{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "i_f5u2x9nn6I",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
" \n",
"\n",
"# Lecture 4: Foundations of Supervised Learning\n",
"\n",
"### Applied Machine Learning\n",
"\n",
"__Volodymyr Kuleshov__ Cornell Tech"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Why Does Supervised Learning Work?\n",
"\n",
"Prevously, we learned about supervised learning, derived our first algorithm, and used it to predict diabetes risk.\n",
"\n",
"In this lecture, we are going to dive deeper into why supevised learning really works."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Part 1: Data Distribution\n",
"\n",
"First, let's look at the data, and define where it comes from.\n",
"\n",
"Later, this will be useful to precisely define when supervised learning is guaranteed to work."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "08ka9qHWnn6J",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Components of A Supervised Machine Learning Problem\n",
"\n",
"At a high level, a supervised machine learning problem has the following structure:\n",
"\n",
"$$ \\underbrace{\\text{Training Dataset}}_\\text{Attributes + Features} + \\underbrace{\\text{Learning Algorithm}}_\\text{Model Class + Objective + Optimizer } \\to \\text{Predictive Model} $$\n",
"\n",
"Where does the dataset come from?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Data Distribution\n",
"\n",
"We will assume that the dataset is sampled from a probability distribution $\\mathbb{P}$, which we will call the *data distribution*. We will denote this as\n",
"$$x, y \\sim \\mathbb{P}.$$\n",
"\n",
"The training set $\\mathcal{D} = \\{(x^{(i)}, y^{(i)}) \\mid i = 1,2,...,n\\}$ consists of *independent and identicaly distributed* (IID) samples from $\\mathbb{P}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Data Distribution: IID Sampling\n",
"\n",
"The key assumption in that the training examples are *independent and identicaly distributed* (IID). \n",
"* Each training example is from the same distribution.\n",
"* This distribution doesn't depend on previous training examples."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"__Example__: Flipping a coin. Each flip has same probability of heads & tails and doesn't depend on previous flips."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"__Counter-Example__: Yearly census data. The population in each year will be close to that of the previous year."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Data Distribution: Example\n",
"\n",
"Let's implement an example of a data distribution in numpy."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"np.random.seed(0)\n",
"\n",
"def true_fn(X):\n",
" return np.cos(1.5 * np.pi * X)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's visualize it."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.rcParams['figure.figsize'] = [12, 4]\n",
"\n",
"X_test = np.linspace(0, 1, 100)\n",
"plt.plot(X_test, true_fn(X_test), label=\"True function\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's now draw samples from the distribution. We will generate random $x$, and then generate random $y$ using\n",
"$$ y = f(x) + \\epsilon $$\n",
"for a random noise variable $\\epsilon$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"n_samples = 30\n",
"\n",
"X = np.sort(np.random.rand(n_samples))\n",
"y = true_fn(X) + np.random.randn(n_samples) * 0.1"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can visualize the samples."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X_test, true_fn(X_test), label=\"True function\")\n",
"plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Data Distribution: Motivation\n",
"\n",
"Why assume that the dataset is sampled from a distribution?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* There is inherent uncertainty in the data. The data may consist of noisy measurements (readings from an imperfect thermometer)."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* There is uncertainty in the process we model. If $y$ is a stock price, there is randomness in the market that cannot be modeled."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* We can use probability and statistics to analyze supervised learning algorithms and prove that they work."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
" \n",
"# Part 2: Why Does Supervised Learning Work?\n",
"\n",
"We made the assumption that the training dataset is sampled from a data distribution.\n",
"\n",
"Let's now use it to gain intuition about why supervised learning works."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Data Distribution\n",
"\n",
"We will assume that the dataset is sampled from a probability distribution $\\mathbb{P}$, which we will call the *data distribution*. We will denote this as\n",
"$$x, y \\sim \\mathbb{P}.$$\n",
"\n",
"The training set $\\mathcal{D} = \\{(x^{(i)}, y^{(i)}) \\mid i = 1,2,...,n\\}$ consists of *independent and identicaly distributed* (IID) samples from $\\mathbb{P}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Supervised Learning Model\n",
"\n",
"We'll say that a model is a function\n",
"$$ f : \\mathcal{X} \\to \\mathcal{Y} $$\n",
"that maps inputs $x \\in \\mathcal{X}$ to targets $y \\in \\mathcal{Y}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"# What Makes A Good Model?\n",
"\n",
"There are several things we may want out of a good model:\n",
"1. Interpretable features that explain how $x$ affects $y$.\n",
"2. Confidence intervals around $y$ (we will see later how to obtain these)\n",
"3. Accurate predictions of the targets $y$ from inputs $x$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"In this lecture, we fill focus on the latter."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# What Makes A Good Model?\n",
"\n",
"A good predictive model is one that makes __accurate predictions__ on __new data__ that it has not seen at training time."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Hold-Out Dataset: Definition\n",
"\n",
"A hold-out dataset \n",
"$$\\dot{\\mathcal{D}} = \\{(\\dot{x}^{(i)}, \\dot{y}^{(i)}) \\mid i = 1,2,...,m\\}$$\n",
"is another dataset that is sampled IID from the same distribution $\\mathbb{P}$ as the training dataset $\\mathcal{D}$ and the two datasets are disjoint."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's genenerate a hold-out dataset for the example we saw earlier."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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qRCFaqqQBraKY+0B//nRLB7anZTH4lcU8PmMjmcdzvS5NREREqgCFaKmyAvz9+FGvZnz5yJX8tE8cUxP2cNXfFvD+sp3k686HIiIiUgoK0VLlhYcE8vvB7fjkwf60bxzO7z/ezOBXlrByR6bXpYmIiEglpRAt1UarBmFMuqcXr/2oG0dP5jH8jWU8OHktaceyvS5NREREKhmFaKlWzIybOjZi3kNX8MDVLfhk4zdc8/eveH/ZTgoKtYqHiIiIXBiFaKmWagT589D1rfnsVwPoElOb33+8mZtfXcKG1MNelyYiIiKVgEK0VGtxkbV4/66eTBjZlQNHsxn66hJ+959NHDmZ53VpIiIiUoEpREu1Z2YM7tyYeb++glG9Y5m0YhfX/P0rZq3fpxu1iIiIyBkpRIv4hIcE8tSQ9swc249GESGM+3Atd7+XQOqhE16XJiIiIhWMQrTIaTo0ieDfP+/D737QjuUpGVz/4kLeWrxDEw9FRETkFIVokTMI8Pfj7n5x/PdXA+gZV5c/zt7CLa8tYfM+3T5cREREFKJFzim6Tk3eGd2DCSO7su/wSYa8soTnP/2a7LwCr0sTERERDylEi5zHqYmHD13BsK5NeG3BdgaNX8TqXbrjoYiISHVVJiHazG40s61mlmxmj53h+GgzSzezdb7HPcWOjTKzJN9jVFnUI3Ip1K4ZxF9v78z7d/UkO6+Q2/6xjKdmbuZ4Tr7XpYmIiEg5s9Iu4WVm/sA24DogFVgFjHTObSnWZjQQ75wbe9p76wIJQDzggNVAd+fcoXOdMz4+3iUkJJSqbpHSyMrJ5/lPv+b9ZbuIrlOD54Z1ol/LSK/LEhERkTJkZqudc/FnOlYWPdE9gWTnXIpzLheYDAy9wPfeAHzunMv0BefPgRvLoCaRSyo0OICnh3ZgypjLCfT34863VvD4jI1kqVdaRESkWiiLEN0E2FNsO9W373S3mtkGM5tuZjElfC9mNsbMEswsIT09vQzKFim9Xs3r8cmD/bm3fxyTV+3mhhcXsjT5oNdliYiIyCVWXhMLZwGxzrlOFPU2v1fSD3DOTXTOxTvn4qOiosq8QJGLFRLoz28HtWP6/b0JCvDjh2+u4Pcfb9JYaRERkSqsLEL0XiCm2Ha0b98pzrkM51yOb/NNoPuFvleksujerC5zH+jP3f3i+OfyXQx8eRErUjK8LktEREQugbII0auAlmYWZ2ZBwAhgZvEGZtao2OYQINH3+jPgejOrY2Z1gOt9+0QqpRpB/vzuB+2YMqY3ZnDHxOU8PWuL1pUWERGpYkodop1z+cBYisJvIjDVObfZzJ42syG+Zg+Y2WYzWw88AIz2vTcT+CNFQXwV8LRvn0il1jOuLp882J+f9G7G20t2MGj8IjakHva6LBERESkjpV7izgta4k4qk0VJ6TwybQPpWTmMu7oFv7iqBYH+us+RiIhIRXepl7gTkXPo3zKKz345gCGdG/PSvCRue30pyWlZXpclIiIipaAQLVIOImoG8uIdXXjtR93YnXmCQeMX8e6SHRQWVr5vgkREREQhWqRc3dSxEZ/9cgB9LqvHU7O2MPrdVaQdzfa6LBERESkhhWiRclY/PIS3R/fgmZs7sHJHBje8tJBPN33jdVkiIiJSAgrRIh4wM+68vBlzHuhPdJ2a3P/Bah6dvl63DRcREakkFKJFPHRZVCgf/awPY69qwfTVqdz08iJW7zrkdVkiIiJyHgrRIh4LCvDj4RtaM+W+3hQ6x/A3ljF+fhIFmnQoIiJSYSlEi1QQPWLrMvfB/gzu1IgXPt/GiInLSD10wuuyRERE5AwUokUqkPCQQF4a0ZUX7+hM4v5jDHx5EbPW7/O6LBERETmNQrRIBXRL12jmPtCfFvVDGffhWn49VZMORUREKhKFaJEKqmm9mky9rzcPXN2Cf69NZdD4RWxIPex1WSIiIoJCtEiFFujvx0PXt+bDey8nN7+QW19fyv8uTNGdDkVERDymEC1SCfRqXo9PHuzP1W3q86e5ifz03VWkH8vxuiwREZFqSyFapJKoXTOIf9zZnT/e3IFlKRkMfHkRi5LSvS5LRESkWlKIFqlEzIwfX96MmWP7UqdmID9+ayXPfpJIXkGh16WJiIhUK2USos3sRjPbambJZvbYGY4/ZGZbzGyDmc03s2bFjhWY2TrfY2ZZ1CNS1bVpGM7Msf0Y2bMpb3yVwvA3lrEnU2tKi4iIlJdSh2gz8wdeBQYC7YCRZtbutGZrgXjnXCdgOvB8sWMnnXNdfI8hpa1HpLqoEeTPs8M68uoPu5F8IItB4xfx6ab9XpclIiJSLZRFT3RPINk5l+KcywUmA0OLN3DOfemc+7abbDkQXQbnFRFgUKdGzHmgP3GRtbj/gzX87j+byM4r8LosERGRKq0sQnQTYE+x7VTfvrO5G/ik2HaImSWY2XIzu/lsbzKzMb52CenpmkwlUlzTejWZdn8f7u0fxz+X7+KW15ayPT3L67JERESqrHKdWGhmdwLxwF+L7W7mnIsHfgi8ZGaXnem9zrmJzrl451x8VFRUOVQrUrkEBfjx20HteHt0PN8cOcngCYv599pUr8sSERGpksoiRO8FYoptR/v2fYeZXQv8FhjinDu1wK1zbq/vOQVYAHQtg5pEqq2r2zTgkwcH0KFJBL+asp7/mb6Bk7ka3iEiIlKWyiJErwJamlmcmQUBI4DvrLJhZl2BNygK0GnF9tcxs2Df60igL7ClDGoSqdYaRoTwr3t6MfaqFkxdvYebX11Cctoxr8sSERGpMkodop1z+cBY4DMgEZjqnNtsZk+b2berbfwVCAWmnbaUXVsgwczWA18CzznnFKJFykCAvx8P39Ca937ak4NZOQyesITpqzW8Q0REpCyYc87rGkosPj7eJSQkeF2GSKVx4Gg2D3y4lhU7Mrm1WzR/vLk9NYMCvC5LRESkQjOz1b65e9+jOxaKVAMNwkOYdE8vxl3dghlrUxn6ioZ3iIiIlIZCtEg1EeDvx6+vLxrekXk8l8ETlmj1DhERkYukEC1SzQxoFcXcB/vT0bd6x2MfbdDNWUREREpIIVqkGmoQHsK/7u3Fz6+8jMmrilbvSNHNWURERC6YQrRINRXg78ejN7bhndE9+OZoNoMnLGbW+n1elyUiIlIpKESLVHNXtanP3Af607phGOM+XMvvP95ETr6Gd4iIiJyLQrSI0Lh2Dabc15t7+8fx/rJd3P6PZezJPOF1WSIiIhWWQrSIABDo78dvB7XjjR93Z8fB4wwav4jPtxzwuiwREZEKSSFaRL7jhvYNmTOuP03r1eTe9xN4dm4ieQWFXpclIiJSoShEi8j3NK1Xk+n39+HOy5vyxsIURk5czjdHsr0uS0REpMJQiBaRMwoJ9OeZmzvy8ogubNl/lEHjF7E46aDXZYmIiFQICtEick5DuzRh5ti+1K0VxI/fXsHL85IoLHRelyUiIuIphWgROa8W9cP4eGxfbunShBfnbWP0u6vIPJ7rdVkiIiKeUYgWkQtSMyiAvw/vzLPDOrI8JYNB4xexetchr8sSERHxhEK0iFwwM2Nkz6bM+FkfAv39uOONZby1eAfOaXiHiIhULwrRIlJiHZpEMGtcP65qU58/zt7Czyet4Vh2ntdliYiIlJsyCdFmdqOZbTWzZDN77AzHg81siu/4CjOLLXbscd/+rWZ2Q1nUIyKXXkSNQCb+uDu/uakN/91ygCGvLCFx/1GvyxIRESkXpQ7RZuYPvAoMBNoBI82s3WnN7gYOOedaAC8Cf/G9tx0wAmgP3Ai85vs8EakEzIwxAy7jw3sv53hOPje/uoRpCXu8LktEROSSK4ue6J5AsnMuxTmXC0wGhp7WZijwnu/1dOAaMzPf/snOuRzn3A4g2fd5IlKJ9Iyry5wH+tO9WR0emb6BR6evJzuvwOuyRESkkisodLw0bxuvfJHkdSnfUxYhuglQvOsp1bfvjG2cc/nAEaDeBb4XADMbY2YJZpaQnp5eBmWLSFmKCgvmn3f3YtzVLZiakMotry1lx8HjXpclIiKVVEZWDqPfWclL85LYmXGiwk1irzQTC51zE51z8c65+KioKK/LEZEz8Pczfn19a975aQ/2HznJkAmL+XTTfq/LEhGRSmb1rkP8YMJiVuzI5NlhHfnrbZ0oGsRQcZRFiN4LxBTbjvbtO2MbMwsAIoCMC3yviFQyV7Wuz5wH+tO8fij3f7CGZ2ZvIa+g0OuyRESkgnPO8fbiHdzxxjIC/I0ZP+vDyJ5NK1yAhrIJ0auAlmYWZ2ZBFE0UnHlam5nAKN/r24AvXFGf/ExghG/1jjigJbCyDGoSEY81qV2Daff1ZnSfWN5cvIMRE5ez/8hJr8sSEZEK6lh2Hj+ftIanZ2/hqjb1mT2uPx2aRHhd1lmVOkT7xjiPBT4DEoGpzrnNZva0mQ3xNXsLqGdmycBDwGO+924GpgJbgE+BXzjnNBtJpIoICvDjqSHtmTCyK1/vP8qg8YtZlKQ5DSIi8l2J+48y5JUl/HfLAR4f2IaJP+5ORI1Ar8s6J6tog7QvRHx8vEtISPC6DBEpgeS0LH4+aTVJaVk8eE1Lxl3dEn+/ivf1nIiIlK+pCXv43X82EVEjkAkju9KreT2vSzrFzFY75+LPdKzSTCwUkcqtRf1Q/vOLvtzSpQkvzUti9DsrycjK8bosERHxyMncAh6Ztp5Hp2+ge7M6zHmgf4UK0OejEC0i5aZmUAB/H96ZZ4d1ZMWOTAaNX0zCzkyvyxIRkXK24+BxbnltCdNWp/LA1S345929iAoL9rqsElGIFpFyZWaM7NmUGT/rQ3CgHyMmLufNRSkVbv1PERG5NOZu3M/gCYs5cDSbd3/ag4eub10ph/cpRIuIJzo0iWDWuH5c07Y+z8xJ5P4PVnPkZJ7XZYmIyCWSm1/IH2Zt5ueT1tCyQShzHujPla3re13WRVOIFhHPhIcE8o87u/PEoLbMT0zjBxMWsTH1iNdliYhIGUs9dILb31jGO0t2clffOKaM6U3j2jW8LqtUFKJFxFNmxj39mzPlvt7kFzhufX0pHyzfpeEdIiJVxBdfH2DQ+MWkpGXxjzu78fvB7QgKqPwRtPL/CkSkSvh2Znbvy+rxxH828csp6ziek+91WSIicpHyCwr5y6dfc9e7CUTXqcHsB/pxY4dGXpdVZgK8LkBE5Ft1awXxzugevLYgmRc+38amvUd47Ufdad0wzOvSRESkBA4czWbch2tZuSOTkT2b8uTgdoQE+ntdVplST7SIVCh+fsbYq1vywT29OHIyn6GvLmZawh6vyxIRkQu0KCmdm14umuPy4h1Fy5pWtQANCtEiUkH1uSySuQ/2o2tMHR6ZvoGHp63nZG6B12WJiMhZFBQ6Xvh8Gz95eyV1awUxc2xfbuka7XVZl4yGc4hIhVU/LIQP7unFy/OTmPBFEhtSD/Paj7rRor6Gd4iIVCRpx7L55eR1LN2ewa3dovnjze2pGVS1Y6Z6okWkQvP3Mx66rhXv39WTjKxchryyhH+vTfW6LBER8Vm6/SA3vbyYNbsP8fxtnfj78M5VPkCDQrSIVBL9W0Yx98H+dGgSwa+mrOexjzaQnafhHSIiXikodLw8L4k731xBRI0APv5FP4bHx3hdVrmp+j8miEiV0SA8hH/d04sX523j1S+3s27PYV75YTda1A/1ujQRkWol/VgOv5yyliXJGdzcpTF/uqUjtYKrV6xUT7SIVCoB/n48ckMb3rurJ2nHchjyymJmrNHwDhGR8rI0+SA3jV9Ews5DPH9rJ168o0u1C9CgEC0ildQVraKY+0DR8I6Hpq7n0elavUNE5FIqKHS8NG8bP3prBeEhAXw8ti/De8RgZl6X5olShWgzq2tmn5tZku+5zhnadDGzZWa22cw2mNkdxY69a2Y7zGyd79GlNPWISPXSMKJoeMe4q1swbXUqQ19dTNKBY16XJSJS5aQdy+bHb63gpXlJ3NK1CTPH9qNNw3Cvy/JUaXuiHwPmO+daAvN926c7AfzEOdceuBF4ycxqFzv+iHOui++xrpT1iEg1E+Dvx6+vb837d/Uk83jR6h1TV+3BOed1aSIiVcLCbUU3T1mz+xB/va0TLwyvnsM3TlfaED0UeM/3+j3g5tMbOOe2OeeSfK/3AWlAVCnPKyLyHf1bFg3v6Nq0No9+tIFfTVlHVk6+12WJiFRaeQWF/OXTr4vdPKUft1ej1TfOp7QhuoFzbr/v9TdAg3M1NrOeQBCwvdjuP/mGebxoZsHneO8YM0sws4T09PRSli0iVVH98BD+eXcvHrquFTPX72PwhMVs2nvE67JERCqd1EMnGDFxOa8v2M7InjF8/It+tGqgG10VZ+f7ytPM5gENz3Dot8B7zrnaxdoecs59b1y071gjYAEwyjm3vNi+bygK1hOB7c65p89XdHx8vEtISDhfMxGpxlakZPDg5HVkHs/lNze1YVSf2Go7+UVEpCQ+2/wNj0xbT6GDPw/ryJDOjb0uyTNmtto5F3+mY+cd0OKcu/YcH3zAzBo55/b7AnHaWdqFA3OA334boH2f/W0vdo6ZvQM8fL56REQuRK/m9Zj7YH8enraep2ZtYcn2DP56Wydq1wzyujQRkQopO6+AZ+cm8t6yXXRsEsGEkV2JjazldVkVVmmHc8wERvlejwI+Pr2BmQUB/wbed85NP+1YI9+zUTSeelMp6xEROaVurSDeGhXPE4PasmBrGgNfXsSKlAyvyxIRqXCS045x86tLeG/ZLu7qG8f0n/VWgD6P0obo54DrzCwJuNa3jZnFm9mbvjbDgQHA6DMsZTfJzDYCG4FI4JlS1iMi8h1mxj39mzPjZ30JDvBj5P8u58XPt5FfUOh1aSIinnPOMWXVbgZPWELasRzeHh3P7we3IzjA3+vSKrzzjomuiDQmWkQuRlZOPr//eBMz1uylZ2xdXhrRhca1a3hdloiIJ45m5/GbGRuZvWE/fS6rx4t3dKFBeIjXZVUo5xoTrTsWiki1ERocwAvDu/DiHZ3ZvO8IA19exKeb9p//jSIiVcya3Ye46eVFfLLpGx65oTX/vLuXAnQJKUSLSLVzS9do5jzQn6Z1a3L/B2t4fMZGTuRqTWkRqfoKCh0T5idx+z+W4RxMva83v7iqBf5+Wr2opHS7GRGplmIja/HRz/rw98+38sZXKazckcHLI7rSoUmE16WJiFwSew+f5FeT17FyZyaDOzfmmZs7EFEj0OuyKi31RItItRUU4MfjA9vywd29OJadz7DXlvLmohQKCyvfXBERkXOZvWEfA19ayOZ9R/j77Z0ZP6KLAnQpKUSLSLXXr2Ukn/5yAFe0juKZOYmMemclaceyvS5LRKTUjufk88i09Yz911riokKZ+2B/bu0erZtPlQGFaBERitaUnvjj7jxzcwdW7cxk4EuL+HzLAa/LEhG5aOv2HOYHExYzfU0qY69qwfT7e9OsntZ+LisK0SIiPmbGnZc3Y9bYfjQID+He9xM06VBEKp38gkLGz0/i1teXkpNXwIf3Xs7DN7Qm0F+xryxpYqGIyGlaNgjjP7/oywufb+ONhdtZnpLBi3d0oUtMba9LExE5p10Zx/nVlHWs2X2Ym7s05g9DNXnwUtGPJCIiZxAU4MdjA9vw4b2Xk5tfyK2vL2X8/CTd6VBEKiTnHFMT9nDTy4tISsvi5RFdeGlEVwXoS0ghWkTkHC5vXo+5D/ZncKdGvPD5Noa/sYxdGce9LktE5JTM47n87IM1PDp9Ax2jI/j0lwMY2qWJ12VVeQrRIiLnEVEjkJdGdOXlEV1ISsti4MuLmLRiF85pKTwR8db8xANc/+JCvvg6jccHtuFf91xOk9o1vC6rWtCYaBGRCzS0SxN6xtXlkWkb+O2/N/HfzQd4/rZOulWuiJS7rJx8npm9hcmr9tCmYRj/vLsnbRuFe11WtWKVsSclPj7eJSQkeF2GiFRThYWOD1bs4s9zEwkO8OeZmzswuHNjr8sSkWpiRUoGv562nn2HT3L/FZfx4LUtCQ7w97qsKsnMVjvn4s90TMM5RERKyM/P+EnvWOY+0J+4yFqM+3AtD3y4lsMncr0uTUSqsOy8Av48N5ER/7scfz9j2v29efTGNgrQHtFwDhGRi9Q8KpTp9/fmH19t56V5SSxLyeDZWzpybbsGXpcmIlXMuj2HeXjaepLTsvhRr6b85qa21ApWjPNSqXqizayumX1uZkm+5zpnaVdgZut8j5nF9seZ2QozSzazKWYWVJp6RETKW4C/H2OvbsnHY/tSr1YQ97yfwK+nrufIyTyvSxORKiAnv4DnP/2aYa8t4XhOPu/f1ZM/3dJRAboCKO1wjseA+c65lsB83/aZnHTOdfE9hhTb/xfgRedcC+AQcHcp6xER8UT7xhHMHNuPB65uwX/W7eX6F7/iy6/TvC5LRCqxjalHGDxhMa8t2M5t3aP57FcDGNAqyuuyxKdUEwvNbCtwpXNuv5k1AhY451qfoV2Wcy70tH0GpAMNnXP5ZtYbeMo5d8P5zquJhSJSkW1MPcKvp61j24Esbu8eze8GtyM8RDc8EJELk5tfyCtfJPHqgu1Ehgbx3LBOXNWmvtdlVUuXcmJhA+fcft/rb4CzDQQMMbMEM1tuZjf79tUDDjvn8n3bqcBZVwY3szG+z0hIT08vZdkiIpdOx+gIZo3rx8+vvIyP1qRy/QsLmZ94wOuyRKQSWL/nMIMnLGb8F8kM7dKY//7yCgXoCuq8A2rMbB7Q8AyHflt8wznnzOxs3drNnHN7zaw58IWZbQSOlKRQ59xEYCIU9USX5L0iIuUtOMCfR29sww3tG/Lo9A3c/V4CQ7s05snB7albS9M/ROS7svMKeOHzbby5KIX6YSG8+ZN4TVKu4M4bop1z157tmJkdMLNGxYZznHEAoHNur+85xcwWAF2Bj4DaZhbg642OBvZexK9BRKTC6hxTm1nj+vHql8m8+mUyi5MO8oeh7RnUsRFFo9pEpLpbkZLB/3y0gZ0ZJxjZM4bHb2qrIWCVQGmHc8wERvlejwI+Pr2BmdUxs2Df60igL7DFFQ3G/hK47VzvFxGp7IIC/PjVda2Y/UA/mtSpwdh/reW+f64m7Wi216WJiIeycvL53X82ccfE5RQ4x7/u6cWzwzopQFcSpZ1YWA+YCjQFdgHDnXOZZhYP3O+cu8fM+gBvAIUUhfaXnHNv+d7fHJgM1AXWAnc653LOd15NLBSRyiq/oJC3Fu/ghc+3ERTgx+MD2zKiRwx+fuqVFqlO5m05wO8+3sQ3R7MZ3SeWR25oTc0gLVtX0ZxrYqFu+y0i4oGU9Cx+8++NLE/JpGdsXf48rCMt6oee/40iUqmlHc3mD7O2MGfjflo1COXZYZ3o3uyMt9mQCkAhWkSkAnLOMW11Kn+ak8jJ3AJ+ftVl/OzKy3QLX5EqqLDQMXnVHp79JJGc/EIeuLoFYwZcRlBAaUfWyqV0rhCt7w1ERDxiZgyPj+HqNvV5etYWXpqXxOwN+3l2WEd6xNb1ujwRKSPJacf4zYxNrNyZyeXN6/LnWzrSPErfPFV26okWEakgvtyaxhP/3sTewye5vXs0j9/UVsvhiVRiJ3MLmPBFEv+7KIWaQQH8dlBbbu8erZV5KhEN5xARqSRO5OYzfn4yby5KITQkgMdubMPweE08FKls5ice4MmZm0k9dJJh3Zrwm5vaEhka7HVZUkIK0SIilcy2A8d44j+bWLkjk25Na/PMzR1p1zjc67JE5Dz2Hj7JH2Zu5r9bDtCifijP3NyBy5vX87osuUgK0SIilZBzjo/W7OXPcxM5cjKP0X1i+eW1LQnTGrIiFU5ufiHvLNnBS/OScDgevKYVd/eL08TBSk4TC0VEKiEz47bu0Vzbtj5/+XQrby/Zwcfr9vHYwDYM69pEQzxEKoivtqXzh1mbSUk/zrVtG/DUkHZE16npdVlyiaknWkSkktiQepjff7yZdXsO061pbf4wpAMdoyO8Lkuk2tqdcYI/ztnC51sOEBdZi98PbsdVret7XZaUIQ3nEBGpIgoLHR+tSeUvn35NxvFcRvSI4ZEb2mgVD5FydDK3gNcXJPOPhSkE+Bnjrm7JXf1itcZ7FaThHCIiVYSfn3F7fAw3dGjIy/OSeG/pTuZs2M+D17bix5c30/hLkUvIOcfM9ft4/tOt7D18kqFdGvP4wLY0jAjxujTxgHqiRUQqsaQDx3h69hYWJR0kLrIWv7mpLde2ra91aEXK2Opdh3hmzhbW7j5M+8bh/P4H7eilVTeqPA3nEBGpwpxzLNiazjNztrA9/Th9LqvHE4PaaUk8kTKQeugEf/l0K7PW76N+WDCP3NCaW7tFa2JvNaEQLSJSDeQVFPKvFbt5cd42jpzMY3j3GB66vhUNwvVVs0hJHcvO4x9fbefNRTsAuG9Ac+674jJqBWskbHWiEC0iUo0cOZHHhC+SeG/ZTgL8/Li7Xxz3XdFc60uLXIDc/EImrdjFhC+SyTyey81dGvPojW1oXLuG16WJBxSiRUSqoV0Zx/nbf7cxa/0+6tYKYuxVLfjR5U21goDIGRQWOmZt2Mff/ruVPZkn6XNZPR4b2IZO0bW9Lk08pBAtIlKNbUw9wnOfJrIkOYOYujV4+PrWDO7UWGM6RXwWJx3kuU8T2bT3KG0bhfPYwDYMaBmpCbpy6UK0mdUFpgCxwE5guHPu0GltrgJeLLarDTDCOfcfM3sXuAI44js22jm37nznVYgWESkZ5xyLkg7y3Cdfs2X/Udo0DOPX17fWSh5Sra3elcnfPtvGspQMousU/YA5pLN+wJT/dylD9PNApnPuOTN7DKjjnPufc7SvCyQD0c65E74QPds5N70k51WIFhG5ON9+Zf3i59vYmXGCztERPHR9a/W6SbWyMfUIf/98Kwu2phMZGszPr7xMQ53kjC7lzVaGAlf6Xr8HLADOGqKB24BPnHMnSnleERG5CH5+xtAuTRjUsREz1u7l5XlJjHp7JT1i6/Dr61tzuda9lSrs62+O8sJ/t/HfLQeoXTOQxwa24Se9m1EzSCtuSMmVtif6sHOutu+1AYe+3T5L+y+AF5xzs33b7wK9gRxgPvCYcy7nLO8dA4wBaNq0afddu3ZddN0iIlIkN7+QKQl7eOWLJA4czaF383qMu6YFvZvXU8+0VBlb9h3l1S+TmbtpP6FBAdw7oDk/7RurFWvkvEo1nMPM5gENz3Dot8B7xUOzmR1yztU5y+c0AjYAjZ1zecX2fQMEAROB7c65p8/3C9JwDhGRspWdV8CkFbt546vtpB3LIb5ZHcZe3YIrWkUpTEultX7PYSZ8kcy8xAOEBQcwqk8s9/SPo3bNIK9Lk0riUo6J3gpc6Zzb7wvEC5xzrc/S9kGgvXNuzFmOXwk87Jz7wfnOqxAtInJpZOcVMC1hD68v2M6+I9l0io5g3NUtNQFRKpWEnZmM/yKZhdvSiagRyF194xjdN5aIGup5lpK5lGOiZwKjgOd8zx+fo+1I4PHTCmvkC+AG3AxsKmU9IiJSCiGB/vy4dyx39GjKjDWpvLZgO/e+n0CbhmHc2785gzs3JijAz+syRb6nsNDx5dY03liYwsodmdSrFcT/3NiGH/duRqjuMiiXQGl7ousBU4GmwC6KlrjLNLN44H7n3D2+drHAEiDGOVdY7P1fAFGAAet878k633nVEy0iUj7yCwqZuX4fb3yVwtYDx2gYHsLd/eIY0TNG40mlQsjJL+DjdfuYuDCF5LQsGkeEcHf/5ozsGaMJg1JqutmKiIiUinOOBdvSmfhVCstSMggLDuCHlzflrr5xNAgP8bo8qYaOnMzjw5W7eXvxDtKO5dC2UTj3DWjOoE6NCPTXtyVSNhSiRUSkzGxIPcwbC1P4ZON+/My4qWMjRveNpWtMbY2blksuOS2L95bu5KM1qZzILaBfi0juu6I5/VporXMpewrRIiJS5nZnnOC9ZTuZumoPx3Ly6Rwdwei+sdzUsZFuWiFlqrDQsWBbGu8s2cmipIME+fsxpEtjRveJpUOTCK/LkypMIVpERC6Z4zn5zFiTyrtLd7I9/TiRocH8sFdTRvSIoXHtGl6XJ5XYoeO5fLQmlQ+W72Jnxgkahodw5+VNGdGzKZGhwV6XJ9WAQrSIiFxyzjkWJx/k3SU7+WJrGgZc2bo+I3s25arWUQRonKpcAOccK3dk8uHK3czd9A25+YV0b1aHn/aN5Yb2DTXeWcqVQrSIiJSrPZknmJqwhymr9pB2LIcG4cEMj49heHwMMXVrel2eVECZx3P5aHUqH67aTUr6ccJCAhjWtQkjejalbaNwr8uTakohWkREPJFfUMgXX6fx4crdLNiWDkDv5vUY1i2aGzs01Pq91VxuftGfjxlrUvlyaxp5BY7uzeowsmdTBnVsRI0gja0XbylEi4iI5/YePsm0hD38e+1edmWcoEagPzd2aMiwbk3oc1kk/n5aWaE6cM6xbs9hZqzZy6wN+zh8Io/I0GCGdmnM8PgYWjcM87pEkVMUokVEpMJwzrFm9yE+WrOX2ev3cTQ7nwbhwQzq2JhBnRrSNaYOfgrUVYpzjm0HspizYR+zN+wn5eBxggP8uKF9Q27p1oT+LSI1Zl4qJIVoERGpkLLzCvjy6zRmrN3LV1vTyS0opFFECAM7NGJQp0Z0jamtQF1JnQrOG/czZ8M+tqcfx8+gV1w9bunahBs7NiRcd72UCk4hWkREKrxj2XnMT0xj9ob9LNxWFKgbR4RwXbsGXNO2Ab2a19X60xVcQaFj3Z5DzEtM4/MtB0hOyzoVnG/q1Igb2zckKkxL00nloRAtIiKVytHsPOYnHmDOhm9YnJxOdl4htYL8GdAqimvaNuCq1lHU0zrBFUJWTj6LtqUzLzGNBVvTyDiei7+f0TO2roKzVHoK0SIiUmmdzC1g6faDzEs8wPzENNKO5WAGnaNr079lJH1bRNKtaR2CAjSmtjwUFDo27zvCoqSDLEk+SMLOQ+QWFBIeEsBVbepzTdsGXNEqiogaGqohlZ9CtIiIVAmFhY5N+44wLzGNRUnprN9zmEIHNQL96dW8Lv1aRNLnskhaNwzTah9lxDnHjoPHWZ6SyeLkdJZuz+DwiTwA2jQMo3/LSK5u04D42Dq6EYpUOQrRIiJSJR3NzmP59gwWJx9kcfJBUtKPAxAWHEDXZnXo0awO8bF16RJTW2sOX6Dc/EI27ztCws5DrNqZyepdh8g4ngtAo4gQ+rWIpF/Loh9WNExDqjqFaBERqRb2HT7Jyh2Zp8Lf1gPHcA4C/Ix2jcPp0CSCDo0j6NgkglYNQ6v9RMX8gkJSDh5nY+oRNu07wqa9R9iQeoSc/EIAmtWrSXyzusTH1qFHbF0ui6qFmXr4pfpQiBYRkWrpyIk81uw+RMKuTNbuPsymvUc4mp0PQKC/0apBGB0aR9CyQSgt6ofSskEYjSNCqlxQdM6RnpVD8oEsktOzSDqQxeZ9R9iy/yjZeUWBuUagP+0ah9M5ujY9YuvQPbYO9cNCPK5cxFuXLESb2e3AU0BboKdz7ozJ1sxuBF4G/IE3nXPP+fbHAZOBesBq4MfOudzznVchWkRELoZzjj2ZJ9m49wgb9x5h874jbN53lMzj//9fT80gf1rUD6VFVCgxdWsSXafGqedGETUq7FjrwsKioJx66AR7Mk+SeugEuzNPsD39OMlpWRw5mXeqbVhwAG0bhdO+STgdmxT1zDePCq2wvzYRr1zKEN0WKATeAB4+U4g2M39gG3AdkAqsAkY657aY2VRghnNuspn9A1jvnHv9fOdViBYRkbKUeTyX5LQsktKOkXQgi+3pWSSnZfHN0WyK/zcZ4Gc0qh1C/bAQokKDiQwLIjI0+NSjds1AQoMDCAsJIDQ4gNCQgIseMpJXUEhWdj5ZOfkc8z0fPZnHwawcDmblkH4sh4NZuaT7Xu89fJJc3zCMb0WGBtM8qhYt64fSsn4oLeqH0bJBKPXDgqtcb7vIpXCuEB1Qmg92ziX6TnCuZj2BZOdciq/tZGComSUCVwM/9LV7j6Je7fOGaBERkbJUt1YQPePq0jOu7nf25+YXsu/wSVIPnWTPoRPsyTxB6qGTpB/LYXt6Fst35JxaqeJsgvz9CA70I8DPCPD3I9D3HOBnYJBf4CgodOQVFJLve87NLzw1LvlswkICioJ8aDDtGoVzXbsGxNSpQXSdmsTUrUGT2jU1mVLkEipViL5ATYA9xbZTgV4UDeE47JzLL7a/ydk+xMzGAGMAmjZtemkqFRERKSYowI/YyFrERtY6a5vc/EIyj+eSfiyHY9l5HMvJP9WDnJWTz9HsPHLyCikodOQXFpJXLDQ7+E6oDvA3Avz8CArwI8zXk/3/PduBhIYEEBla1PsdEqiALOKl84ZoM5sHNDzDod865z4u+5LOzDk3EZgIRcM5yuu8IiIi5xIU4EfDiBAaRmgSnkh1ct4Q7Zy7tpTn2AvEFNuO9u3LAGqbWYCvN/rb/SIiIiIiFVp53FpoFdDSzOLMLAgYAcx0RTMavwRu87UbBZRbz7aIiIiIyMUqVYg2s1vMLBXoDcwxs898+xub2VwAXy/zWOAzIBGY6pzb7PuI/wEeMrNkisZIv1WaekREREREyoNutiIiIiIicgbnWuKuPIZziIiIiIhUKQrRIiIiIiIlpBAtIiIiIlJCCtEiIiIiIiVUKScWmlk6sMuDU0cCBz04r5QvXefqQde56tM1rh50nasHr65zM+dc1JkOVMoQ7RUzSzjbDE2pOnSdqwdd56pP17h60HWuHiriddZwDhERERGRElKIFhEREREpIYXokpnodQFSLnSdqwdd56pP17h60HWuHircddaYaBERERGRElJPtIiIiIhICSlEi4iIiIiUkEL0GZjZjWa21cySzeyxMxwPNrMpvuMrzCzWgzKllC7gOj9kZlvMbIOZzTezZl7UKaVzvutcrN2tZubMrEItoSTndyHX2MyG+/4+bzazf5V3jVJ6F/BvdlMz+9LM1vr+3b7Jizrl4pnZ22aWZmabznLczGy878/ABjPrVt41FqcQfRoz8wdeBQYC7YCRZtbutGZ3A4eccy2AF4G/lG+VUloXeJ3XAvHOuU7AdOD58q1SSusCrzNmFgY8CKwo3wqltC7kGptZS+BxoK9zrj3wy/KuU0rnAv8uPwFMdc51BUYAr5VvlVIG3gVuPMfxgUBL32MM8Ho51HRWCtHf1xNIds6lOOdygcnA0NPaDAXe872eDlxjZlaONUrpnfc6O+e+dM6d8G0uB6LLuUYpvQv5+wzwR4p+GM4uz+KkTFzINb4XeNU5dwjAOZdWzjVK6V3IdXZAuO91BLCvHOuTMuCcWwhknqPJUOB9V2Q5UNvMGpVPdd+nEP19TYA9xbZTffvO2MY5lw8cAeqVS3VSVi7kOhd3N/DJJa1ILoXzXmff14Exzrk55VmYlJkL+bvcCmhlZkvMbLmZnaunSyqmC7nOTwF3mlkqMBcYVz6lSTkq6f/dl1SAVycWqSzM7E4gHrjC61qkbJmZH/ACMNrjUuTSCqDo698rKfpGaaGZdXTOHfayKClzI4F3nXN/N7PewD/NrINzrtDrwqRqUk/09+0FYoptR/v2nbGNmQVQ9LVRRrlUJ2XlQq4zZnYt8FtgiHMup5xqk7JzvuscBnQAFpjZTuByYKYmF1YqF/J3ORWY6ZzLc87tALZRFKql8riQ63w3MBXAObcMCAEiy6U6KS8X9H93eVGI/r5VQEszizOzIIomJ8w8rc1MYJTv9W3AF053ralsznudzawr8AZFAVpjKCunc15n59wR51ykcy7WORdL0dj3Ic65BG/KlYtwIf9m/4eiXmjMLJKi4R0p5VijlN6FXOfdwDUAZtaWohCdXq5VyqU2E/iJb5WOy4Ejzrn9XhWj4Ryncc7lm9lY4DPAH3jbObfZzJ4GEpxzM4G3KPqaKJmiAfAjvKtYLsYFXue/AqHANN+80d3OuSGeFS0ldoHXWSqxC7zGnwHXm9kWoAB4xDmnbw8rkQu8zr8G/tfMfkXRJMPR6uCqXMzsQ4p+4I30jW1/EggEcM79g6Kx7jcBycAJ4KfeVFpEt/0WERERESkhDecQERERESkhhWgRERERkRJSiBYRERERKSGFaBERERGRElKIFhEREREpIYVoEREREZESUogWERERESmh/wN7sDjIxwb54wAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"np.random.seed(0)\n",
"\n",
"def true_fn(X):\n",
" return np.cos(1.5 * np.pi * X)\n",
"\n",
"X_test = np.linspace(0, 1, 100)\n",
"plt.plot(X_test, true_fn(X_test), label=\"True function\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's genenerate a hold-out dataset for the example we saw earlier."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"n_samples, n_holdout_samples = 30, 30\n",
"\n",
"X = np.sort(np.random.rand(n_samples))\n",
"y = true_fn(X) + np.random.randn(n_samples) * 0.1\n",
"X_holdout = np.sort(np.random.rand(n_holdout_samples))\n",
"y_holdout = true_fn(X_holdout) + np.random.randn(n_holdout_samples) * 0.1\n",
"\n",
"plt.plot(X_test, true_fn(X_test), label=\"True function\")\n",
"plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
"plt.scatter(X_holdout, y_holdout, edgecolor='r', s=20, label=\"Holdout Samples\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Defining What is an Accurate Prediction\n",
"\n",
"Suppose that we have a function $\\texttt{isaccurate}(y, y')$ that determines if $y$ is an accurate estimate of $y'$, e.g.:\n",
"* Is the the target variable close enough to the true target?\n",
"$$\\texttt{isaccurate}(y, y') = \\text{true if } (|y - y'| \\text{ is small), else false}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* Did we predict the right class?\n",
"$$\\texttt{isaccurate}(y, y') = \\text{true if } (y = y') \\text{ else false} $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"This defines accuracy on a data point. We say a supervised learning model is accurate if it correctly predicts the target on *new (held-out) data*."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Defining What is an Accurate Model\n",
"\n",
"We can say that a predictive model $f$ is accurate if it's probability of making an error on a random holdout sample is small:\n",
"\n",
"$$ 1 - \\mathbb{P} \\left[ \\texttt{isaccurate}(\\dot y, f(\\dot x)) \\right] \\leq \\epsilon $$\n",
"\n",
"for $\\dot{x}, \\dot{y} \\sim \\mathbb{P}$, for some small $\\epsilon > 0$ and some definition of accuracy."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can also say that a predictive model $f$ is inaccurate if it's probability of making an error on a random holdout sample is large:\n",
"\n",
"$$ 1 - \\mathbb{P} \\left[ \\texttt{isaccurate}(\\dot y, f(\\dot x)) \\right] \\geq \\epsilon $$\n",
"\n",
"or equivalently\n",
"\n",
"$$\\mathbb{P} \\left[ \\texttt{isaccurate}(\\dot y, f(\\dot x)) \\right] \\leq 1-\\epsilon.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Generalization\n",
"\n",
"In machine learning, __generalization__ is the property of predictive models to achieve good performance on new, heldout data that is distinct from the training set.\n",
"\n",
"Will supervised learning return a model that generalizes?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"# Recall: Supervised Learning\n",
"\n",
"Recall our intuitive definition of supervised learning.\n",
"\n",
" \n",
"\n",
"1. First, we collect a dataset of labeled training examples.\n",
"2. We train a model to output accurate predictions on this dataset.\n",
"3. When the model sees new, similar data, it will also be accurate."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Recall: Supervised Learning\n",
"\n",
"Recall that supervised learning at a high level performs the following procedure:\n",
"1. Collect a training dataset $\\mathcal{D}$ of labeled examples.\n",
"2. Output a model that is accurate on $\\mathcal{D}$.\n",
"\n",
"I claim that the output model is also guaranteed to generalize if $\\mathcal{D}$ is large enough."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Applying Supervised Learning\n",
"\n",
"In order to prove that supervised learning works, we will make two simplifying assumptions:\n",
"1. We define a model class $\\mathcal{M}$ containing $H$ different models.\n",
"2. One of these models fits the training data perfectly (is accurate on every point) and we choose that model.\n",
"\n",
"(Both of these assumptions can be relaxed.)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Why Supervised Learning Works\n",
"\n",
"__Claim__: The probability that supervised learning will return an inaccurate model decreases exponentially with training set size $n$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"1. A model $f$ is inaccurate if $\\mathbb{P} \\left[ \\texttt{isaccurate}(\\dot y, f(\\dot x)) \\right] \\leq 1-\\epsilon$. The probability that an inaccurate model $f$ perfectly fits the training set is at most $\\prod_{i=1}^n \\mathbb{P} \\left[ \\texttt{isaccurate}(y^{(i)}, f(x^{(i)})) \\right] \\leq (1-\\epsilon)^n$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"2. We have $H$ models in $\\mathcal{M}$, and any of them could be in accurate. The probability that at least one the at most $H$ inaccurate models willl fit the training set perfectly is $\\leq H (1-\\epsilon)^n$.\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Therefore, the claim holds."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
" \n",
"# Part 3: Overfitting and Underfitting\n",
"\n",
"Let's now dive deeper into the concept of generalization and two possible failure modes of supervised learning: overfitting and underfitting."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Generalization\n",
"\n",
"We will assume that the dataset is governed by a probability distribution $\\mathbb{P}$, which we will call the *data distribution*. We will denote this as\n",
"$$x, y \\sim \\mathbb{P}.$$\n",
"\n",
"A hold-out set $\\dot{\\mathcal{D}} = \\{(\\dot{x^{(i)}}, \\dot{y^{(i)}}) \\mid i = 1,2,...,n\\}$ consists of *independent and identicaly distributed* (IID) samples from $\\mathbb{P}$ and is distinct from the training set."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"A model that __generalizes__ is accurate on a hold-out set."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Polynomial Regression\n",
"\n",
"In 1D polynomial regression, we fit a model\n",
"$$ f_\\theta(x) := \\theta^\\top \\phi(x) $$\n",
"that is linear in $\\theta$ but non-linear in $x$ because the features $\\phi(x) : \\mathbb{R} \\to \\mathbb{R}^p$ are non-linear.\n",
"\n",
"By using polynomial features such as $\\phi(x) = [1\\; x\\; \\ldots\\; x^p]$, we can fit any polynomial of degree $p$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Polynomials Better Fit the Data\n",
"\n",
"When we switch from linear models to polynomials, we can better fit the data and increase the accuracy of our models."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Consider the synthetic dataset that we have seen earlier."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from sklearn.pipeline import Pipeline\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"np.random.seed(0)\n",
"n_samples = 30\n",
"X = np.sort(np.random.rand(n_samples))\n",
"y = true_fn(X) + np.random.randn(n_samples) * 0.1\n",
"\n",
"X_test = np.linspace(0, 1, 100)\n",
"plt.plot(X_test, true_fn(X_test), label=\"True function\")\n",
"plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Although fitting a linear model does not work well, qudratic or cubic polynomials improve the fit."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"degrees = [1, 2, 3]\n",
"plt.figure(figsize=(14, 5))\n",
"for i in range(len(degrees)):\n",
" ax = plt.subplot(1, len(degrees), i + 1)\n",
"\n",
" polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)\n",
" linear_regression = LinearRegression()\n",
" pipeline = Pipeline([(\"pf\", polynomial_features), (\"lr\", linear_regression)])\n",
" pipeline.fit(X[:, np.newaxis], y)\n",
"\n",
" ax.plot(X_test, true_fn(X_test), label=\"True function\") \n",
" ax.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
" ax.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
" ax.set_xlim((0, 1))\n",
" ax.set_ylim((-2, 2))\n",
" ax.legend(loc=\"best\")\n",
" ax.set_title(\"Polynomial of Degree {}\".format(degrees[i]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Towards Higher-Degree Polynomial Features?\n",
"\n",
"As we increase the complexity of our model class $\\mathcal{M}$ to even higher degree polynomials, we are able to fit the data increasingly even better."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"What happens if we further increase the degree of the polynomial?"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"degrees = [30]\n",
"plt.figure(figsize=(14, 5))\n",
"for i in range(len(degrees)):\n",
" ax = plt.subplot(1, len(degrees), i + 1)\n",
"\n",
" polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)\n",
" linear_regression = LinearRegression()\n",
" pipeline = Pipeline([(\"pf\", polynomial_features), (\"lr\", linear_regression)])\n",
" pipeline.fit(X[:, np.newaxis], y)\n",
"\n",
" X_test = np.linspace(0, 1, 100)\n",
" ax.plot(X_test, true_fn(X_test), label=\"True function\") \n",
" ax.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
" ax.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
" ax.set_xlim((0, 1))\n",
" ax.set_ylim((-2, 2))\n",
" ax.legend(loc=\"best\")\n",
" ax.set_title(\"Polynomial of Degree {}\".format(degrees[i]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# The Problem With Increasing Model Capacity\n",
"\n",
"As the degree of the polynomial increases to the size of the dataset, we are increasingly able to fit every point in the dataset.\n",
"\n",
"However, this results in a highly irregular curve: its behavior outside the training set is wildly inaccurate."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Overfitting\n",
"\n",
"Overfitting is one of the most common failure modes of machine learning.\n",
"* A very expressive model (a high degree polynomial) fits the training dataset perfectly.\n",
"* The model also makes wildly incorrect prediction outside this dataset, and doesn't generalize."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Underfitting\n",
"\n",
"A related failure mode is underfitting.\n",
"\n",
"* A small model (e.g. a straight line), will not fit the training data well.\n",
"* Held-out data is similar to training data, so it will not be accurate either.\n",
"\n",
"\n",
"\n",
"Finding the tradeoff between overfitting and underfitting is one of the main challenges in applying machine learning."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Overfitting vs. Underfitting: Evaluation\n",
"\n",
"We can measure overfitting and underfitting by estimating accuracy on held-out data and comparing it to the training data.\n",
"* If training perforance is high but held-out performance is low, we are overfitting.\n",
"* If training perforance is low but held-out performance is low, we are underfitting."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"degrees = [1, 20, 5]\n",
"titles = ['Underfitting', 'Overfitting', 'A Good Fit']\n",
"plt.figure(figsize=(14, 5))\n",
"for i in range(len(degrees)):\n",
" ax = plt.subplot(1, len(degrees), i + 1)\n",
"\n",
" polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)\n",
" linear_regression = LinearRegression()\n",
" pipeline = Pipeline([(\"pf\", polynomial_features), (\"lr\", linear_regression)])\n",
" pipeline.fit(X[:, np.newaxis], y)\n",
"\n",
" ax.plot(X_test, true_fn(X_test), label=\"True function\") \n",
" ax.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
" ax.scatter(X, y, edgecolor='b', s=20, label=\"Samples\", alpha=0.2)\n",
" ax.scatter(X_holdout[::3], y_holdout[::3], edgecolor='r', s=20, label=\"Samples\")\n",
" ax.set_xlim((0, 1))\n",
" ax.set_ylim((-2, 2))\n",
" ax.legend(loc=\"best\")\n",
" ax.set_title(\"{} (Degree {})\".format(titles[i], degrees[i]))\n",
" ax.text(0.05,-1.7, 'Holdout MSE: %.4f' % ((y_holdout-pipeline.predict(X_holdout[:, np.newaxis]))**2).mean())"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Dealing with Underfitting\n",
"\n",
"Balancing overfitting vs. underfitting is a major challenges in applying machine learning. Briefly, here are some approaches:\n",
"* To fight under-fitting, we may increase our model class to encompass more expressive models.\n",
"* We may also create richer features for the data that will make the dataset easier to fit."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Dealing with Overfitting\n",
"\n",
"We will see many ways of dealing with overftting, but here are some ideas:\n",
"* If we're overfitting, we may reduce the complexity of our model by reducing the size of $\\mathcal{M}$\n",
"* We may also modify our objective to penalize complex models that may overfit the data."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
" \n",
"# Part 4: Regularization\n",
"\n",
"We will now see a very important way to reduce overfitting --- regularization. We will also see several important new algorithms."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Generalization\n",
"\n",
"We will assume that the dataset is governed by a probability distribution $\\mathbb{P}$, which we will call the *data distribution*. We will denote this as\n",
"$$x, y \\sim \\mathbb{P}.$$\n",
"\n",
"A hold-out set $\\dot{\\mathcal{D}} = \\{(\\dot{x^{(i)}}, \\dot{y^{(i)}}) \\mid i = 1,2,...,n\\}$ consists of *independent and identicaly distributed* (IID) samples from $\\mathbb{P}$ and is distinct from the training set."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Review: Overfitting\n",
"\n",
"Overfitting is one of the most common failure modes of machine learning.\n",
"* A very expressive model (a high degree polynomial) fits the training dataset perfectly.\n",
"* The model also makes wildly incorrect prediction outside this dataset, and doesn't generalize."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can visualize overfitting by trying to fit a small dataset with a high degree polynomial."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"degrees = [30]\n",
"plt.figure(figsize=(14, 5))\n",
"for i in range(len(degrees)):\n",
" ax = plt.subplot(1, len(degrees), i + 1)\n",
"\n",
" polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)\n",
" linear_regression = LinearRegression()\n",
" pipeline = Pipeline([(\"pf\", polynomial_features), (\"lr\", linear_regression)])\n",
" pipeline.fit(X[:, np.newaxis], y)\n",
"\n",
" X_test = np.linspace(0, 1, 100)\n",
" ax.plot(X_test, true_fn(X_test), label=\"True function\") \n",
" ax.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
" ax.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
" ax.set_xlim((0, 1))\n",
" ax.set_ylim((-2, 2))\n",
" ax.legend(loc=\"best\")\n",
" ax.set_title(\"Polynomial of Degree {}\".format(degrees[i]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Regularization: Intuition\n",
"\n",
"The idea of regularization is to penalize complex models that may overfit the data."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"In the previous example, a less complex would rely less on polynomial terms of high degree."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Regularization: Definition\n",
"\n",
"The idea of regularization is to train models with an augmented objective $J : \\mathcal{M} \\to \\mathbb{R}$ defined over a training dataset $\\mathcal{D}$ of size $n$ as\n",
"$$J(f) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, f(x^{(i)})) + \\lambda \\cdot R(f).$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's dissect the components of this objective:\n",
"\n",
"$$J(f) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, f(x^{(i)})) + \\lambda \\cdot R(f).$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* A loss function $L(y, f(x))$ such as the mean squared error."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* A regularizer $R : \\mathcal{M} \\to \\mathbb{R}$ that penalizes models that are overly complex."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* A regularization parameter $\\lambda > 0$, which controls the strength of the regularizer."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"When the model $f_\\theta$ is parametrized by parameters $\\theta$, we can also use the following notation:\n",
"\n",
"$$J(\\theta) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, f_\\theta(x^{(i)})) + \\lambda \\cdot R(\\theta).$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# L2 Regularization: Definition\n",
"\n",
"How can we define a regularizer $R: \\mathcal{M} \\to \\mathbb{R}$ to control the complexity of a model $f \\in \\mathcal{M}$?\n",
"\n",
"In the context of linear models $f(x) = \\theta^\\top x$, a widely used approach is L2 regularization, which defines the following objective:\n",
"$$J(\\theta) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, \\theta^\\top x^{(i)}) + \\frac{\\lambda}{2} \\cdot ||\\theta||_2^2.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's dissect the components of this objective.\n",
"$$J(\\theta) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, \\theta^\\top x^{(i)}) + \\frac{\\lambda}{2} \\cdot ||\\theta||_2^2.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* The regularizer $R : \\mathcal{M} \\to \\mathbb{R}$ is the function \n",
"$R(\\theta) = ||\\theta||_2^2 = \\sum_{j=1}^d \\theta_j^2.$ \n",
"This is also known as the L2 norm of $\\theta$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* The regularizer penalizes large parameters. This prevents us from over-relying on any single feature and penalizes wildly irregular solutions."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* L2 regularization can be used with most models (linear, neural, etc.)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# L2 Regularization for Polynomial Regression\n",
"\n",
"Let's consider an application to the polynomial model we have seen so far. Given polynomial features $\\phi(x)$, we optimize the following objective:\n",
"$$ J(\\theta) = \\frac{1}{2n} \\sum_{i=1}^n \\left( y^{(i)} - \\theta^\\top \\phi(x^{(i)}) \\right)^2 + \\frac{\\lambda}{2} \\cdot ||\\theta||_2^2. $$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We are going to implement regularized and standard polynomial regression on three random training sets sampled from the same distribution."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from sklearn.linear_model import Ridge\n",
"\n",
"degrees = [15, 15, 15]\n",
"plt.figure(figsize=(14, 5))\n",
"for idx, i in enumerate(range(len(degrees))):\n",
" # sample a dataset\n",
" np.random.seed(idx)\n",
" n_samples = 30\n",
" X = np.sort(np.random.rand(n_samples))\n",
" y = true_fn(X) + np.random.randn(n_samples) * 0.1\n",
"\n",
" # fit a least squares model\n",
" polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)\n",
" linear_regression = LinearRegression()\n",
" pipeline = Pipeline([(\"pf\", polynomial_features), (\"lr\", linear_regression)])\n",
" pipeline.fit(X[:, np.newaxis], y)\n",
" \n",
" # fit a Ridge model\n",
" polynomial_features = PolynomialFeatures(degree=degrees[i], include_bias=False)\n",
" linear_regression = Ridge(alpha=0.1) # sklearn uses alpha instead of lambda\n",
" pipeline2 = Pipeline([(\"pf\", polynomial_features), (\"lr\", linear_regression)])\n",
" pipeline2.fit(X[:, np.newaxis], y) \n",
"\n",
" # visualize results\n",
" ax = plt.subplot(1, len(degrees), i + 1)\n",
" # ax.plot(X_test, true_fn(X_test), label=\"True function\") \n",
" ax.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"No Regularization\")\n",
" ax.plot(X_test, pipeline2.predict(X_test[:, np.newaxis]), label=\"L2 Regularization\") \n",
" ax.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
" ax.set_xlim((0, 1))\n",
" ax.set_ylim((-2, 2))\n",
" ax.legend(loc=\"best\")\n",
" ax.set_title(\"Dataset sample #{}\".format(idx))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can show that by usinng small weights, we prevent the model from learning irregular functions."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Non-regularized weights of the polynomial model need to be large to fit every point:\n",
"[-3.02370887e+03 1.16528860e+05 -2.44724185e+06 3.20288837e+07]\n",
"\n",
"By regularizing the weights to be small, we force the curve to be more regular:\n",
"[-2.70114811 -1.20575056 -0.09210716 0.44301292]\n"
]
}
],
"source": [
"print('Non-regularized weights of the polynomial model need to be large to fit every point:')\n",
"print(pipeline.named_steps['lr'].coef_[:4])\n",
"print()\n",
"\n",
"print('By regularizing the weights to be small, we force the curve to be more regular:')\n",
"print(pipeline2.named_steps['lr'].coef_[:4])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# How to Choose $\\lambda$?\n",
"\n",
"In brief, the most common approach is to choose the value of $\\lambda$ that results in the best performance on a held-out *validation* set.\n",
"\n",
"We will later see this strategies and several other in more detail"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Normal Equations for Regularized Models\n",
"\n",
"How, do we fit regularized models? In the linear case, we can do this easily by deriving generalized normal equations! \n",
"\n",
"Let $L(\\theta) = \\frac{1}{2} (X \\theta - y)^\\top (X \\theta - y)$ be our least squares objective. We can write the Ridge objective as:\n",
"$$ J(\\theta) = \\frac{1}{2} (X \\theta - y)^\\top (X \\theta - y) + \\frac{1}{2} \\lambda ||\\theta||_2^2 $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"This allows us to derive the gradient as follows:\n",
"\\begin{align*}\n",
"\\nabla_\\theta J(\\theta) \n",
"& = \\nabla_\\theta \\left( \\frac{1}{2} (X \\theta - y)^\\top (X \\theta - y) + \\frac{1}{2} \\lambda ||\\theta||_2^2 \\right) \\\\\n",
"& = \\nabla_\\theta \\left( L(\\theta) + \\frac{1}{2} \\lambda ||\\theta||_2^2 \\right) \\\\\n",
"& = \\nabla_\\theta L(\\theta) + \\lambda \\theta \\\\\n",
"& = (X^\\top X) \\theta - X^\\top y + \\lambda \\theta \\\\\n",
"& = (X^\\top X + \\lambda I) \\theta - X^\\top y\n",
"\\end{align*}\n",
"\n",
"We used the derivation of the normal equations for least squares to obtain $\\nabla_\\theta L(\\theta)$ as well as the fact that: $\\nabla_x x^\\top x = 2 x$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can set the gradient to zero to obtain normal equations for the Ridge model:\n",
"$$ (X^\\top X + \\lambda I) \\theta = X^\\top y. $$\n",
"\n",
"Hence, the value $\\theta^*$ that minimizes this objective is given by:\n",
"$$ \\theta^* = (X^\\top X + \\lambda I)^{-1} X^\\top y.$$\n",
"\n",
"Note that the matrix $(X^\\top X + \\lambda I)$ is always invertible, which addresses a problem with least squares that we saw earlier."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Algorithm: Ridge Regression\n",
"\n",
"* __Type__: Supervised learning (regression)\n",
"* __Model family__: Linear models\n",
"* __Objective function__: L2-regularized mean squared error\n",
"* __Optimizer__: Normal equations"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
" \n",
"# Part 5: Regularization and Sparsity\n",
"\n",
"We will now look another form of regularization, which will have an important new property called sparsity."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Regularization: Definition\n",
"\n",
"The idea of regularization is to train models with an augmented objective $J : \\mathcal{M} \\to \\mathbb{R}$ defined over a training dataset $\\mathcal{D}$ of size $n$ as\n",
"$$ J(f) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, f(x^{(i)})) + \\lambda \\cdot R(f). $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's dissect the components of this objective:\n",
"\n",
"$$ J(f) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, f(x^{(i)})) + \\lambda \\cdot R(f). $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* A loss function $L(y, f(x))$ such as the mean squared error."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* A regularizer $R : \\mathcal{M} \\to \\mathbb{R}$ that penalizes models that are overly complex."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# L1 Regularizion: Definition\n",
"\n",
"Another closely related approach to regularization is to penalize the size of the weights using the L1 norm.\n",
"\n",
"In the context of linear models $f(x) = \\theta^\\top x$, L1 regularization yields the following objective:\n",
"$$ J(\\theta) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, \\theta^\\top x^{(i)}) + \\lambda \\cdot ||\\theta||_1. $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Let's dissect the components of this objective.\n",
"$$ J(\\theta) = \\frac{1}{n} \\sum_{i=1}^n L(y^{(i)}, \\theta^\\top x^{(i)}) + \\lambda \\cdot ||\\theta||_1. $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* The regularizer $R : \\mathcal{M} \\to \\mathbb{R}$ is the function \n",
"$R(\\theta) = ||\\theta||_1 = \\sum_{j=1}^d |\\theta_j|.$ \n",
"This is also known as the L1 norm of $\\theta$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* The regularizer also penalizes large weights. It also forces more weights to decay to zero, as opposed to just being small."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Algorithm: Lasso\n",
"\n",
"L1-regularized linear regression is also known as the Lasso (least absolute shrinkage and selection operator).\n",
"\n",
"* __Type__: Supervised learning (regression)\n",
"* __Model family__: Linear models\n",
"* __Objective function__: L1-regularized mean squared error"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"* __Optimizer__: gradient descent, coordinate descent, least angle regression (LARS) and others"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Regularizing via Constraints\n",
"\n",
"Consider regularized problem with a penalty term:\n",
"$$ \\min_{\\theta \\in \\Theta} L(\\theta) + \\lambda \\cdot R(\\theta). $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We may also enforce an explicit constraint on the complexity of the model:\n",
"\\begin{align*}\n",
"\\min_{\\theta \\in \\Theta} \\; & L(\\theta) \\\\\n",
"\\text{such that } \\; & R(\\theta) \\leq \\lambda'\n",
"\\end{align*}\n",
"We will not prove this, but solving this problem is equivalent so solving the penalized problem for some $\\lambda > 0$ that's different from $\\lambda'$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"In other words, \n",
"* We can regularize by explicitly enforcing $R(\\theta)$ to be less than a value instead of penalizing it.\n",
"* For each value of $\\lambda$, we are implicitly setting a constraint of $R(\\theta)$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Regularizing via Constraints: Example\n",
"\n",
"This is what it looks like for a linear model:\n",
"\\begin{align*}\n",
"\\min_{\\theta \\in \\Theta} \\; & \\frac{1}{2n} \\sum_{i=1}^n \\left( y^{(i)} - \\theta^\\top x^{(i)} \\right)^2 \\\\\n",
"\\text{such that } \\; & ||\\theta|| \\leq \\lambda'\n",
"\\end{align*}\n",
"where $||\\cdot||$ can either be the L1 or L2 norm."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# L1 vs. L2 Regularization\n",
"\n",
"The following image by Divakar Kapil and Hastie et al. explains the difference between the two norms.\n",
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Sparsity: Definition\n",
"\n",
"A vector is said to be sparse if a large fraction of its entires is zero."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"L1-regularized linear regression produces *sparse weights*.\n",
"* This is makes the model more interpretable\n",
"* It also makes it computationally more tractable in very large dimensions."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Sparsity: Ridge Model\n",
"\n",
"To better understand sparsity, we will fit L2-regularized linear models to the UCI diabetes dataset and observe the magnitude of each weight (colored lines) as a function of the regularization parameter."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(4.466835921509635e-06,\n",
" 223.872113856834,\n",
" -868.4051623855127,\n",
" 828.0533448059361)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# based on https://scikit-learn.org/stable/auto_examples/linear_model/plot_ridge_path.html\n",
"from sklearn.datasets import load_diabetes\n",
"from sklearn.linear_model import Ridge\n",
"from matplotlib import pyplot as plt\n",
"\n",
"X, y = load_diabetes(return_X_y=True)\n",
"\n",
"# create ridge coefficients\n",
"alphas = np.logspace(-5, 2, )\n",
"ridge_coefs = []\n",
"for a in alphas:\n",
" ridge = Ridge(alpha=a, fit_intercept=False)\n",
" ridge.fit(X, y)\n",
" ridge_coefs.append(ridge.coef_)\n",
"\n",
"# plot ridge coefficients\n",
"plt.figure(figsize=(14, 5))\n",
"plt.plot(alphas, ridge_coefs)\n",
"plt.xscale('log')\n",
"plt.xlabel('Regularization parameter (lambda)')\n",
"plt.ylabel('Magnitude of model parameters')\n",
"plt.title('Ridge coefficients as a function of the regularization')\n",
"plt.axis('tight')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Sparsity: Lasso Model\n",
"\n",
"The above Ridge model did not produce sparse weights. Let's now compare it to a Lasso model."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(3673.0002477572816,\n",
" -133.00520290291772,\n",
" -869.3573357636973,\n",
" 828.4524952229636)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Based on: https://scikit-learn.org/stable/auto_examples/linear_model/plot_lasso_lars.html\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"from sklearn.datasets import load_diabetes\n",
"from sklearn.linear_model import lars_path\n",
"\n",
"# create lasso coefficients \n",
"_, _, lasso_coefs = lars_path(X, y, method='lasso')\n",
"xx = np.sum(np.abs(lasso_coefs.T), axis=1)\n",
"\n",
"# plot ridge coefficients\n",
"plt.figure(figsize=(14, 5))\n",
"plt.subplot('121') \n",
"plt.plot(alphas, ridge_coefs)\n",
"plt.xscale('log')\n",
"plt.ylabel('Regularization Strength (alpha)')\n",
"plt.ylabel('Coefficents')\n",
"plt.title('Ridge coefficients as a function of the regularization')\n",
"plt.axis('tight')\n",
"\n",
"# plot lasso coefficients\n",
"plt.subplot('122') \n",
"plt.plot(3500-xx, lasso_coefs.T)\n",
"ymin, ymax = plt.ylim()\n",
"plt.xlim(ax.get_xlim()[::-1]) # reverse axis\n",
"plt.ylabel('Coefficients')\n",
"plt.ylabel('Regularization Strength')\n",
"plt.title('LASSO Path')\n",
"plt.axis('tight')"
]
}
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