slides/lecture13-svm-dual.ipynb

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    "<left><img width=25% src=\"img/cornell_tech2.svg\"></left>\n",
    "\n",
    "# Lecture 13: Dual Formulation of Support Vector Machines\n",
    "\n",
    "### Applied Machine Learning\n",
    "\n",
    "__Volodymyr Kuleshov__<br>Cornell Tech"
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    "# Announcements\n",
    "\n",
    "* Assignment 3 is due on Wed\n",
    "* Graded project proposals will be released today\n",
    "* Prelim will be on 10/30, in class\n",
    "* Practice prelim will be released today or tomorrow"
   ]
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    "# Part 1: Nearest Neighbors and Non-Parametric ML\n",
    "\n",
    "In this lecture, we continue looking at Support Vector Machines (SVMs), and define a new formulation of the max-margin problem.\n",
    "\n",
    "Before we do that, we start with a general concept---non-parametric algorithms."
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    "# A Simple Classification Algorithm: Nearest Neighbors\n",
    "\n",
    "Suppose we are given a training dataset ${D} = \\{(x^{(1)}, y^{(1)}), (x^{(2)}, y^{(2)}), \\ldots, (x^{(n)}, y^{(n)})\\}$. At inference time, we receive a query point $x'$ and we want to predict its label $y'$."
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    "A really simple but suprisingly effective way of returning $y'$ is the *nearest neighbors* approach.\n",
    "* Given a query datapoint $x'$, find the training example $(x, y)$ in ${D}$ that's closest to $x'$, in the sense that $x$ is \"nearest\" to $x'$\n",
    "* Return $y$, the label of the \"nearest neighbor\" $x$."
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    "In the example below on the Iris dataset, the red cross denotes the query $x'$. The closest class to it is \"Virginica\". (We're only using the first two features in the dataset for simplicity.)"
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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [12, 4]\n",
    "\n",
    "# Plot also the training points\n",
    "p1 = plt.scatter(iris_X.iloc[:, 0], iris_X.iloc[:, 1], c=iris_y,\n",
    "            edgecolor='k', s=50, cmap=plt.cm.Paired)\n",
    "p2 = plt.plot([7.5], [4], 'rx', ms=10, mew=5)\n",
    "plt.xlabel('Sepal Length')\n",
    "plt.ylabel('Sepal Width')\n",
    "plt.legend(['Query Point', 'Training Data'], loc='lower right')\n",
    "plt.legend(handles=p1.legend_elements()[0]+p2, labels=['Setosa', 'Versicolour', 'Virginica', 'Query'], loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Choosing a Distance Function\n",
    "\n",
    "How do we select the point $x$ that is the closest to the query point $x'$? There are many options:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* The Euclidean distance $|| x - x' ||_2 = \\sqrt{\\sum_{j=1}^d |x_j - x'_j|^2)}$ is a popular choice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* The Minkowski distance $|| x - x' ||_p = (\\sum_{j=1}^d |x_j - x'_j|^p)^{1/p}$ generalizes the Euclidean, L1 and other distances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* The Mahalanobis distance $\\sqrt{x^\\top V x}$ for a positive semidefinite matrix $V \\in \\mathbb{R}^{d \\times d}$ also generalizes the Euclidean distnace."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* Discrete-valued inputs can be examined via the Hamming distance $|\\{j : x_j \\neq x_j'\\}|$ and other distances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Let's apply Nearest Neighbors to the above dataset using the Euclidean distance (or equiavalently, Minkowski with $p=2$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sepal Width')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html\n",
    "from sklearn import neighbors\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "# Train a Nearest Neighbors Model\n",
    "clf = neighbors.KNeighborsClassifier(n_neighbors=1, metric='minkowski', p=2)\n",
    "clf.fit(iris_X.iloc[:,:2], iris_y)\n",
    "\n",
    "# Create color maps\n",
    "cmap_light = ListedColormap(['orange', 'cyan', 'cornflowerblue'])\n",
    "cmap_bold = ListedColormap(['darkorange', 'c', 'darkblue'])\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, x_max]x[y_min, y_max].\n",
    "x_min, x_max = iris_X.iloc[:, 0].min() - 1, iris_X.iloc[:, 0].max() + 1\n",
    "y_min, y_max = iris_X.iloc[:, 1].min() - 1, iris_X.iloc[:, 1].max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),\n",
    "                     np.arange(y_min, y_max, 0.02))\n",
    "Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure()\n",
    "plt.pcolormesh(xx, yy, Z, cmap=cmap_light)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(iris_X.iloc[:, 0], iris_X.iloc[:, 1], c=iris_y, cmap=cmap_bold,\n",
    "            edgecolor='k', s=60)\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "\n",
    "plt.xlabel('Sepal Length')\n",
    "plt.ylabel('Sepal Width')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "In the above example, the regions of the 2D space that are assigned to each class are highly irregular. In areas where the two classes overlap, the decision of the boundary flips between the classes, depending on which point is closest to it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# K-Nearest Neighbors\n",
    "\n",
    "Intuitively, we expect the true decision boundary to be smooth. Therefore, we average $K$ nearest neighbors at a query point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Given a query datapoint $x'$, find the $K$ training examples ${N} = \\{(x^{(1)}, y^{(1)}), (x^{(2)}, y^{(2)}), \\ldots, (x^{(K)}, y^{(K)})\\} \\subseteq D$  closest to $x'$.\n",
    "* Return $y_{N}$, the consensus label of the neighborhood ${N}$.\n",
    "\n",
    "The consesus $y_{N}$ can be determined by voting, weighted average, kernels, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's look at Nearest Neighbors with a neighborhood of 30. The decision boundary is much smoother than before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sepal Width')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html\n",
    "# Train a Nearest Neighbors Model\n",
    "clf = neighbors.KNeighborsClassifier(n_neighbors=30, metric='minkowski', p=2)\n",
    "clf.fit(iris_X.iloc[:,:2], iris_y)\n",
    "Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure()\n",
    "plt.pcolormesh(xx, yy, Z, cmap=cmap_light)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(iris_X.iloc[:, 0], iris_X.iloc[:, 1], c=iris_y, cmap=cmap_bold,\n",
    "            edgecolor='k', s=60)\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "\n",
    "plt.xlabel('Sepal Length')\n",
    "plt.ylabel('Sepal Width')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Algorithm: K-Nearest Neighbors\n",
    "\n",
    "* __Type__: Supervised learning (regression and classification)\n",
    "* __Model family__: Consensus over $K$ training instances.\n",
    "* __Objective function__: Euclidean, Minkowski, Hamming, etc.\n",
    "* __Optimizer__: Non at training. Nearest neighbor search at inference using specialized search algorithms (Hashing, KD-trees).\n",
    "* __Probabilistic interpretation__: Directly approximating the density $P_\\text{data}(y|x)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Non-Parametric Models\n",
    "\n",
    "Nearest neighbors is an example of a *non-parametric* model. \n",
    "<!-- Parametric vs. non-parametric are is a key distinguishing characteristic for machine learning models. -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A parametric model $f_\\theta(x) : {X} \\times \\Theta \\to {Y}$ is defined by a finite set of parameters $\\theta \\in \\Theta$ whose dimensionality is constant with respect to the dataset. Linear models of the form\n",
    "$$ f_\\theta(x) = \\theta^\\top x $$\n",
    "are an example of a parametric model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In a non-parametric model, the function $f$ uses the entire training dataset (or a post-proccessed version of it) to make predictions, as in $K$-Nearest Neighbors. \n",
    "\n",
    "In other words, the complexity of the model increases with dataset size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Pros and Cons of KNN\n",
    "\n",
    "Pros:\n",
    "* No information is lost at train time.\n",
    "* Can approximate any data distribution arbtrarily well.\n",
    "\n",
    "Cons:\n",
    "* Need to store entire dataset to make queries, which is computationally prohibitive.\n",
    "* Number of data needed scale exponentially with dimension (\"curse of dimensionality\")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<left><img width=25% src=\"img/cornell_tech2.svg\"></left>\n",
    "# Part 2: Dual Formulation of SVMs\n",
    "\n",
    "Let's now apply Lagrange duality to support vector machines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Review: Binary Classification & Linear Model\n",
    "\n",
    "In this lecture, we will work with linear models of the form:\n",
    "\\begin{align*}\n",
    "f_\\theta(x) & = \\theta_0 + \\theta_1 \\cdot x_1 + \\theta_2 \\cdot x_2 + ... + \\theta_d \\cdot x_d\n",
    "\\end{align*}\n",
    "where $x \\in \\mathbb{R}^d$ is a vector of features and $y \\in \\{-1, 1\\}$ is the target. The $\\theta_j$ are the *parameters* of the model.\n",
    "\n",
    "We can represent the model in a vectorized form\n",
    "\\begin{align*}\n",
    "f_\\theta(x) = \\theta^\\top x + \\theta_0.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Review: Classification Margins\n",
    "\n",
    "The margin $\\gamma^{(i)}$ is the distance between the separating hyperplane and the datapoint $x^{(i)}$.\n",
    "<center><img width=30% src=\"img/margin.png\"></center>\n",
    "Large margins are good: data should be far from the decision boundary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Review: Maximizing the Margin\n",
    "\n",
    "We saw that maximizing the margin of a linear model amounts to solving the following optimization problem.\n",
    "\\begin{align*}\n",
    "\\min_{\\theta,\\theta_0} \\frac{1}{2}||\\theta||^2 \\; &  \\\\\n",
    "\\text{subject to } \\; & y^{(i)} f(x^{(i)}) \\geq 1 \\; \\text{for all $i$}\n",
    "\\end{align*}\n",
    "\n",
    "We are going to look at a different way of optimizing this objective. But first, we start by defining Lagrange duality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Penalties vs. Constraints\n",
    "\n",
    "Penalties and constraints are closely related. Consider our constrained optimization problem:\n",
    "\\begin{align*}\n",
    "\\min_{\\theta \\in \\mathbb{R}^d} \\; & \\frac{1}{2}||\\theta||^2 \\\\\n",
    "\\text{such that } \\; & 1 - y^{(i)} f_\\theta(x^{(i)}) \\leq 0 \\text{ for $k =1,2,\\ldots,K$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We define its *primal Lagrange form* to be\n",
    "$$\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} \\left(J(\\theta) + \\sum_{k=1}^K \\lambda_k c_k(\\theta) \\right)$$\n",
    "where $c_k = 1 - y^{(i)} f_\\theta(x^{(i)})$ and $J(\\theta) = \\frac{1}{2}||\\theta||^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "These two forms have the same optimum $\\theta^*$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Penalties vs. Constraints\n",
    "\n",
    "Penalties and constraints are closely related. Consider our constrained optimization problem:\n",
    "\\begin{align*}\n",
    "\\min_{\\theta \\in \\mathbb{R}^d} \\; & J(\\theta) \\\\\n",
    "\\text{such that } \\; & c_k(\\theta) \\leq 0 \\text{ for $k =1,2,\\ldots,K$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We define its *primal Lagrange form* to be\n",
    "$$\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} \\left(J(\\theta) + \\sum_{k=1}^K \\lambda_k c_k(\\theta) \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "These two forms have the same optimum $\\theta^*$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Why is this true? Consider again\n",
    "$$\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} \\left(J(\\theta) + \\sum_{k=1}^K \\lambda_k c_k(\\theta) \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* If a $c_k$ is violated ($c_k > 0$) then $\\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda)$ is $\\infty$ as $\\lambda_k \\to \\infty$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* If no $c_k$ is violated and $c_k < 0$ then the optimal $\\lambda_k = 0$ (any bigger value makes the inner objective smaller).\n",
    "    * If $c_k < 0$ for all $k$ then $\\lambda_k=0$ for all $k$ and\n",
    "    $$\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda) = \\min_{\\theta \\in \\mathbb{R}^d} J(\\theta)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Thus, $\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta)$ is the solution to our original optimization problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Lagrangian of the SVM Problem\n",
    "\n",
    "Consider the following objective, the Lagrangian of the max-margin optimization problem.\n",
    "\n",
    "\\begin{align*}\n",
    "L(\\theta, \\theta_0, \\lambda) = \\frac{1}{2}||\\theta||^2 + \\sum_{i=1}^n \\lambda_i \\left(1-y^{(i)}((x^{(i)})^\\top\\theta+\\theta_0)\\right)\n",
    "\\end{align*}\n",
    "\n",
    "We have put each constraint inside the objective function and added a penalty $\\lambda_i$ to it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lagrange Dual\n",
    "\n",
    "Now consider the following two problem over $\\lambda\\geq 0$:\n",
    "$$\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta) = \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda) \\;\\;\\;\\;\\;\\;\\;\\; \\max_{\\lambda \\geq 0}{D}(\\lambda) = \\max_{\\lambda \\geq 0} \\min_{\\theta \\in \\mathbb{R}^d} {L}(\\theta, \\lambda). $$\n",
    "<!-- = \\max_{\\lambda \\geq 0} \\min_{\\theta \\in \\mathbb{R}^d} \\left(J(\\theta) + \\sum_{k=1}^K \\lambda_k c_k(\\theta) \\right).$$ -->\n",
    "\n",
    "We call the second one the *Lagrange dual* of the primal optimization problem $\\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta)$. \n",
    "\n",
    "We can always construct a dual for the primal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<!-- # Lagrange Duality -->\n",
    "\n",
    "The dual is interesting because we always have:\n",
    "$$ \\max_{\\lambda \\geq 0}{D}(\\lambda) = \\max_{\\lambda \\geq 0} \\min_{\\theta \\in \\mathbb{R}^d} {L}(\\theta, \\lambda) \\leq \\min_{\\theta \\in \\mathbb{R}^d} \\max_{\\lambda \\geq 0} {L}(\\theta, \\lambda) = \\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Moreover, in many cases (including SVMs), we have\n",
    "$$ \\max_{\\lambda \\geq 0}{D}(\\lambda) = \\min_{\\theta \\in \\mathbb{R}^d} {P}(\\theta).$$\n",
    "Thus, the primal and the dual are equivalent!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Dual of the SVM Problem\n",
    "\n",
    "Consider optimizing the above Lagrangian over $\\theta, \\theta_0$ for any value of $\\lambda$.\n",
    "$$\\min_{\\theta, \\theta_0} L(\\theta, \\theta_0, \\lambda) = \\min_{\\theta, \\theta_0} \\left( \\frac{1}{2}||\\theta||^2 + \\sum_{i=1}^n \\lambda_i \\left(1-y^{(i)}((x^{(i)})^\\top\\theta+\\theta_0)\\right)\\right)$$\n",
    "This objective is quadratic in $\\theta$; hence it has a single minimum in $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can find it by setting the derivative to zero and solving for $\\theta, \\theta_0$:\n",
    "\\begin{align*}\n",
    "\\theta & = \\sum_{i=1}^n \\lambda_i y^{(i)} x^{(i)} \\\\\n",
    "0 & = \\sum_{i=1}^n \\lambda_i y^{(i)}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Substituting this into the Lagrangian we obtain the following expression for the dual $\\max_{\\lambda\\geq 0} {D}(\\lambda) = \\max_{\\lambda\\geq 0} \\min_{\\theta, \\theta_0} L(\\theta, \\theta_0, \\lambda)$:\n",
    "\\begin{align*}\n",
    "\\max_{\\lambda} & \\sum_{i=1}^n \\lambda_i - \\frac{1}{2} \\sum_{i=1}^n \\sum_{k=1}^n \\lambda_i \\lambda_k y^{(i)} y^{(k)} (x^{(i)})^\\top x^{(k)}  \\\\\n",
    "\\text{subject to } \\; & \\sum_{i=1}^n \\lambda_i y^{(i)} = 0 \\\\\n",
    "& \\lambda_i \\geq 0 \\; \\text{for all $i$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Properties of the Dual\n",
    "\n",
    "We can make several observations about the dual\n",
    "\\begin{align*}\n",
    "\\max_{\\lambda} & \\sum_{i=1}^n \\lambda_i - \\frac{1}{2} \\sum_{i=1}^n \\sum_{k=1}^n \\lambda_i \\lambda_k y^{(i)} y^{(k)} (x^{(i)})^\\top x^{(k)}  \\\\\n",
    "\\text{subject to } \\; & \\sum_{i=1}^n \\lambda_i y^{(i)} = 0 \\;\\text{and}\\; \\lambda_i \\geq 0 \\; \\text{for all $i$}\n",
    "\\end{align*}\n",
    "\n",
    "* This is a constrained quadratic optimization problem.\n",
    "* The number of variables $\\lambda_i$ equals $n$, the number of data points.\n",
    "* Objective only depends on products $(x^{(i)})^\\top x^{(j)}$ (more on this soon!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# When to Solve the Dual\n",
    "\n",
    "When should we be solving the dual vs. the primal?\n",
    "* The dimensionality of the primal depends on the number of features. If we have a few features and many datapoints, we should use the primal.\n",
    "* Conversely, if we have a lot of features, but fewer datapoints, we want to use the dual.\n",
    "\n",
    "In the next lecture, we will see how we can use this property to solve machine learning problems with a very large number of features (even possibly infinite!)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<left><img width=25% src=\"img/cornell_tech2.svg\"></left>\n",
    "# Part 3: Practical Considerations for SVM Duals\n",
    "\n",
    "We continue our discussion of the dual formulation of the SVM with additional practical details about the dual formulation is defined an used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Review: Primal and Dual Formulations\n",
    "\n",
    "Recall that the the max-margin hyperplane can be formulated as the solution to the following *primal* optimization problem.\n",
    "\\begin{align*}\n",
    "\\min_{\\theta,\\theta_0} \\frac{1}{2}||\\theta||^2 \\; &  \\\\\n",
    "\\text{subject to } \\; & y^{(i)}((x^{(i)})^\\top\\theta+\\theta_0)\\geq 1 \\; \\text{for all $i$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The solution to this problem also happens to be given by the following *dual* problem:\n",
    "\\begin{align*}\n",
    "\\max_{\\lambda} & \\sum_{i=1}^n \\lambda_i - \\frac{1}{2} \\sum_{i=1}^n \\sum_{k=1}^n \\lambda_i \\lambda_k y^{(i)} y^{(k)} (x^{(i)})^\\top x^{(k)}  \\\\\n",
    "\\text{subject to } \\; & \\sum_{i=1}^n \\lambda_i y^{(i)} = 0 \\\\\n",
    "& \\lambda_i \\geq 0 \\; \\text{for all $i$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Review: Non-Separable Problems\n",
    "\n",
    "Our dual problem assumes that a separating hyperplane exists. If it doesn't, our optimization problem does not have a solution and we need to modify it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Our solution is going to be to make each constraint \"soft\", by introducing \"slack\" variables, which allow the constraint to be violated.\n",
    "$$\n",
    "y^{(i)}((x^{(i)})^\\top\\theta+\\theta_0)\\geq 1 - \\xi_i.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In the optimization problem, we assign a penalty $C$ to these slack variables to obtain:\n",
    "\\begin{align*}\n",
    "\\min_{\\theta,\\theta_0, \\xi}\\; & \\frac{1}{2}||\\theta||^2 + C \\sum_{i=1}^n \\xi_i \\;  \\\\\n",
    "\\text{subject to } \\; & y^{(i)}((x^{(i)})^\\top\\theta+\\theta_0)\\geq 1 - \\xi_i \\; \\text{for all $i$} \\\\\n",
    "& \\xi_i \\geq 0\n",
    "\\end{align*}\n",
    "\n",
    "This is the primal problem. Let's now form its dual."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Non-Separable Dual\n",
    "\n",
    "We can also formulate the dual to this problem. First, the Lagrangian $L(\\lambda, \\mu,\\theta,\\theta_0,\\xi)$ equals\n",
    "\\begin{align*}\n",
    "\\frac{1}{2}||\\theta||^2 + C \\sum_{i=1}^n \\xi_i - \\sum_{i=1}^n \\lambda_i \\left(y^{(i)}((x^{(i)})^\\top\\theta+\\theta_0)- 1\\right) - \\sum_{i=1}^n \\mu_i\\xi_i.\n",
    "\\end{align*}\n",
    "\n",
    "The dual objective of this problem will equal \n",
    "$${D}(\\lambda, \\mu) = \\min_{\\theta,\\theta_0,\\xi} L(\\lambda, \\mu,\\theta,\\theta_0,\\xi).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As earlier, we can solve for the optimal $\\theta, \\theta_0$ in closed form and plug back the resulting values into the objective. \n",
    "\n",
    "We can then show that the dual takes the following form:\n",
    "\\begin{align*}\n",
    "\\max_{\\lambda} & \\sum_{i=1}^n \\lambda_i - \\frac{1}{2} \\sum_{i=1}^n \\sum_{k=1}^n \\lambda_i \\lambda_k y^{(i)} y^{(k)} (x^{(i)})^\\top x^{(k)}  \\\\\n",
    "\\text{subject to } \\; & \\sum_{i=1}^n \\lambda_i y^{(i)} = 0 \\\\\n",
    "& C \\geq \\lambda_i \\geq 0 \\; \\text{for all $i$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Coordinate Descent\n",
    "\n",
    "Coordinate descent is a general way to optimize functions $f(x)$ of multiple variables $x \\in \\mathbb{R}^d$:\n",
    "\n",
    "1. Choose a dimension $j \\in \\{1,2,\\ldots,d\\}$.\n",
    "2. Optimize $f(x_1, x_2, \\ldots, x_j, \\ldots, x_d)$ over $x_j$ while keeping the other variables fixed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Here, we visualize coordinate descent applied to a 2D quadratic function.\n",
    "<center><img width=50% src=\"img/coordinate_descent.png\"></center>\n",
    "The red line shows the trajectory of coordinate descent. Each \"step\" in the trajectory is an iteration of the algorithm. Image from Wikipedia."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Sequential Minimal Optimization\n",
    "\n",
    "We can apply a form of coordinate descent to solve the dual:\n",
    "\\begin{align*}\n",
    "\\max_{\\lambda} & \\sum_{i=1}^n \\lambda_i - \\frac{1}{2} \\sum_{i=1}^n \\sum_{k=1}^n \\lambda_i \\lambda_k y^{(i)} y^{(k)} (x^{(i)})^\\top x^{(k)}  \\\\\n",
    "\\text{subject to } \\; & \\sum_{i=1}^n \\lambda_i y^{(i)} = 0 \\;\\text{and}\\; C \\geq \\lambda_i \\geq 0 \\; \\text{for all $i$}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A popular, efficient algorithm is Sequential Minimal Optimization (SMO):\n",
    "* Take a pair $\\lambda_i, \\lambda_j$, possibly using heuristics to guide choice of $i,j$.\n",
    "* Reoptimize over $\\lambda_i, \\lambda_j$ while keeping the other variables fixed.\n",
    "* Repeat the above until convergence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Obtaining a Primal Solution from the Dual\n",
    "\n",
    "Next, assuming we can solve the dual, how do we find a separating hyperplane $\\theta, \\theta_0$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Recall that we already found an expression for the optimal $\\theta^*$ (in the separable case) as a function of $\\lambda$:\n",
    "$$\n",
    "\\theta^* = \\sum_{i=1}^n \\lambda_i y^{(i)} x^{(i)}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Once we know $\\theta^*$ it easy to check that the solution to $\\theta_0$ is given by\n",
    "$$\n",
    "\\theta_0^* = -\\frac{\\max_{i:y^{(i)}=-1} (\\theta^*)^\\top x^{(i)} + \\min_{i:y^{(i)}=-1} (\\theta^*)^\\top x^{(i)}}{2}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Support Vectors\n",
    "\n",
    "A powerful property of the SVM dual is that at the optimum, most variables $\\lambda_i$ are zero! Thus, $\\theta$ is a sum of a small number of points:\n",
    "$$\n",
    "\\theta^* = \\sum_{i=1}^n \\lambda_i y^{(i)} x^{(i)}.\n",
    "$$\n",
    "\n",
    "The points for which $\\lambda_i > 0$ are precisely the points that lie on the margin (are closest to the hyperplane). \n",
    "\n",
    "These are called *support vectors*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Dual SVMs are Non-Parametric\n",
    "\n",
    "Consider now a prediction $(\\theta^*)^\\top x'$ from the model at $x'$:\n",
    "$$\n",
    "(\\theta^*)^\\top x' = \\sum_{i=1}^n \\lambda_i y^{(i)} \\left( (x^{(i)})^\\top x' \\right).\n",
    "$$\n",
    "\n",
    "The prediction is a weighted average of the data, just as in k-NN!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Notation and The Iris Dataset\n",
    "\n",
    "To demonstrate how to use the dual version of the SVM, we are going to again use the Iris flower dataset.\n",
    "\n",
    "We will look at the binary classification version of this dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
       "0                 5.1               3.5                1.4               0.2   \n",
       "4                 5.0               3.6                1.4               0.2   \n",
       "8                 4.4               2.9                1.4               0.2   \n",
       "12                4.8               3.0                1.4               0.1   \n",
       "16                5.4               3.9                1.3               0.4   \n",
       "\n",
       "    target  \n",
       "0       -1  \n",
       "4       -1  \n",
       "8       -1  \n",
       "12      -1  \n",
       "16      -1  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn import datasets\n",
    "\n",
    "# Load the Iris dataset\n",
    "iris = datasets.load_iris(as_frame=True)\n",
    "iris_X, iris_y = iris.data, iris.target\n",
    "\n",
    "# subsample to a third of the data points\n",
    "iris_X = iris_X.loc[::4]\n",
    "iris_y = iris_y.loc[::4]\n",
    "\n",
    "# create a binary classification dataset with labels +/- 1\n",
    "iris_y2 = iris_y.copy()\n",
    "iris_y2[iris_y2==2] = 1\n",
    "iris_y2[iris_y2==0] = -1\n",
    "\n",
    "# print part of the dataset\n",
    "pd.concat([iris_X, iris_y2], axis=1).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's visualize this dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x120be94e0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = [12, 4]\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "# create 2d version of dataset and subsample it\n",
    "X = iris_X.to_numpy()[:,:2]\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, .02), np.arange(y_min, y_max, .02))\n",
    "\n",
    "# Plot also the training points\n",
    "p1 = plt.scatter(X[:, 0], X[:, 1], c=iris_y2, s=60, cmap=plt.cm.Paired)\n",
    "plt.xlabel('Petal Length')\n",
    "plt.ylabel('Petal Width')\n",
    "plt.legend(handles=p1.legend_elements()[0], labels=['Setosa', 'Not Setosa'], loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can run the dual version of the SVM by importing an implementation from `sklearn`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#https://scikit-learn.org/stable/auto_examples/svm/plot_separating_hyperplane.html\n",
    "from sklearn import svm\n",
    "\n",
    "# fit the model, don't regularize for illustration purposes\n",
    "clf = svm.SVC(kernel='linear', C=1000) # this optimizes the dual\n",
    "# clf = svm.LinearSVC() # this optimizes for the primal\n",
    "clf.fit(X, iris_y2)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=iris_y2, s=30, cmap=plt.cm.Paired)\n",
    "Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "\n",
    "# plot decision boundary and margins\n",
    "plt.contour(xx, yy, Z, colors='k', levels=[-1, 0, 1], alpha=0.5,\n",
    "           linestyles=['--', '-', '--'])\n",
    "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], s=100,\n",
    "           linewidth=1, facecolors='none', edgecolors='k')\n",
    "plt.xlim([4.6, 6])\n",
    "plt.ylim([2.25, 4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Algorithm: Support Vector Machine Classification (Dual Form)\n",
    "\n",
    "* __Type__: Supervised learning (binary classification)\n",
    "* __Model family__: Linear decision boundaries.\n",
    "* __Objective function__: Dual of SVM optimization problem.\n",
    "* __Optimizer__: Sequential minimal optimization.\n",
    "* __Probabilistic interpretation__: No simple interpretation!"
   ]
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "celltoolbar": "Slideshow",
  "colab": {
   "collapsed_sections": [],
   "name": "neural-ode.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "rise": {
   "controlsTutorial": false,
   "height": 900,
   "help": false,
   "margin": 0,
   "maxScale": 2,
   "minScale": 0.2,
   "progress": true,
   "scroll": true,
   "theme": "simple",
   "width": 1200
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}