0.000000     0.000000     0.000000  0.000000e+00   \n",
       "max       0.043073     0.085126     0.069338     0.036711  2.034724e-03   \n",
       "\n",
       "                10  \n",
       "count  2257.000000  \n",
       "mean      0.000002  \n",
       "std       0.000080  \n",
       "min       0.000000  \n",
       "25%       0.000000  \n",
       "50%       0.000000  \n",
       "75%       0.000000  \n",
       "max       0.003824  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "desc.loc[:, 0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "desc.loc['iqr', :] = desc.loc['75%', :].values - desc.loc['25%', :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "z = desc.loc['std', :].sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "z2 = desc.loc['iqr', :].sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "good_cols = z2.iloc[0:50].index.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "colors_dict = dict(zip(set(twenty_train.target), sns.color_palette(palette='deep', n_colors=len(set(twenty_train.target)))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: (0.2980392156862745, 0.4470588235294118, 0.6901960784313725),\n",
       " 1: (0.3333333333333333, 0.6588235294117647, 0.40784313725490196),\n",
       " 2: (0.7686274509803922, 0.3058823529411765, 0.3215686274509804),\n",
       " 3: (0.5058823529411764, 0.4470588235294118, 0.6980392156862745)}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "colors_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAABECAYAAABtXrKpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAATpJREFUeJzt1j1KA1EARtGJf5tyDSGFoGuwzg7srV1DBIuQNbgpRZ6t\njYOCcbxyTjs8+Iq5vLcaY4wJyDhZegDwPaKFGNFCjGghRrQQMxvty+vbb+0APrjbHj79djZ38OL8\ndFpv9z8+6K843G+m693t0jOO5vHmYXreXC0942gu90+zP/d/5XkMMaKFGNFCjGghRrQQI1qIES3E\niBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEtxIgWYkQLMaKFGNFC\njGghRrQQI1qIES3EiBZiRAsxooUY0UKMaCFGtBAjWogRLcSIFmJECzGihRjRQoxoIUa0ECNaiBEt\nxIgWYkQLMaKFGNFCjGghRrQQsxpjjKVHAF/npoUY0UKMaCFGtBAjWogRLcS8A/mSF9FegU4gAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa5dfaaf278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.palplot(sns.color_palette('deep', 4))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "r_colors = [colors_dict[y] for y in twenty_train.target]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['alt.atheism', 'comp.graphics', 'sci.med', 'soc.religion.christian']"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "twenty_train.target_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "names_dict = {0:'Atheism', 1:'Graphics', 2:'Medicine', 3:'Christianity'}\n",
    "names_to_colors = dict(zip(names_dict.values(), colors_dict.values()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Atheism': (0.2980392156862745, 0.4470588235294118, 0.6901960784313725),\n",
       " 'Christianity': (0.5058823529411764, 0.4470588235294118, 0.6980392156862745),\n",
       " 'Graphics': (0.3333333333333333, 0.6588235294117647, 0.40784313725490196),\n",
       " 'Medicine': (0.7686274509803922, 0.3058823529411765, 0.3215686274509804)}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names_to_colors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/matt/anaconda2/envs/py35/lib/python3.5/site-packages/matplotlib/cbook.py:136: MatplotlibDeprecationWarning:\n",
      "\n",
      "The axisbg attribute was deprecated in version 2.0. Use facecolor instead.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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VLhNmne7hxCeXlgmWSewZAd7opqlxjZZIyUCEpI0Vz3CJ/K1xBbEObpDF1O3Gg+kcTJ5S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\nJ1eXRwIKAzI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JWu2mse9WMZVd/MXxn9+hq30nHgZQIB6Xw00uriiFemPGa5mkxJhIEEpf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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa631b319e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sys\n",
    "import matplotlib.patches as mpatches\n",
    "sys.setrecursionlimit(40000)\n",
    "\n",
    "g=sns.clustermap(X_pd.loc[:,good_cols], \n",
    "               yticklabels=False, \n",
    "               xticklabels=False,\n",
    "               col_cluster=True,\n",
    "               row_cluster=True,\n",
    "               method='ward',\n",
    "               z_score=1,\n",
    "               row_colors=r_colors)\n",
    "\n",
    "g.ax_col_dendrogram.set_visible(False)\n",
    "g.cax.set_visible(False)\n",
    "\n",
    "\n",
    "\n",
    "legend_TN = [mpatches.Patch(color=c, label=l) for l,c in names_to_colors.items()]\n",
    "\n",
    "l2=g.ax_heatmap.legend(loc='center left',bbox_to_anchor=(1.01,0.85),handles=legend_TN,frameon=True)\n",
    "l2.set_title(title='Document Class',prop={'size':10})\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Feature Extraction\n",
    "TF-IDF features and clustering of news documents, used to get a unique signal for each document based on the words contained within it. Documents with similar words tend to cluster together.\n",
    "![tfidf](assets/images/tfidf_cluster.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Feature Extraction\n",
    "* These are a few examples of how to collect features from various datsets.\n",
    "* With robust and reliable feature extraction, features can then be used in a number of downstream applications\n",
    "* Features can be used for either supervised or unsupervised learning.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model Selection and Training\n",
    "* Many models are available\n",
    "* Important questions to ask:\n",
    "    1. How much do I care about predictive accuracy?\n",
    "    2. Do I care if the model parameters are interpretable?\n",
    "    3. How much data do I have available for training?\n",
    "    4. Underfitting and overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model Selection and Training\n",
    "How much do I care about predictive accuracy?\n",
    "- Simpler models make more assumptions about the relationship between input data and output\n",
    "- May sacrifice accuracy for simplicity\n",
    "- Example: Linear model vs. neural networks\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model Selection and Training\n",
    "In the case of a linear function, we are limited by the assumption that our input $X$ is proportionally related to the output $y$ by some value, $m$.\n",
    "\n",
    "\n",
    "$$y = m X + b$$\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "However, a neural network can model a much more complex relationship between $X$ and $y$ by taking the input $X$ and passing it through several \"layers\" of functions:\n",
    "\n",
    "$$ y = f(f(X;\\beta_{0}); \\beta_{1})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Therefore, you may get better predictions with a neural network, as it makes fewer assumptions about how $X$ and $y$ are related."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model Selection and Training\n",
    "\n",
    "<img src=\"assets/images/murphy_probability_mass.png\" style=\"width:600px;\"/>\n",
    "\n",
    "This figure from Kevin Murphy illustrates the relationship between model complexity (increasing from blue to green) and the complexity of a dataset. More complex models \"spread\" their ability to model more datasets but are less likely to model any particular dataset well. Models that are too simple (blue) make too many assumptions about the dataset and fail to model many more complex datasets.\n",
    "\n",
    "\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>\n",
    "Murphy KP. Machine Learning, A Probabilistic Perspective. MIT Press; 2012. Page 157\n",
    "</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model Selection and Training\n",
    "Do I care if the model parameters are interpretable?\n",
    "* Some models (linear models, in particular Generalized Linear Models or GLMs) are well studied and are frequently used in many fields for interpreting a relationship between two variables\n",
    "* GLMs have robust literature and statistical tests for comparing model parameters\n",
    "* Can discuss \"statistical significance\" of a correlation between input variables (i.e. Wald test in logistic regression models)\n",
    "* $y = mX + b$ is a GLM that assumes $y$ is a Gaussian distributed random variable\n",
    "* In this case we have an intuitive explanation of what $m$ is - a parameter that controls how variations in $X$ *proportionally* affect the output $y$\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model Selection and Training\n",
    "Do I care if the model parameters are interpretable?\n",
    "* However, other newer models are not as well studied but have been shown to be very flexible predictive models\n",
    "* Models such as Random Forest regression models and neural networks are very flexible and general models (i.e. they can model $f(x) = y$ no matter how complex the relationship between $x$ and $y$ is).\n",
    "* The problem is that we don't have a good way to interpret the meaning of the $\\beta$ values \"learned\" after model training for a neural network\n",
    "\n",
    "$$ y = f(f(X;\\beta_{0}); \\beta_{1})$$\n",
    "\n",
    "* The bottom line - if you need to make accurate predictions but don't care about model interpretation you should use whatever works best, whether that is a neural network, random forest, support vector machine or a GLM\n",
    "* If you need to have some kind of understanding of the model parameters or need to report statistical significance of relationships of input and output, use a GLM (logistic regression, Poisson regression, Gaussian etc)\n",
    "\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning, Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013. Chapters 4, 6, 10 and 15</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model selection and training\n",
    "How much data do I have available for training?\n",
    "* Big assumption with most machine learning models - your training data \"covers\" all the variance you expect to encounter in the real world (testing data)\n",
    "* Therefore if you have a small number of samples available to train on, it is more likely that your model will overfit the training data and make poor predictions with new samples\n",
    "* Analogous to learning a few examples but not learning the general \"rule\"\n",
    "\n",
    "\n",
    "* **General rule of thumb: ** *the more complex your model (i.e. number of parameters, layers etc), and more variables you are going to use (i.e. the number of features used to make predictions) the more samples you need to train a competent model*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model selection and training\n",
    "Underfitting and overfitting\n",
    "* The concepts described above are at the crux of machine learning\n",
    "* Poor prediction can come from two main sources\n",
    "    1. Underestimating the complexity between input and output (underfitting)\n",
    "    2. Overfitting the training data (learning specific examples and not the rule)\n",
    "* Framed as the bias-variance tradeoff\n",
    "    1. Models with high \"bias\" make more assumptions about input features and target output\n",
    "    2. Models with low \"bias\" make less assumptions about input features and target output and puts a greater emphasis on relationships in training data to estimate model parameters\n",
    "    3. While it may seem logical to reach for models with the lowest bias, there is a risk of overfitting training data that may contain noise not relevant to prediction, or the model ends up learning specific examples from training that do not generalize well"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine Learning Workflow - Model selection and training\n",
    "Underfitting and overfitting\n",
    "* These summarized in this figure \n",
    "\n",
    "<img src=\"assets/images/hastie_bias_var.png\" style=\"width:600px;\"/>\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning, Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013. Chapter 7</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "**Main goal of developing any machine learning model is to use a model that hits the middle of the above figure for your dataset!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Commonly Used Models\n",
    "* This section will go over a few commonly used models\n",
    "* Discuss model structure\n",
    "* A few pros and cons of each model\n",
    "* Many, can be found ready to use with the Python [scikit-learn](http://scikit-learn.org/stable/) package\n",
    "* Models:\n",
    "    1. Generalized Linear Models\n",
    "    2. Decision Trees\n",
    "    3. Random Forests\n",
    "    4. Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Generalized Linear Models\n",
    "* Some of the best studied models\n",
    "* Idea is to model the target ($y$) as the mean (or expected value, $\\mu$) of a member of the family of exponential distribution\n",
    "* The general form of the model is:\n",
    "\n",
    "\n",
    "<center> $$E(Y) = \\mu = g^{-1}(\\beta X)$$ </center>\n",
    "\n",
    "\n",
    "* Where the function $g$ is called the link function, and is dependent on the type of distribution modeled\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Generalized Linear Models\n",
    "<table>\n",
    "  <caption> <center> Generalized Linear Models and Link Functions </center></caption>\n",
    "  \n",
    "  <tr>\n",
    "      <th> Data Type </th>\n",
    "      <th> Distribution </th>\n",
    "      <th> Link function </th>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "      <td> Binary </td>\n",
    "      <td> Bernoulli </td>\n",
    "      <td> $\\mu = \\frac{1}{1+e^{-\\beta X}}$ </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "      <td> Linear response </td>\n",
    "      <td> Gaussian (aka Normal) </td>\n",
    "      <td> $\\mu = \\beta X$ (sometimes called the \"identity\" function) </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "      <td> Count (integer) </td>\n",
    "      <td> Poisson </td>\n",
    "      <td> $\\mu = e^{\\beta X}$ </td>\n",
    "  </tr>\n",
    "  \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Generalized Linear Models\n",
    "<table>\n",
    "  <caption> <center> Generalized Linear Models Pros and Cons </center></caption>\n",
    "  \n",
    "  <tr>\n",
    "      <th> Pros </th>\n",
    "      <th> Cons </th>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> The parameters $\\beta$ learned from data are interpretable </td>\n",
    "        <td> Are only capable of modeling simple behaviors in output </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Can run statistical tests on the $\\beta$ values for significance of correlation </td>\n",
    "        <td> Typically need a large sample number for good model performance </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Available through many open source software packages </td>\n",
    "        <td> Commonly used optimization algorithms assume $X$ is normally distributed, and get the maximum likelihood estimate of $\\beta$ which may not result in optimal predictions for every distribution of $X$! Bayesian estimation of $\\beta$ can overcome this, but the software for this use case is not as easy for beginners.</td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "      <td> Models can be constrained through regularization to prevent overfitting, or select for strong predictors for datasets with a large number of features. </td>\n",
    "      <td>  </td>\n",
    "  </tr>\n",
    "  \n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "import graphviz\n",
    "\n",
    "iris_data = load_iris()\n",
    "tree_classifier = DecisionTreeClassifier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(iris_data.data, iris_data.target, train_size=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_split=1e-07, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            presort=False, random_state=None, splitter='best')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_classifier.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.93333333333333335"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_classifier.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import sklearn.tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'iris.png.pdf'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot_data_from_tree = sklearn.tree.export_graphviz(tree_classifier, out_file=None, feature_names=iris_data.feature_names)\n",
    "g = graphviz.Source(dot_data_from_tree)\n",
    "g.render(filename='iris.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Decision Trees\n",
    "* Decision Trees are one of the simplest models available\n",
    "* Make binary splits based on values of input features\n",
    "* Seen throughout medical literature, typically in diagnostic or therapeutic algorithms\n",
    "* See [this link](http://www.r2d3.us/visual-intro-to-machine-learning-part-1/) for a fantasic visualization of the training process of decision trees\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\"> <p>Stephanie Lee and Tony Chu. Available at: http://www.r2d3.us/visual-intro-to-machine-learning-part-1/. Accessed November 24, 2017.</p></footer>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Decision Trees\n",
    "Decision tree model for classifying types of iris flowers based on sepal width, petal length and petal width\n",
    "<img src=\"assets/images/iris.png\" style=\"width:600px;\"/> \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Decision Trees\n",
    "Code for training and testing the above model:\n",
    "```python\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "iris_data = load_iris()\n",
    "tree_classifier = DecisionTreeClassifier()\n",
    "X_train, X_test, y_train, y_test = train_test_split(iris_data.data, iris_data.target, train_size=0.7)\n",
    "tree_classifier.fit(X_train, y_train)\n",
    "tree_classifier.score(X_test, y_test)\n",
    "Out: 0.93333333333333335\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Decision Trees\n",
    "<table>\n",
    "  <caption> <center> Decision Trees Pros and Cons </center></caption>\n",
    "  \n",
    "  <tr>\n",
    "      <th> Pros </th>\n",
    "      <th> Cons </th>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> The learned model is very interpretable. </td>\n",
    "        <td> Have a tendency to severely overfit training data. </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Very fast to train, can train large trees with limited computing power. </td>\n",
    "        <td> May require a complex tree to model all nuance within a dataset, making interpretability difficult.  </td>\n",
    "  </tr>\n",
    "  \n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Random Forests\n",
    "* Problem with one decision tree is that it will overfit the training data\n",
    "* This can be overcome by \"averaging\" a large number of trees\n",
    "* Basic ideas:\n",
    "    1. Train a large number of trees in parallel\n",
    "    2. Each tree sees a limited subset of training samples **and** a limited number of features\n",
    "    3. Model makes ultimate predictions by averaging predictions of all trees\n",
    "* Analogous to guidelines developed by expert committees - each expert's training and experience is different\n",
    "* Each expery may have \"overfit\" their mental model to the data they saw in training\n",
    "* Debating and communication between committee members \"averages\" out the differences, resulting in a good model\n",
    "* Called more generally an \"ensemble\" model (ensemble of small, weak predictors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97777777777777775"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(iris_data.data, iris_data.target, train_size=0.7)\n",
    "\n",
    "rfc = RandomForestClassifier(n_estimators=100, max_depth=3)\n",
    "rfc.fit(X_train, y_train)\n",
    "rfc.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Random Forests\n",
    "Let's return to the iris data from before and see if a random forest model performs better.\n",
    "\n",
    "```python\n",
    "X_train, X_test, y_train, y_test = train_test_split(iris_data.data, iris_data.target, train_size=0.7)\n",
    "\n",
    "rfc = RandomForestClassifier(n_estimators=100, max_depth=3)\n",
    "rfc.fit(X_train, y_train)\n",
    "rfc.score(X_test, y_test)\n",
    "Out: 0.97777777777777775 \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Random Forests\n",
    "<table>\n",
    "  <caption> <center> Random Forests Pros and Cons </center></caption>\n",
    "  \n",
    "  <tr>\n",
    "      <th> Pros </th>\n",
    "      <th> Cons </th>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Very powerful models, capable of modeling very complex relationships. </td>\n",
    "        <td> Final model is not easily interpreted. Can get an estimate of feature importance for prediction based on average reduction in entropy or with Gini index across all trees. </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Fast to train, all trees in the forest can be trained in parallel. Excellent for low resource settings. </td>\n",
    "        <td> No good rules for selecting parameters. Often need to fit a number of models to the dataset, varying forest size and maximum tree depth. May not be able to easily explain why one set of parameters was better/worse. </td>\n",
    "  </tr>\n",
    "  \n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Neural Networks\n",
    "* Modeled after behavior of neurons within brains\n",
    "* Idea is to pass output from one layer of neurons to another and so forth\n",
    "* Connections between neurons are modeled by weights between neurons\n",
    "* During training, weights are weakened and strengthened to improve model prediction\n",
    "* Popular with recent developments in computational power of graphical processing units (GPUs)\n",
    "    * GPUs are capable to carrying out large matrix calculations quickly, which are a core part of network computation\n",
    "    * Speed at which large networks can be trained has been reduced\n",
    "    * Networks with many layers (referred to as \"deep\" networks) are now feasible to train for many problems\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Neural Networks\n",
    "Core idea behind model is a nested function with \"weights\" between layers:\n",
    "\n",
    "$$y = f(\\beta_{n}... ,f(\\beta_{2},f( \\beta_{1},f(\\beta_{0},X))))$$\n",
    "\n",
    "Where the function $f$ is (classically) a well defined function with a continuous derivative. \n",
    "\n",
    "The first neural networks modeled the activation functions neurons (on/off behavior) using the sigmoid function.\n",
    "\n",
    "$$f(X, \\beta) = \\frac{1}{1+e^{-X\\beta}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "def sigmoid(x, beta):\n",
    "    return 1./(1.0 + math.exp(-beta * x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa090b15fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xx = np.linspace(-10.0, 10.0)\n",
    "yy = np.array([sigmoid(i, 1.0) for i in xx])\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.plot(xx, yy)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()\n",
    "fig.savefig('assets/images/sigmoid.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Neural Networks\n",
    "* Another way to think about this model - it's a nested set of GLMs. \n",
    "* Allows the GLM to overcome limitations in the complexity of the function it can model\n",
    "* [Tensorflow (Google's open-source deep learning library) neural network playground](http://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=circle&regDataset=reg-plane&learningRate=0.03&regularizationRate=0&noise=0&networkShape=4,2&seed=0.09844&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false)\n",
    "<p float=\"left\">\n",
    "    <img src=\"assets/images/sigmoid.png\" align=\"left\" width=\"50%\"/>\n",
    "    <img src=\"assets/images/NN_diagram.png\" align=\"left\" width=\"50%\"/>\n",
    "</p>\n",
    "\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning, Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013. Chapter 10 Page 5</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Commonly Used Models - Neural Networks\n",
    "<table>\n",
    "  <caption> <center> Neural Networks Pros and Cons </center></caption>\n",
    "  \n",
    "  <tr>\n",
    "      <th> Pros </th>\n",
    "      <th> Cons </th>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Very powerful models, capable of modeling very complex relationships. </td>\n",
    "        <td> Final model is not easily interpreted. Can get a sense of what features are learned at various layers of the network by looking at weights, but cannot test for significance of patterns. </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "        <td> Can be used with many different types of data, can be used with images, text, tabular data etc. </td>\n",
    "        <td> Notoriously finnicky to train, takes a long time to train due to diminishing error gradient as error signal is \"backpropagated\" through network (it can take a long time to optimize model weights) </td>\n",
    "  </tr>\n",
    "  \n",
    "  <tr>\n",
    "      <td> Given the flexibility and predictive power, huge research interest, lots of active development. </td>\n",
    "      <td> Still poorly understood, although progress on better theoretical understanding is being made. Some refer to the current period as analogous to \"engineering before Newtonian physics\". We are exploring how to build and use neural networks, but don't understand all the details and can't predict behavior. </td>\n",
    "  </tr>\n",
    "  \n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Applications in Radiology\n",
    "* Wide range of developing applications\n",
    "* Huge amount of labeled data - a precious resource for developing models\n",
    "* Already shown promise in development of automated disease classification\n",
    "\n",
    "<figure>\n",
    "    <img src=\"assets/images/lakhani_deep_TB.png\" align=\"center\" width=\"300px\"/>\n",
    "    <figcaption> An image from Lakhani et. al showing the areas of an image that activate a deep CNN for detecting tuberculosis lesions in chest radiographs. </figcaption>\n",
    "</figure>\n",
    "<footer id=\"attribution\" style=\"float:left; color:#999; background:#fff;\">\n",
    "<p>Lakhani P, Sundaram B. Deep Learning at Chest Radiography: Automated Classification of Pulmonary Tuberculosis by Using Convolutional Neural Networks. Radiology. 2017;284(2):574-582.</p>\n",
    "</footer>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Applications in Radiology\n",
    "* Automated processing of text, images, EKG signals....\n",
    "* Data from multiple sources can be combined to handle difficult problems\n",
    "* Few limitations on what can be done\n",
    "* More important questions are what *should* be done\n",
    "* Key point to remember is that machine learning relies on <font style=\"font-size:24px;\">data</font> - the more the better\n",
    "* Key questions:\n",
    "    * What information is hard to collect? \n",
    "    * How can that process of collecting difficult information be automated?\n",
    "    * What piecewise steps can I use to make something new? Better prognostics? Better diagnostics? More precise measurements?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Notes and Tips\n",
    "* Many great resources to learn machine learning\n",
    "* Books:\n",
    "    * [Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning, Data Mining, Inference, and Prediction. Springer Science & Business Media; 2013](https://www.amazon.com/Elements-Statistical-Learning-Prediction-Statistics/dp/0387848576/ref=sr_1_1?ie=UTF8&qid=1511587358&sr=8-1&keywords=the+elements+of+statistical+learning)\n",
    "        * One of the most respected materials in the field\n",
    "        * Covers fundamentals of all models discussed in this talk and beyond\n",
    "        * Requires undergraduate understanding of mathematics (calculus, linear algebra)\n",
    "    * [Murphy KP. Machine Learning, A Probabilistic Perspective. MIT Press; 2012.](https://www.amazon.com/Machine-Learning-Probabilistic-Perspective-Computation/dp/0262018020/ref=sr_1_1?ie=UTF8&qid=1511587446&sr=8-1&keywords=machine+learning+a+probabilistic+perspective)\n",
    "        * Covers almost all models discussed in *The Elements of Statisical Learning*, but takes a Bayesian approach to model derivation and analysis\n",
    "        * More in depth statisical and probabilitic perspective\n",
    "        * Written for graduate level students and beyond\n",
    "    * [How to Think Like a Computer Scientist, Learning With Python 3](http://openbookproject.net/thinkcs/python/english3e/#)\n",
    "        * For learning the basics of programming with Python\n",
    "        * Well written, easy to read\n",
    "        * For any learner from middle school and beyond\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Notes and Tips\n",
    "* Online Courses:\n",
    "    * [Stanford Online Machine Learning via Coursera](https://www.coursera.org/learn/machine-learning)\n",
    "        * Early online course\n",
    "        * Contains programming exercises with solutions\n",
    "        * Requires calculus and linear algebra\n",
    "    * [Duke Image Processing Course via Coursera](https://www.coursera.org/learn/image-processing)\n",
    "        * Covers basics of image processing and image analysis\n",
    "        * Covers some machine learning models\n",
    "        * Excellent for understanding feature extraction and preprocessing for downstream applications\n",
    "    * [3Blue1Brown Linear Algebra Youtube Course](https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)\n",
    "        * Covers fundamental mathematics for understanding many techniques and ML models\n",
    "        * Best graphical/intuitive description of linear algebra concepts "
   ]
  }
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