slides/lecture21-boosting.ipynb

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   "source": [
    "<left><img width=25% src=\"img/cornell_tech2.svg\"></left>\n",
    "\n",
    "# Lecture 21: Boosting\n",
    "\n",
    "### Applied Machine Learning\n",
    "\n",
    "__Volodymyr Kuleshov__<br>Cornell Tech"
   ]
  },
  {
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   "source": [
    "# Announcement\n",
    "\n",
    "* Project proposals have been graded over the weekend. \n",
    "* Milestone due on 11/7.\n",
    "* HW3 will be graded next week. Prelim will be graded after that.\n",
    "* We will hold review session for the prelim."
   ]
  },
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   "source": [
    "# Part 1: Boosting and Ensembling\n",
    "\n",
    "We will look at ways in which multiple machine learning can be combined.\n",
    "\n",
    "In particular, we will look at a way of combining models called *boosting*.\n",
    "<!-- We are now going to see a different way of combining models called *boosting*. -->"
   ]
  },
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   "source": [
    "# Review: Overfitting\n",
    "\n",
    "Overfitting is one of the most common failure modes of machine learning.\n",
    "* An expressive model (e.g., polynomial) fits training data perfectly.\n",
    "* But it makes incorrect test set predictions, and doesn't generalize."
   ]
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   "source": [
    "# Review: Bagging\n",
    "\n",
    "*Bagging* reduces *overfitting* by averaging many expressive models .\n",
    "\n",
    "```python\n",
    "for i in range(n_models):\n",
    "    # collect data samples and fit models\n",
    "    X_i, y_i = sample_with_replacement(X, y, n_samples)\n",
    "    model = Model().fit(X_i, y_i)\n",
    "    ensemble.append(model)\n",
    "\n",
    "# output average prediction at test time:\n",
    "y_test = ensemble.average_prediction(x_test)\n",
    "```\n",
    "<!-- Data samples taken with replacement are known as bootstrap samples. -->"
   ]
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   "source": [
    "# Review: Underfitting\n",
    "\n",
    "Underfitting is another common problem in machine learning.\n",
    "* The model is too simple to fit the data well.\n",
    "* Training performance is low, hence test performance is low."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# Boosting\n",
    "\n",
    "The idea of *boosting* is to reduce *underfitting* by combining models that correct each others' errors."
   ]
  },
  {
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   "source": [
    "* As in bagging, we combine many models $g_t$ into one *ensemble* $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "* Unlike bagging, the $g_t$ are __small__ and tend to __underfit__."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "* Each $g_t$ fits the points where the previous models made errors."
   ]
  },
  {
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   "source": [
    "# Weak Learners\n",
    "\n",
    "A key ingredient of a boosting algorithm is a *weak learner*.\n",
    "\n",
    "* Intuitively, this is a model that is slightly better than random.\n",
    "* Examples of weak learners include: small linear models, small decision trees."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "# Structure of a Boosting Algorithm\n",
    "\n",
    "Boosting reduces *underfitting* via models that correct each others' errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "1. Compute weights $w^{(i)}$ for each $i$ based on $t$-th model predictions $f_t(x^{(i)})$ and targets $y^{(i)}$. Give more weight to points with errors."
   ]
  },
  {
   "cell_type": "markdown",
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    }
   },
   "source": [
    "2. Fit new weak learner $g_t$ on $\\mathcal{D} = \\{(x^{(i)}, y^{(i)})\\}$ with weights $w^{(i)}$."
   ]
  },
  {
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   "source": [
    "3. Set $f_{t+1} = f_t + \\alpha_t g_t$ for some weight $\\alpha_t$. Go to Step 1 and repeat."
   ]
  },
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   "source": [
    "In Python-like pseudocode this looks as follows:\n",
    "\n",
    "```python\n",
    "weights, ensemble = np.ones(n_data,), Ensemble([])\n",
    "for i in range(n_models):\n",
    "    model = SimpleBaseModel().fit(X, y, weights)\n",
    "    predictions = ensemble.predict(X)\n",
    "    model_weight, weights = update_weights(weights, predictions)\n",
    "    ensemble.add(model, model_weight)\n",
    "\n",
    "# output consensus prediction at test time:\n",
    "y_test = ensemble.predict(y_test)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "# Origins of Boosting\n",
    "\n",
    "Boosting was initially developed in the 90s within theoretical ML."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "* Boosting originally addressed a theoretical question: can weak learners (>50% accuracy) can be combined into a strong learner?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   "source": [
    "* This research led to a practical algorithm called *AdaBoost*."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "There are now many types of boosting algorithms.\n",
    "<!-- Today, there exist many algorithms that are considered types of boosting, even though they're not derived from the perspective of theoretical ML. -->"
   ]
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   "source": [
    "# Algorithm: AdaBoost\n",
    "\n",
    "* __Type__: Supervised learning (classification).\n",
    "* __Model family__: Ensembles of weak learners (often decision trees).\n",
    "* __Objective function__: Exponential loss.\n",
    "* __Optimizer__: Forward stagewise additive model building."
   ]
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  {
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   "source": [
    "# Defining AdaBoost\n",
    "\n",
    "One of the first practical boosting algorithms was *AdaBoost*.\n",
    "\n",
    "We start with uniform $w^{(i)} = 1/n$ and $f = 0$. Then for $t=1,2,...,T$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "1. Fit weak learner $g_t$ on $\\mathcal{D}$ with weights $w^{(i)}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "2. Compute misclassification error $e_t = \\frac{\\sum_{i=1}^n w^{(i)} \\mathbb{I}\\{y^{(i)} \\neq f(x^{(i)})\\}}{\\sum_{i=1}^n w^{(i)}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "3. Compute model weight $\\alpha_t = \\log[(1-e_t)/e_t]$. Set $f \\gets f + \\alpha_t g_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "4. Compute new data weights $w^{(i)} \\gets w^{(i)}\\exp[\\alpha_t \\mathbb{I}\\{y^{(i)} \\neq f(x^{(i)})\\} ]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "# AdaBoost: An Example\n",
    "\n",
    "Let's implement AdaBoost on a simple dataset to see what it can do."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's start by creating a classification dataset."
   ]
  },
  {
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   "execution_count": 1,
   "metadata": {
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   "outputs": [],
   "source": [
    "# https://scikit-learn.org/stable/auto_examples/ensemble/plot_AdaBoost_twoclass.html\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_gaussian_quantiles\n",
    "\n",
    "# Construct dataset\n",
    "X1, y1 = make_gaussian_quantiles(cov=2., n_samples=200, n_features=2, n_classes=2, random_state=1)\n",
    "X2, y2 = make_gaussian_quantiles(mean=(3, 3), cov=1.5, n_samples=300, n_features=2, n_classes=2, random_state=1)\n",
    "X = np.concatenate((X1, X2))\n",
    "y = np.concatenate((y1, - y2 + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "We can visualize this dataset using `matplotlib`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
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      "text/plain": [
       "<matplotlib.legend.Legend at 0x12afda198>"
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",
      "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_colors, plot_step, class_names = \"br\", 0.02, \"AB\"\n",
    "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "\n",
    "for i, n, c in zip(range(2), class_names, plot_colors):\n",
    "    idx = np.where(y == i)\n",
    "    plt.scatter(X[idx, 0], X[idx, 1], cmap=plt.cm.Paired, s=60, edgecolor='k', label=\"Class %s\" % n)\n",
    "plt.xlim(x_min, x_max)\n",
    "plt.ylim(y_min, y_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's now train AdaBoost on this dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AdaBoostClassifier(algorithm='SAMME',\n",
       "                   base_estimator=DecisionTreeClassifier(max_depth=1),\n",
       "                   n_estimators=200)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "# Create and fit an AdaBoosted decision tree\n",
    "bdt = AdaBoostClassifier(DecisionTreeClassifier(max_depth=1),\n",
    "                         algorithm=\"SAMME\",\n",
    "                         n_estimators=200)\n",
    "bdt.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Visualizing the output of the algorithm, we see that it can learn a highly non-linear decision boundary to separate the two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12b3b8438>"
      ]
     },
     "execution_count": 14,
     "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": [
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step), np.arange(y_min, y_max, plot_step))\n",
    "\n",
    "# plot decision boundary\n",
    "Z = bdt.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "Z = Z.reshape(xx.shape)\n",
    "cs = plt.contourf(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "\n",
    "# plot training points\n",
    "for i, n, c in zip(range(2), class_names, plot_colors):\n",
    "    idx = np.where(y == i)\n",
    "    plt.scatter(X[idx, 0], X[idx, 1], cmap=plt.cm.Paired, s=60, edgecolor='k', label=\"Class %s\" % n)\n",
    "plt.xlim(x_min, x_max)\n",
    "plt.ylim(y_min, y_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Ensembling\n",
    "\n",
    "Boosting and bagging are special cases of *ensembling*.\n",
    "\n",
    "The idea of ensembling is to combine many models into one. \n",
    "* Bagging is a form of ensembling to reduce overfitting\n",
    "* Boosting is a form of ensembling to reduce underfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* In stacking, we train $m$ independent models $g_j(x)$ (possibly from different model classes) and then train another model $f(x)$ to predict $y$ from the outputs of the $g_j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* The Bayesian approach can also be seen as form of ensembling\n",
    "$$ P(y\\mid x) = \\int_\\theta P(y\\mid x,\\theta) P(\\theta \\mid \\mathcal{D}) d\\theta $$\n",
    "where we average models $P(y\\mid x,\\theta)$ using weights $P(\\theta \\mid \\mathcal{D})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Pros and Cons of Ensembling\n",
    "\n",
    "Ensembling is a useful technique in machine learning.\n",
    "* It often helps squeeze out additional performance out of ML algorithms.\n",
    "* Many algorithms (like AdaBoost) are forms of ensembling.\n",
    "\n",
    "Disadvantages include:\n",
    "* It can be computationally expensive to train and use ensembles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Pros and Cons of Boosting\n",
    "\n",
    "Boosting algorithms generalize AdaBoost and offer many advantages:\n",
    "* High accuracy via a highly expressive non-linear model family.\n",
    "* Low pre-processing requirements if trees are used as weak learners.\n",
    "\n",
    "Disadvantages include:\n",
    "* Large ensembles can be expensive to train.\n",
    "* The interpretability of the weak learners is lost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<left><img width=25% src=\"img/cornell_tech2.svg\"></left>\n",
    "# Part 2: Additive Models\n",
    "\n",
    "Next, we are going to see another perspective on boosting and derive new boosting algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Review: Underfitting\n",
    "\n",
    "Underfitting is another common problem in machine learning.\n",
    "* The model is too simple to fit the data well (e.g., approximating a high degree polynomial with linear regression).\n",
    "* As a result, the model is not accurate on training data and is not accurate on new data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Review: Boosting\n",
    "\n",
    "The idea of *boosting* is to reduce *underfitting* by combining models that correct each others' errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* As in bagging, we combine many models $g_i$ into one *ensemble* $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* Unlike bagging, the $g_i$ are small and tend to underfit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* Each $g_i$ fits the points where the previous models made errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Additive Models\n",
    "\n",
    "Boosting can be seen as a way of fitting an *additive model*:\n",
    "$$ f(x) = \\sum_{t=1}^T \\alpha_t g(x; \\phi_t). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* $f(x)$ consists of $T$ smaller models $g$ with weights $\\alpha_t$ & params $\\phi_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* The parameters are the $\\alpha_t$ plus the parameters $\\phi_t$ of each $g$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that $g$ can be non-linear in $\\phi_t$ (therefore so is $f$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Example: Boosting Algorithms\n",
    "\n",
    "Boosting is one way of training additive models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "1. Compute weights $w^{(i)}$ for each $i$ based on $t$-th model predictions $f_t(x^{(i)})$ and targets $y^{(i)}$. Give more weight to points with errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. Fit new weak learner $g_t$ on $\\mathcal{D} = \\{(x^{(i)}, y^{(i)})\\}$ with weights $w^{(i)}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "3. Set $f_{t+1} = f_t + \\alpha_t g_t$ for some weight $\\alpha_t$. Go to Step 1 and repeat."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Forward Stagewise Additive Modeling\n",
    "\n",
    "A general way to fit additive models is the forward stagewise approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Suppose we have a loss $L : \\mathcal{Y} \\times \\mathcal{Y} \\to [0, \\infty)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Start with $f_0 = \\arg \\min_\\phi \\sum_{i=1}^n L(y^{(i)}, g(x^{(i)}; \\phi))$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* At each $t$, freeze $f_{t-1}$ and fit best new addition $\\alpha_t g(x, \\phi_t)$ to $f_{t-1}$:\n",
    "$$ \\alpha_t, \\phi_t = \\arg\\min_{\\alpha, \\phi} \\sum_{i=1}^n L(y^{(i)}, f_{t-1}(x^{(i)}) + \\alpha g(x^{(i)}; \\phi))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Example: Squared Loss\n",
    "\n",
    "A popular choice of loss is the squared loss.\n",
    "$$ L(y, f) = (y-f)^2. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The resulting algorithm is often called L2Boost. At step $t$ we minimize\n",
    "$$\\sum_{i=1}^n (r^{(i)}_t - \\alpha g(x^{(i)}; \\phi))^2, $$\n",
    "where $r^{(i)}_t = y^{(i)} - f(x^{(i)})_{t-1}$ is the residual from the model $f_{t-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Exponential Loss\n",
    "\n",
    "Give a binary classification problem with labels $\\mathcal{Y} = \\{-1, +1\\}$, the exponential loss is defined as\n",
    "\n",
    "$$ L(y, f) = \\exp(-y \\cdot f). $$\n",
    "\n",
    "* When $y=1$, $L$ is small when $f \\to \\infty$.\n",
    "* When $y=-1$, $L$ is small when $f \\to - \\infty$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Let's visualize the exponential loss and compare it to other losses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams['figure.figsize'] = [12, 4]\n",
    "\n",
    "# define the losses for a target of y=1\n",
    "losses = {\n",
    "    'Hinge' : lambda f: np.maximum(1 - f, 0),\n",
    "    'L2': lambda f: (1-f)**2,\n",
    "    'L1': lambda f: np.abs(f-1),\n",
    "    'Exponential': lambda f: np.exp(-f)\n",
    "}\n",
    "\n",
    "# plot them\n",
    "f = np.linspace(0, 2)\n",
    "fig, axes = plt.subplots(2,2)\n",
    "for ax, (name, loss) in zip(axes.flatten(), losses.items()):\n",
    "    ax.plot(f, loss(f))\n",
    "    ax.set_title('%s Loss' % name)\n",
    "    ax.set_xlabel('Prediction f')\n",
    "    ax.set_ylabel('L(y=1,f)')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Special Case: AdaBoost\n",
    "\n",
    "AdaBoost is an instance of forward stagewise additive modeling with the exponential loss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "At each step $t$ we minimize\n",
    "$$L_t = \\sum_{i=1}^n e^{-y^{(i)}(f_{t-1}(x^{(i)}) + \\alpha g(x^{(i)}; \\phi))} = \\sum_{i=1}^n w^{(i)} \\exp\\left(-y^{(i)}\\alpha g(x^{(i)}; \\phi)\\right) $$\n",
    "with $w^{(i)} = \\exp(-y^{(i)}f_{t-1}(x^{(i)}))$.\n",
    "\n",
    "We can derive the AdaBoost update rules from this equation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Suppose that $g(y; \\phi) \\in \\{-1,1\\}$. With a bit of algebraic manipulations, we get that:\n",
    "\\begin{align*}\n",
    "L_t & = e^{\\alpha} \\sum_{y^{(i)} \\neq g(x^{(i)})} w^{(i)} + e^{-\\alpha} \\sum_{y^{(i)} = g(x^{(i)})} w^{(i)} \\\\\n",
    "& = (e^{\\alpha} - e^{-\\alpha}) \\sum_{i=1}^n w^{(i)} \\mathbb{I}\\{{y^{(i)} \\neq g(x^{(i)})}\\} + e^{-\\alpha} \\sum_{i=1}^n w^{(i)}.\\\\\n",
    "\\end{align*}\n",
    "where $\\mathbb{I}\\{\\cdot\\}$ is the indicator function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "From there, we get that:\n",
    "\\begin{align*}\n",
    "\\phi_t & = \\arg\\min_{\\phi} \\sum_{i=1}^n w^{(i)} \\mathbb{I}\\{{y^{(i)} \\neq g(x^{(i)}; \\phi)}\\} \\\\\n",
    "\\alpha_t & = \\log[(1-e_t)/e_t]\n",
    "\\end{align*}\n",
    "where $e_t = \\frac{\\sum_{i=1}^n w^{(i)} \\mathbb{I}\\{y^{(i)} \\neq f(x^{(i)})\\}}{\\sum_{i=1}^n w^{(i)}\\}}$.\n",
    "\n",
    "These are update rules for AdaBoost, and it's not hard to show that the update rule for $w^{(i)}$ is the same as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Logistic Loss\n",
    "\n",
    "Another common loss is the log-loss. When $\\mathcal{Y}=\\{-1,1\\}$ it is defined as:\n",
    "\n",
    "$$L(y, f) = \\log(1+\\exp(-2\\cdot y\\cdot f)).$$\n",
    "\n",
    "This looks like the log of the exponential loss; it is less sensitive to outliers since it doesn't penalize large errors as much."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams['figure.figsize'] = [12, 4]\n",
    "\n",
    "# define the losses for a target of y=1\n",
    "losses = {\n",
    "    'Hinge' : lambda f: np.maximum(1 - f, 0),\n",
    "    'L2': lambda f: (1-f)**2,\n",
    "    'Logistic': lambda f: np.log(1+np.exp(-2*f)),\n",
    "    'Exponential': lambda f: np.exp(-f)\n",
    "}\n",
    "\n",
    "# plot them\n",
    "f = np.linspace(0, 2)\n",
    "fig, axes = plt.subplots(2,2)\n",
    "for ax, (name, loss) in zip(axes.flatten(), losses.items()):\n",
    "    ax.plot(f, loss(f))\n",
    "    ax.set_title('%s Loss' % name)\n",
    "    ax.set_xlabel('Prediction f')\n",
    "    ax.set_ylabel('L(y=1,f)')\n",
    "    ax.set_ylim([0,1])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "In the context of boosting, we minimize\n",
    "$$J(\\alpha, \\phi) = \\sum_{i=1}^n \\log\\left(1+\\exp\\left(-2y^{(i)}(f_{t-1}(x^{(i)}) + \\alpha g(x^{(i)}; \\phi)\\right)\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "This gives a different weight update compared to AdaBoost. This algorithm is called LogitBoost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Facts About Additive Modeling\n",
    "\n",
    "Boosting and additive models are closely connected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Forward stagewise training (FST) is a form of boosting with $g_t$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Classical boosting algorithms (AdaBoost) are special cases of FST."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Additive modeling is more general, supports many different losses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Additive modeling is a principled way of doing boosting for any loss $L$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Practical Considerations\n",
    "\n",
    "* Popular choices of $g$ include decision trees or cubic splines.\n",
    "* We may use a fixed number of iterations $T$ or early stopping when the error on a hold-out set no longer improves.\n",
    "* An important design choice is the loss $L$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Pros and Cons of Additive Models\n",
    "\n",
    "The algorithms we have seen so far improve over AdaBoost.\n",
    "* They optimize a wide range of objectives.\n",
    "* Thus, they are more robust to outliers and extend beyond classification.\n",
    "\n",
    "Cons:\n",
    "* Computational time is still an issue.\n",
    "* Optimizing greedily over each $\\phi_t$ can take time.\n",
    "* Each loss requires specialized derivations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Summary\n",
    "\n",
    "* Additive models have the form\n",
    "$$ f(x) = \\sum_{t=1}^T \\alpha_t g(x; \\phi_t). $$\n",
    "* These models can be fit using the forward stagewise additive approach.\n",
    "* This reproduces AdaBoost and can be used to derive new boosting-type algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<left><img width=25% src=\"img/cornell_tech2.svg\"></left>\n",
    "# Part 3: Gradient Boosting\n",
    "\n",
    "We are now going to see another way of deriving boosting algorithms that is inspired by gradient descent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Review: Boosting\n",
    "\n",
    "The idea of *boosting* is to reduce *underfitting* by combining models that correct each others' errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* As in bagging, we combine many models $g_i$ into one *ensemble* $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* Unlike bagging, the $g_i$ are small and tend to underfit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* Each $g_i$ fits the points where the previous models made errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Review: Additive Models\n",
    "\n",
    "Boosting can be seen as a way of fitting an *additive model*:\n",
    "$$ f(x) = \\sum_{t=1}^T \\alpha_t g(x; \\phi_t). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* The main model $f(x)$ consists of $T$ smaller models $g$ with weights $\\alpha_t$ and parameters $\\phi_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "* The parameters are the $\\alpha_t$ plus the parameters $\\phi_t$ of each $g$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "This is not a linear model, because $g$ can be non-linear in $\\phi_t$ (therefore so is $f$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Review: Forward Stagewise Additive Modeling\n",
    "\n",
    "A general way to fit additive models is the forward stagewise approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Suppose we have a loss $L : \\mathcal{Y} \\times \\mathcal{Y} \\to [0, \\infty)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Start with $f_0 = \\arg \\min_\\phi \\sum_{i=1}^n L(y^{(i)}, g(x^{(i)}; \\phi))$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* At each iteration $t$ we fit the best addition to the current model.\n",
    "$$ \\alpha_t, \\phi_t = \\arg\\min_{\\alpha, \\phi} \\sum_{i=1}^n L(y^{(i)}, f_{t-1}(x^{(i)}) + \\alpha g(x^{(i)}; \\phi))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Limitations of Forward Stagewise Additive Modeling\n",
    "\n",
    "Forward stagewise additive modeling is not without limitations.\n",
    "* There may exist other losses for which it is complex to derive boosting-type weight update rules.\n",
    "* At each step, we may need to solve a costly optimization problem over $\\phi_t$.\n",
    "* Optimizing each $\\phi_t$ greedily may cause us to overfit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# What Do Weak Learners Learn?\n",
    "\n",
    "Consider, for example, L2Boost, which optimizes the L2 loss.\n",
    "<!-- $$ L(y, f) = \\frac{1}{2}(y-f)^2. $$ -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "At step $t$ we minimize\n",
    "$$\\sum_{i=1}^n (r^{(i)}_t - \\alpha g(x^{(i)}; \\phi))^2, $$\n",
    "where $r^{(i)}_t = y^{(i)} - f_{t-1}(x^{(i)})$ is the residual error of the model $f_{t-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The residual error of model $f_{t-1}$ is given by:\n",
    "$$r^{(i)}_t = y^{(i)} - f_{t-1}(x^{(i)})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that $r_t^{(i)}$ is the derivative of the $L_2$ loss with respect to $f_{t-1}(x^{(i)})$:\n",
    "$$\\frac{1}{2}\\left(y^{(i)} - f_{t-1}(x^{(i)})\\right)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "To be more precise, we can write this as:\n",
    "$$r^{(i)}_t = \\frac{\\partial L(y^{(i)}, \\text{f})}{\\partial \\text{f}} \\bigg\\rvert_{\\text{f} = f_{t-1}(x^{(i)})}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Thus, at step $t$ we minimize\n",
    "$$\\sum_{i=1}^n \\left( \\underbrace{\\left(y^{(i)} - f_{t-1}(x^{(i)})\\right)}_\\text{derivative of $L$ at $f_{t-1}(x^{(i)})$} - g(x^{(i)}; \\phi)\\right)^2. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Why does L2Boost fit the derivatives of the L2 loss?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Recall: Supervised Learning\n",
    "\n",
    "Recall that in regular supervised learning, we minimize an objective $J(\\theta)$\n",
    "$$J(\\theta) = \\sum_{i=1}^n  L\\left( y^{(i)}, f_\\theta( x^{(i)}) \\right)$$\n",
    "over a dataset, where $L$ is a loss and $f_\\theta$ is a model with parameters $\\theta$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# A High-Level Look at Supervised Learning\n",
    "\n",
    "To explain this phenomenon, let's first recap classical supervised learning, and then contrast it against a different approach (gradient boosting)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Supervised Learning: The Model\n",
    "\n",
    "Recall that a machine learning model is a function\n",
    "$$ f_\\theta : \\mathcal{X} \\to \\mathcal{Y} $$\n",
    "that maps inputs $x \\in \\mathcal{X}$ to targets $y \\in \\mathcal{Y}$. \n",
    "\n",
    "The model has a $d$-dimensional set of parameters $\\theta$:\n",
    "$$\\theta = (\\theta_1, \\theta_2, ..., \\theta_d). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Supervised Learning: The Learning Objective\n",
    "\n",
    "Intuitively, $f_\\theta$ should perform well in expectation on new data $x, y$ sampled from the data distribution $\\mathbb{P}$:\n",
    "\n",
    "$$\n",
    "J (\\theta) = \\mathbb{E}_{(x, y)\\sim \\mathbb{P}} \\left[ L\\left( y, f_\\theta( x \\right)) \\right] \\text{ is \"good\"}.\n",
    "$$\n",
    "\n",
    "Here, $L : \\mathcal{X}\\times\\mathcal{Y} \\to \\mathbb{R}$ is a performance metric and we take its expectation or average over all the possible samples $ x, y$ from $\\mathbb{P}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Recall that formally, an expectation $\\mathbb{E}_{x\\sim {P}} f(x)$ is $\\sum_{x \\in \\mathcal{X}} f(x) P(x)$ if $x$ is discrete and $\\int_{x \\in \\mathcal{X}} f(x) P(x) dx$ if $x$ is continuous."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Intuitively,\n",
    "$$J(\\theta) = \\mathbb{E}_{(x, y)\\sim \\mathbb{P}} \\left[ L\\left( y, f_\\theta( x) \\right) \\right]\n",
    "= \\sum_{x \\in \\mathcal{X}} \\sum_{y \\in \\mathcal{Y}} L\\left(y, f_\\theta(x) \\right) \\mathbb{P}(x, y)\n",
    "$$\n",
    "is the performance on an *infinite-sized* holdout set, where we have sampled every possible point.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Supervised Learning: The Optimizer (Gradient Descent)\n",
    "\n",
    "The gradient $\\nabla J(\\theta)$ is the $d$-dimensional vector of partial derivatives:\n",
    "\n",
    "$$ \\nabla J (\\theta) = \\begin{bmatrix}\n",
    "\\frac{\\partial J(\\theta)}{\\partial \\theta_1} \\\\\n",
    "\\frac{\\partial J(\\theta)}{\\partial \\theta_2} \\\\\n",
    "\\vdots \\\\\n",
    "\\frac{\\partial J(\\theta)}{\\partial \\theta_d}\n",
    "\\end{bmatrix}.$$\n",
    "\n",
    "The $j$-th entry of the vector $\\nabla J (\\theta)$ is the partial derivative $\\frac{\\partial J(\\theta)}{\\partial \\theta_j}$ of $J$ with respect to the $j$-th component of $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We can optimize $J(\\theta)$ using gradient descent via the usual update rule:\n",
    "$$\\theta_t \\gets \\theta_{t-1} - \\alpha_t \\nabla J(\\theta_{t-1}).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "However, in practice, we cannot measure\n",
    "$$\\nabla J(\\theta) = \\mathbb{E}_{( x, y)\\sim \\mathbb{P}} \\left[ \\nabla L\\left( y, f_\\theta( x) \\right) \\right]$$\n",
    "on infinite data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We substitute $\\nabla J(\\theta)$ with an approximation $\\hat \\nabla J(\\theta)$ measured on a dataset $\\mathcal{D}$ sampled from $\\mathbb{P}$:\n",
    "$$\n",
    "\\hat \\nabla J (\\theta) = \\frac{1}{m} \\sum_{i=1}^m \\nabla L\\left( y^{(i)}, f_\\theta( x^{(i)}) \\right).\n",
    "$$\n",
    "If the number of IID samples $m$ is large, this approximation holds (we call this a Monte Carlo approximation)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Functional Optimization\n",
    "\n",
    "Instead of optimizing $J(\\theta)$, let's directly optimize $J(f)$ over *functions* $f$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This requires a few simplifying assumptions (for now):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* The set $\\mathcal{X}=\\{x_1, ..., x_m\\}$ of possible $x$ is finite and has size $m$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Thus, each $f(x)$ is a finite dimensional vector of size $m$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In other words, we can view $f : \\mathcal{X} \\to \\mathcal{Y}$ over a finite $\\mathcal{X}$ as a vector in $\\mathbb{R}^m$:\n",
    "\n",
    "$$ f = \\begin{bmatrix}\n",
    "f_1 \\\\\n",
    "f_2 \\\\\n",
    "\\vdots \\\\\n",
    "f_m\n",
    "\\end{bmatrix}\n",
    "= \\begin{bmatrix}\n",
    "f(x_1) \\\\\n",
    "f(x_2) \\\\\n",
    "\\vdots \\\\\n",
    "f(x_m)\n",
    "\\end{bmatrix}.$$\n",
    "\n",
    "$f$ is an $m$-dimensional vector; its $j$-th component is the prediction $f(x_j)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Supervised Learning Over Functions\n",
    "\n",
    "Now, supervised learning becomes a functional optimization problem over\n",
    "$$J(f) = \\sum_{i=1}^n  L\\left( y^{(i)}, f( x^{(i)}) \\right)$$\n",
    "where $f \\in \\mathbb{R}^m$ is a vector $L$ is a loss over a dataset $\\{x^{(i)}, y^{(i)}\\}_{i=1}^n$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can think of this as setting the parameters $\\theta$ directly to values of $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Functional Gradients\n",
    "\n",
    "How do we optimize $J(f)$ over $f$? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$f$ is a finite-dimensional vector; thus we use the *functional gradient* of $J$:\n",
    "\n",
    "$$ \\nabla J(f)= \\begin{bmatrix}\n",
    "\\frac{d J}{d f_1} \\\\\n",
    "\\frac{d J}{d f_2} \\\\\n",
    "\\vdots \\\\\n",
    "\\frac{d J}{d f_m} \\\\\n",
    "\\end{bmatrix}\n",
    "= \\begin{bmatrix}\n",
    "\\frac{d J}{d f(x_1)} \\\\\n",
    "\\frac{d J}{d f(x_2)} \\\\\n",
    "\\vdots \\\\\n",
    "\\frac{d J}{d f(x_m)} \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "This is very similar to taking the gradient with respect to parameters $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's further compare the parametric and the functional gradients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* $\\nabla J(\\theta_0)$ tells how to modify $\\theta_0$ to decrease $J$ at $J(\\theta_0)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* $\\nabla J(f_0)$ tells how to modify $f_0$ to decrease $J$ at $J(f_0)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Functional Gradient Descent\n",
    "\n",
    "How do we optimize the functional supervised learning objective?\n",
    "$$J(f) = \\sum_{i=1}^n  L\\left( y^{(i)}, f( x^{(i)}) \\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We perform gradient descent over $f$:\n",
    "$$f_t \\gets f_{t-1} - \\alpha_t \\nabla J(f_{t-1}).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is analogous to regular gradient descent:\n",
    "$$\\theta_t \\gets \\theta_{t-1} - \\alpha_t \\nabla J(\\theta_{t-1}).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This is best understood via a picture.\n",
    "\n",
    "<center><img width=100% src=\"img/functional_gradient.png\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After $T$ steps of $f_t \\gets f_{t-1} - \\alpha_t \\nabla J(f_{t-1})$, we get a model of the form\n",
    "$$f_T = \\sum_{t=0}^{T-1} \\alpha_t \\nabla J(f_{t})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Each $\\nabla J(f_{t})$ is a function of $x$, thus so is $f_T$\n",
    "* This also looks like an additive model!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Problems With Functional Supervised Learning\n",
    "\n",
    "However, in its current form, this approach is not practical."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Typically $m = |\\mathcal{X}|$ is very large (even infinite). Thus, we cannot estimate $\\nabla J(f)$ everywhere."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Even if we could, the model $f$ would be too expressive and overfit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Approximating Functional Gradients\n",
    "\n",
    "Our approach will be to estimate $\\nabla J(f_t)$ from data using a model $g_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We will then perform approximate functional gradient descent using\n",
    "\n",
    "$$f_t \\gets f_{t-1} - \\alpha_t g_t$$\n",
    "\n",
    "which is approximately $f_t \\gets f_{t-1} - \\alpha_t \\nabla J(f_{t-1}).$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Estimating Functional Gradients From Data\n",
    "\n",
    "How do we approximate $\\nabla J(f)$ using a parametric model $g_\\phi$ with parameters $\\phi$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Recall: $\\nabla J(f)$ is a vector. We can evaluate $\\nabla J(f)(x_j)$ at any $x_j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* We also have a dataset $\\mathcal{D} = \\{x^{(i)}, y^{(i)} \\mid i=1,...,n\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's use supervised learning to build a model $g_t(x) \\approx \\nabla J(f)(x)$ on $\\mathcal{D}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "First, we need a formula for $\\nabla J(f)(x^{(i)})$. Assume all $x^{(i)}$ are unique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Recall that we defined $J(f) = \\sum_{i=1}^n  L\\left( y^{(i)}, f( x^{(i)}) \\right)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Then we have that\n",
    "$$ \\nabla J(f)(x^{(i)}) = \\frac{d}{d f(x^{(i)})} J(f) = \\frac{d}{d f(x^{(i)})} L( y^{(i)}, f(x^{(i)})).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* For example, if $L$ is the $L_2$ loss, then $\\nabla J(f)(x^{(i)}) = y^{(i)} - f(x^{(i)})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Fitting Functional Gradients\n",
    "\n",
    "In order to fit functional gradients, we apply supervised learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "1. We compute $\\nabla J(f)$ on the training dataset:\n",
    "$$\\mathcal{D}_g = \\left\\{ \\left(x^{(i)}, \\nabla J(f)(x^{(i)}) \\right), i=1,2,\\ldots,n \\right\\} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. We train a model $g : \\mathcal{X} \\to \\mathbb{R}$ on $\\mathcal{D}_g$ to predict extrapolated functional gradients at any $x$:\n",
    "$$ g(x) \\approx \\nabla J(f)(x).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient Boosting\n",
    "\n",
    "Gradient boosting is functional gradient descent with estimated gradients.\n",
    "\n",
    "Start with $f(x) = 0$. Then, at each step $t>1$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "1. Create a training dataset $\\mathcal{D}_g$ and fit $g_t$ on $\\mathcal{D}_g$ such that\n",
    "$$ g_t(x) \\approx \\nabla J(f)(x).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. Take a step of grad descent using approximate grads with step $\\alpha_t$:\n",
    "$$f_t = f_{t-1} - \\alpha_t \\cdot g_t.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Interpreting Gradient Boosting\n",
    "\n",
    "Notice how after $T$ steps we get an additive model of the form\n",
    "$$ f(x) = \\sum_{t=1}^T \\alpha_t g_t(x). $$\n",
    "This looks like the output of a boosting algorithm!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* This works for any differentiable loss $L$.\n",
    "* It does not require any mathematical derivations for new $L$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Boosting vs. Gradient Boosting\n",
    "\n",
    "Consider, for example, L2Boost, which optimizes the L2 loss.\n",
    "<!-- $$ L(y, f) = \\frac{1}{2}(y-f)^2. $$ -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "At step $t$ we minimize\n",
    "$$\\sum_{i=1}^n (r^{(i)}_t - \\alpha g(x^{(i)}; \\phi))^2, $$\n",
    "where $r^{(i)}_t = y^{(i)} - f_{t-1}(x^{(i)})$ is the residual from $f_{t-1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Observe that the residual\n",
    "$$r^{(i)}_t = y^{(i)} - f(x^{(i)})_{t-1}$$\n",
    "\n",
    "is also the gradient of the $L2$ loss with respect to $f$ as $f(x^{(i)})$\n",
    "$$r^{(i)}_t = \\nabla J(f)(x^{(i)})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Many boosting methods are special cases of gradient boosting in this way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Losses for Additive Models\n",
    "\n",
    "We have seen several losses that can be used with the forward stagewise additive approach.\n",
    "* The exponential loss $L(y,f) = \\exp(-yf)$ gives us AdaBoost.\n",
    "* The log-loss $L(y,f) = \\log(1+\\exp(-2yf))$ is more robust to outliers.\n",
    "* The squared loss $L(y,f) = (y-f)^2$ can be used for regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Losses for Gradient Boosting\n",
    "\n",
    "Gradient boosting can optimize a wide range of losses.\n",
    "\n",
    "1. Regression losses:\n",
    "    * L2, L1, and Huber (L1/L2 interpolation) losses.\n",
    "    * Quantile loss: estimates quantiles of distribution of $p(y|x)$.\n",
    "2. Classification losses:\n",
    "    * Log-loss, softmax loss, exponential loss, negative binomial likelihood, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Practical Considerations\n",
    "\n",
    "When using gradient boosting these additional facts are useful:\n",
    "* We often use decision trees as $g_t$ for minimal input processing.\n",
    "* We can regularize via size of $g_t$, step size $\\alpha$, and using *early stopping*.\n",
    "* We can scale-up gradient boosting to big data by subsampling data at each iteration (a form of *stochastic* gradient descent)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Algorithm: Gradient Boosting\n",
    "\n",
    "* __Type__: Supervised learning (classification and regression).\n",
    "* __Model family__: Ensembles of weak learners (often decision trees).\n",
    "* __Objective function__: Any differentiable loss function.\n",
    "* __Optimizer__: Gradient descent in functional space. Weak learner uses its own optimizer.\n",
    "* __Probabilistic interpretation__: None in general; certain losses may have one."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gradient Boosting: An Example\n",
    "\n",
    "Let's now try running Gradient Boosted Decision Trees on a small regression dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "First we create the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12ed61898>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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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/ensemble/plot_gradient_boosting_quantile.html\n",
    "X = np.atleast_2d(np.random.uniform(0, 10.0, size=100)).T\n",
    "X = X.astype(np.float32)\n",
    "f = lambda x: x * np.sin(x)\n",
    "y = f(X).ravel()\n",
    "dy = 1.5 + 1.0 * np.random.random(y.shape)\n",
    "y += np.random.normal(0, dy)\n",
    "\n",
    "xx = np.atleast_2d(np.linspace(0, 10, 1000)).T\n",
    "plt.plot(xx, f(xx), 'g:', label=r'$f(x) = x\\,\\sin(x)$')\n",
    "plt.plot(X, y, 'b.', markersize=10, label=u'Observations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Next, we train a GBDT regressor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingRegressor(alpha=0.95, min_samples_leaf=9, min_samples_split=9,\n",
       "                          n_estimators=250)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "alpha = 0.95\n",
    "clf = GradientBoostingRegressor(loss='ls', alpha=alpha,\n",
    "                                n_estimators=250, max_depth=3,\n",
    "                                learning_rate=.1, min_samples_leaf=9,\n",
    "                                min_samples_split=9)\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We may now visualize its predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12c98e438>]"
      ]
     },
     "execution_count": 22,
     "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": [
    "y_pred = clf.predict(xx)\n",
    "plt.plot(xx, f(xx), 'g:', label=r'$f(x) = x\\,\\sin(x)$')\n",
    "plt.plot(X, y, 'b.', markersize=10, label=u'Observations')\n",
    "plt.plot(xx, y_pred, 'r-', label=u'Prediction')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Pros and Cons of Gradient Boosting\n",
    "\n",
    "Gradient boosted decision trees (GBTs) are one of the best off-the-shelf ML algorithms that exist, often on par with deep learning.\n",
    "* Attain state-of-the-art performance. GBTs rule on Kaggle. \n",
    "* Require little data pre-processing and tuning.\n",
    "* Work with any objective, including probabilistic ones.\n",
    "\n",
    "Their main limitations are:\n",
    "* GBTs don't work with unstructured data like images, audio.\n",
    "* Implementations not as flexible as modern neural net libraries."
   ]
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "celltoolbar": "Slideshow",
  "colab": {
   "collapsed_sections": [],
   "name": "neural-ode.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "aml",
   "language": "python",
   "name": "aml"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  },
  "rise": {
   "controlsTutorial": false,
   "enable_chalkboard": true,
   "height": 900,
   "help": false,
   "margin": 0,
   "maxScale": 2,
   "minScale": 0.2,
   "progress": true,
   "scroll": true,
   "theme": "simple",
   "width": 1200
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}