Lectures/Lecture09/3dasm_Lecture9.ipynb

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   "source": [
    "<img src=../figures/Brown_logo.svg width=50%>\n",
    "\n",
    "## Data-Driven Design & Analyses of Structures & Materials (3dasm)\n",
    "\n",
    "## Lecture 9\n",
    "\n",
    "### Miguel A. Bessa | <a href = \"mailto: miguel_bessa@brown.edu\">miguel_bessa@brown.edu</a>  | Associate Professor"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "**What:** A lecture of the \"3dasm\" course\n",
    "\n",
    "**Where:** This notebook comes from this [repository](https://github.com/bessagroup/3dasm_course)\n",
    "\n",
    "**Reference for entire course:** Murphy, Kevin P. *Probabilistic machine learning: an introduction*. MIT press, 2022. Available online [here](https://probml.github.io/pml-book/book1.html)\n",
    "\n",
    "**How:** We try to follow Murphy's book closely, but the sequence of Chapters and Sections is different. The intention is to use notebooks as an introduction to the topic and Murphy's book as a resource.\n",
    "* If working offline: Go through this notebook and read the book.\n",
    "* If attending class in person: listen to me (!) but also go through the notebook in your laptop at the same time. Read the book.\n",
    "* If attending lectures remotely: listen to me (!) via Zoom and (ideally) use two screens where you have the notebook open in 1 screen and you see the lectures on the other. Read the book."
   ]
  },
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   "source": [
    "**Optional reference (the \"bible\" by the \"bishop\"... pun intended 😆) :** Bishop, Christopher M. *Pattern recognition and machine learning*. Springer Verlag, 2006.\n",
    "\n",
    "**References/resources to create this notebook:**\n",
    "* [Car figure](https://korkortonline.se/en/theory/reaction-braking-stopping/)\n",
    "\n",
    "Apologies in advance if I missed some reference used in this notebook. Please contact me if that is the case, and I will gladly include it here."
   ]
  },
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   "source": [
    "## **OPTION 1**. Run this notebook **locally in your computer**:\n",
    "1. Confirm that you have the '3dasm' mamba (or conda) environment (see Lecture 1).\n",
    "2. Go to the 3dasm_course folder in your computer and pull the last updates of the [repository](https://github.com/bessagroup/3dasm_course):\n",
    "```\n",
    "git pull\n",
    "```\n",
    "    - Note: if you can't pull the repo due to conflicts (and you can't handle these conflicts), use this command (with **caution**!) and your repo becomes the same as the one online:\n",
    "```\n",
    "git reset --hard origin/main\n",
    "```\n",
    "3. Open command window and load jupyter notebook (it will open in your internet browser):\n",
    "```\n",
    "jupyter notebook\n",
    "```\n",
    "5. Open notebook of this Lecture and choose the '3dasm' kernel."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## **OPTION 2**. Use **Google's Colab** (no installation required, but times out if idle):\n",
    "\n",
    "1. go to https://colab.research.google.com\n",
    "2. login\n",
    "3. File > Open notebook\n",
    "4. click on Github (no need to login or authorize anything)\n",
    "5. paste the git link: https://github.com/bessagroup/3dasm_course\n",
    "6. click search and then click on the notebook for this Lecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [],
   "source": [
    "# Basic plotting tools needed in Python.\n",
    "\n",
    "import matplotlib.pyplot as plt # import plotting tools to create figures\n",
    "import numpy as np # import numpy to handle a lot of things!\n",
    "from IPython.display import display, Math # to print with Latex math\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\" # render higher resolution images in the notebook\n",
    "plt.rcParams[\"figure.figsize\"] = (8,4) # rescale figure size appropriately for slides"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "## Outline for today\n",
    "\n",
    "* Linear models for regression: Practical tutorial (**Part I**: noiseless 1D example; underfitting vs. overfitting; interpolation vs. extrapolation)\n",
    "    - A practical session on how to train linear regression models (no theory!)\n",
    "\n",
    "**Reading material**: This notebook + Chapter 11"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Today's lecture is going to be more practical\n",
    "\n",
    "Since we covered the fundamentals of Bayesian and non-Bayesian machine learning..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Today we will focus on how to train **linear regression models** using [scikit-learn](https://scikit-learn.org)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "* Soon we will derive the models that we are going to cover today..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "As we learned in Lecture 2, let's load the pandas dataframe that is in the \"../data\" folder:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            x           y\n",
      "0    9.516939   29.749036\n",
      "1   72.398757  642.132203\n",
      "2   17.950326   36.648484\n",
      "3    9.440853   18.604106\n",
      "4   78.791008  769.656168\n",
      "5   16.961121   57.971010\n",
      "6   65.410368  559.093313\n",
      "7   58.671099  463.686613\n",
      "8   21.550603   92.242676\n",
      "9   36.866913  197.688573\n",
      "10  15.728748   56.885233\n",
      "11  58.511494  388.753795\n",
      "12  57.419190  399.807488\n",
      "13  38.459157  213.181519\n",
      "14   8.841742   20.387384\n",
      "15  60.733051  516.341724\n",
      "16  49.256663  307.931956\n",
      "17  35.895121  181.123049\n",
      "18  79.195652  750.178284\n",
      "19  69.156669  553.153541\n",
      "20  77.634896  746.031880\n",
      "21   9.254011   20.810698\n",
      "22  15.451468   39.872527\n",
      "23  14.438247   42.118771\n",
      "24  13.410999   44.775122\n",
      "25  53.747057  375.013937\n",
      "26  10.283719   19.438868\n",
      "27  82.005477  742.336845\n",
      "28  81.805562  706.620282\n",
      "29  51.837742  345.212876\n",
      "30  20.283785   65.303165\n",
      "31  28.359647  155.185137\n",
      "32  74.993715  676.628982\n",
      "33  21.827564   81.150935\n",
      "34  70.519111  700.520033\n",
      "35  74.208532  622.453560\n",
      "36  14.518958   40.927570\n",
      "37  13.357644   39.770922\n",
      "38  75.346253  707.973754\n",
      "39  44.923956  251.300805\n",
      "40  26.801159  124.098654\n",
      "41  29.906265  118.100900\n",
      "42  40.226356  215.082100\n",
      "43  66.282662  537.845048\n",
      "44  47.342777  308.558833\n",
      "45   3.087674    5.947997\n",
      "46  21.254611  101.295276\n",
      "47  46.939484  345.778352\n",
      "48  38.875692  219.095582\n",
      "49  76.705452  742.720134\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "# read csv data provided by someone else (this time I also specify that the first column provides the indices)\n",
    "car_prob_df = pd.read_csv(\"../data/data_for_car_prob.csv\", index_col=0)\n",
    "print(car_prob_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "As before, we can separate the data into inputs (features) $x$ and outputs $y$ (targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data_x is:\n",
      " [ 9.51693942 72.39875748 17.95032583  9.44085299 78.79100778 16.96112056\n",
      " 65.4103675  58.67109927 21.55060313 36.86691294 15.72874781 58.51149357\n",
      " 57.41918959 38.45915667  8.84174221 60.73305107 49.25666345 35.89512052\n",
      " 79.19565172 69.15666925 77.63489641  9.25401128 15.45146824 14.43824684\n",
      " 13.41099874 53.74705712 10.28371886 82.00547705 81.80556249 51.8377421\n",
      " 20.28378484 28.35964692 74.99371524 21.82756352 70.51911096 74.20853195\n",
      " 14.51895792 13.35764354 75.34625316 44.92395642 26.80115926 29.90626522\n",
      " 40.22635624 66.28266205 47.34277718  3.08767411 21.25461134 46.93948443\n",
      " 38.87569199 76.70545196]\n",
      "\n",
      "Data_y is:\n",
      " [ 29.74903647 642.13220315  36.64848446  18.60410602 769.65616843\n",
      "  57.97101034 559.09331318 463.68661322  92.24267632 197.68857288\n",
      "  56.88523327 388.75379474 399.80748803 213.18151905  20.38738432\n",
      " 516.34172363 307.93195589 181.12304936 750.17828361 553.15354059\n",
      " 746.03187971  20.81069833  39.87252654  42.11877078  44.77512244\n",
      " 375.01393668  19.43886782 742.33684483 706.62028237 345.21287569\n",
      "  65.30316533 155.18513747 676.62898211  81.15093549 700.52003305\n",
      " 622.45356019  40.92757044  39.77092163 707.97375405 251.30080489\n",
      " 124.09865438 118.10089977 215.08209978 537.84504756 308.55883254\n",
      "   5.94799685 101.29527607 345.77835213 219.09558165 742.72013356]\n"
     ]
    }
   ],
   "source": [
    "Data_x = car_prob_df['x'].values # select the input VALUES from your dataframe into Data_x\n",
    "Data_y = car_prob_df['y'].values # select the output VALUES from your dataframe inta Data_y\n",
    "print(\"Data_x is:\\n\",Data_x)\n",
    "print(\"\\nData_y is:\\n\",Data_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "And we can plot the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 708
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_car_data, ax_car_data = plt.subplots() # create a plot\n",
    "ax_car_data.plot(Data_x, Data_y, 'b.')\n",
    "ax_car_data.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "ax_car_data.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "ax_car_data.set_title(\"Car stopping distance problem\", fontsize=20); # create title with font size 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Supervised learning: regression models\n",
    "\n",
    "As we have been discussing, when we do regression via supervised learning we want to:\n",
    "\n",
    "* create a machine learning model\n",
    "* train it on known data (known inputs $x$ and outputs $y$)\n",
    "* predict for new (unseen) data points, i.e. predict $y^*$ for a new value of $x^*$.\n",
    "\n",
    "Today we will talk about the simplest models: **linear regression**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear regression models\n",
    "\n",
    "Linear regression models encompass a class of machine learning methods that is larger than you might think..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As we will see, despite being called \"linear\" these models can do more than fitting a simple \"line\" to our data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For now, let's consider 1d datasets, i.e. where we have one input $x$ and one output $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simplest 1d linear regression model: fitting a line to your data\n",
    "\n",
    "1. Observation distribution:\n",
    "\n",
    "Usually, assumed as a Gaussian distribution,\n",
    "\n",
    "$$\n",
    "p(y|x, \\mathbf{z}) = \\mathcal{N}(y| \\mu_{y|z} = \\mathbf{w}^T \\boldsymbol{\\phi}(x), \\sigma_{y|z}^2 = \\sigma^2)\n",
    "$$\n",
    "\n",
    "where $\\mathbf{z} = (\\mathbf{w}, \\sigma)$ are all the hidden rv's of the model, i.e. the model parameters.\n",
    "* the vector $\\mathbf{w} = [w_0, w_1]^T$ includes the **bias** term $w_0$ and the **weight** $w_1$.\n",
    "* the vector $\\boldsymbol{\\phi}(x) = [1, x]^T$ includes the **basis functions**.\n",
    "\n",
    "2. A chosen Prior distribution on each hidden rv of $\\mathbf{z}$:\n",
    "\n",
    "Usually, the prior on $w_0$ and $\\sigma$ is the Uniform distribution.\n",
    "\n",
    "However, the prior on the weight $w_1$ is often chosen as something else (but it can also be Uniform)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Does this model remind you of something we did?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Car stopping distance problem when we knew one of the rv's and fixed $x$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that,\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "p(y|x, \\mathbf{z}) &= \\mathcal{N}(y| \\mathbf{w}^T \\boldsymbol{\\phi}(x), \\sigma^2) \\\\\n",
    "&= \\mathcal{N}(y| w_0 + w_1 x, \\sigma^2) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where we previously called $w_0 \\equiv b$, $w_1 \\equiv z$ and $\\sigma^2 \\equiv \\sigma_{y|z}^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Therefore, the only difference is that we now start to consider more than one rv, so we group them into vector $\\mathbf{z} = (\\mathbf{w}, \\sigma)$.\n",
    "\n",
    "About notation:\n",
    "\n",
    "* We can also write $\\mathbf{z}^T = [\\mathbf{w}^T, \\sigma]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### 1d linear regression models with different basis functions: fitting a polynomial to your data\n",
    "\n",
    "However, we know that usually a straight line does not provide a good fit to most data sets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A very important realization:\n",
    "\n",
    "* The basis functions vector $\\boldsymbol{\\phi}(x)$ does not need to be a *linear transformation*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* It could be a polynomial or any other **nonlinear** transformation of the feature (input) $x$.\n",
    "\n",
    "As long as the parameters of the basis functions vector $\\boldsymbol{\\phi}(x)$ are **fixed**, the model remains **linear in the parameters**, even if is not linear in the input (feature). That's why we still call this a **linear model**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here's how our **linear** regression model looks like for a polynomial basis functions vector $\\boldsymbol{\\phi}(x)$.\n",
    "\n",
    "1. Observation distribution:\n",
    "\n",
    "$$\n",
    "p(y|x, \\mathbf{z}) = \\mathcal{N}(y| \\mu_{y|z} = \\mathbf{w}^T \\boldsymbol{\\phi}(x), \\sigma_{y|z}^2 = \\sigma^2)\n",
    "$$\n",
    "\n",
    "where $\\mathbf{z} = (\\mathbf{w}, \\sigma)$ are all the hidden rv's of the model, i.e. the model parameters.\n",
    "* the vector $\\mathbf{w} = [w_0, w_1, w_2 ..., w_d]^T$ includes the **bias** term $w_0$ and the remaining **weights** $w_i$ with $i=1,..., d$.\n",
    "* the vector $\\boldsymbol{\\phi}(x) = [1, x, x^2, ..., x^d]^T$ includes the **basis functions**, which now correspond to a polynomial of degree $d$.\n",
    "\n",
    "2. A chosen Prior distribution for each hidden rv of $\\mathbf{z}$, as mentioned previously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear regression models from a Bayesian perspective\n",
    "\n",
    "The choice of likelihood and prior determines what is the linear regression model that you are choosing!\n",
    "\n",
    "| Likelihood | Prior (on the weights)    | Posterior      | Name of the model | Book section  |\n",
    "|---        |---         |---             |---              |---            |\n",
    "| Gaussian  | Uniform    | Point estimate | Least Squares regression  | 11.2.2  |\n",
    "| Gaussian  | Gaussian    | Point estimate | Ridge regression   | 11.3  |\n",
    "| Gaussian  | Laplace    | Point estimate | Lasso regression  | 11.4  |\n",
    "| Student-$t$  | Uniform    | Point estimate | Robust regression   | 11.6.1  |\n",
    "| Laplace  | Uniform    | Point estimate | Robust regression   | 11.6.2  |\n",
    "| Gaussian  | Gaussian    | Gaussian | Bayesian linear regression   | 11.7 |\n",
    "\n",
    "We will derive some of these models soon but not today. Today, we focus on the practical aspects!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Training (fitting) a linear model with Scikit-learn\n",
    "\n",
    "Let's see how to use [scikit-learn](https://scikit-learn.org) to train linear regression models.\n",
    "\n",
    "* [scikit-learn](https://scikit-learn.org) is a well-documented and user-friendly library that is great for introducing machine learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* You should really read the documentation.\n",
    "    - It includes many useful examples.\n",
    "    - It provides a short introduction to common machine learning algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example 1: training a linear model for the car stopping distance problem\n",
    "\n",
    "<img src=\"../figures/reaction-braking-stopping.svg\" title=\"Car stopping distance\" width=\"50%\" align=\"right\">\n",
    "\n",
    "Let's start by importing from scikit-learn the simplest linear regression model:\n",
    "\n",
    "* Least Squares Regression (i.e. model with Gaussian likelihood, Uniform prior and Point estimate posterior).\n",
    "\n",
    "And let's consider the simplest basis function:\n",
    "\n",
    "* A line (polynomial of degree 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression # For Least Squares Regression\n",
    "from sklearn.preprocessing import PolynomialFeatures # For Polynomial basis functions\n",
    "from sklearn.pipeline import make_pipeline # to link different objects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now let's define the model (Least Squares Regression + polynomial of degree 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# We start by defining the model (polynomial basis + Least Squares Regression)\n",
    "degree = 1 # degree of polynomial we want to fit\n",
    "poly_model = make_pipeline(PolynomialFeatures(degree),LinearRegression())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Then we train the model for our data (input Data_x and output Data_y that were loaded with pandas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Uncomment line below (this is just for students to understand: don't panic when encountering an error!)\n",
    "#poly_model.fit(Data_x,Data_y) # but it gives an ERROR!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This gives an error! Fortunately, scikit-learn tells us what happened..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Scikit-learn expects the inputs to be formatted as a 2D array (matrix), instead of a 1D array (vector).\n",
    "\n",
    "This happens because usually we fit machine learning models for multidimensional inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Reshape the input vector into a 2D array:\n",
    "Data_X = np.reshape(Data_x, (-1, 1)) # we use capital letters for matrices and lower case for vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.51693942]\n",
      " [72.39875748]\n",
      " [17.95032583]\n",
      " [ 9.44085299]\n",
      " [78.79100778]\n",
      " [16.96112056]\n",
      " [65.4103675 ]\n",
      " [58.67109927]\n",
      " [21.55060313]\n",
      " [36.86691294]\n",
      " [15.72874781]\n",
      " [58.51149357]\n",
      " [57.41918959]\n",
      " [38.45915667]\n",
      " [ 8.84174221]\n",
      " [60.73305107]\n",
      " [49.25666345]\n",
      " [35.89512052]\n",
      " [79.19565172]\n",
      " [69.15666925]\n",
      " [77.63489641]\n",
      " [ 9.25401128]\n",
      " [15.45146824]\n",
      " [14.43824684]\n",
      " [13.41099874]\n",
      " [53.74705712]\n",
      " [10.28371886]\n",
      " [82.00547705]\n",
      " [81.80556249]\n",
      " [51.8377421 ]\n",
      " [20.28378484]\n",
      " [28.35964692]\n",
      " [74.99371524]\n",
      " [21.82756352]\n",
      " [70.51911096]\n",
      " [74.20853195]\n",
      " [14.51895792]\n",
      " [13.35764354]\n",
      " [75.34625316]\n",
      " [44.92395642]\n",
      " [26.80115926]\n",
      " [29.90626522]\n",
      " [40.22635624]\n",
      " [66.28266205]\n",
      " [47.34277718]\n",
      " [ 3.08767411]\n",
      " [21.25461134]\n",
      " [46.93948443]\n",
      " [38.87569199]\n",
      " [76.70545196]]\n"
     ]
    }
   ],
   "source": [
    "print(Data_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "After reshaping the input as a 2D array, we see that we can fit the model!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
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       "    --sklearn-color-icon: #878787;\n",
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       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
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       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
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       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
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       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
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       "#sk-container-id-1 div.sk-parallel-item::after {\n",
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       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
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       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
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       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
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       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
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       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
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       "\n",
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       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
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       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
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       "  padding-left: 1em;\n",
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       "*/\n",
       "\n",
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       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
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       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
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       "\n",
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       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
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       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
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       "  float: left;\n",
       "  margin-right: 0.25em;\n",
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       "\n",
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       "  color: var(--sklearn-color-text);\n",
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       "/* Toggleable content - dropdown */\n",
       "\n",
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       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
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       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
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       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
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       "\n",
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       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;, PolynomialFeatures(degree=1)),\n",
       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;, PolynomialFeatures(degree=1)),\n",
       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;PolynomialFeatures<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.PolynomialFeatures.html\">?<span>Documentation for PolynomialFeatures</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>PolynomialFeatures(degree=1)</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=1)),\n",
       "                ('linearregression', LinearRegression())])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_model.fit(Data_X,Data_y) # now we were able to train (fit) our linear model to the data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "That's it! Here's your first ML model: fitting a straight line 😆"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now that we have a model, we can predict the output $y^*$ for any new input point $x^*$.\n",
    "\n",
    "In particular, we can predict the output for each of the input points $x$ that we used for training the model (i.e. at Data_X)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "y_pred = poly_model.predict(Data_X) # In scikit-learn, predicting from a model is a one-liner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Done! These are the predictions for all your training points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "But we can also predict the output $y^*$ for other points.\n",
    "\n",
    "This enables us to visualize the model by predicting the output for a uniformly spaced set of points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Now create linearly spaced points for plotting our linear model\n",
    "x_plot = np.linspace(0, 90, 200) # 200 points uniformly spaced\n",
    "y_plot = poly_model.predict(np.reshape(x_plot, (-1, 1))) # prediction of those points (note the reshape again)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Finally, we can just plot the data, the predictions for each input training point, and the linear model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# The usual plotting style for this model and the data.\n",
    "fig_poly, ax_poly = plt.subplots() # create a plot\n",
    "ax_poly.plot(Data_x, Data_y, 'b.', markersize=12,label=\"Data\") # Markers locating data points\n",
    "ax_poly.plot(Data_x, y_pred, 'm*', markersize=12,label=\"Predictions\") # Markers locating prediction points)\n",
    "legend_str = \"Linear regression with Polynomial of degree \" + str(degree)\n",
    "ax_poly.plot(x_plot, y_plot, 'm-', linewidth=2,label=legend_str) # polynomial interpolation plotted\n",
    "ax_poly.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "ax_poly.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "ax_poly.set_title(\"Car stopping distance problem\", fontsize=20) # create title with font size 20\n",
    "ax_poly.legend(loc='upper left', fontsize=15) # replot legend\n",
    "fig_poly.set_size_inches(7.5, 6) # scale figure to be taller\n",
    "plt.close(fig_poly) # do not plot the figure now. We will show it in a later cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x600 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "image/png": {
       "height": 567,
       "width": 669
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig_poly # just call the figure that we created in the previous cell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can see all the things that we have done in a single plot!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## In-class Exercise\n",
    "\n",
    "1. Put it all together and create a linear model using a polynomial of degree 2 for the same data.\n",
    "\n",
    "\n",
    "2. Compare your plot with the one obtained for the straight line (polynomial of degree 1).\n",
    "\n",
    "\n",
    "3. Play a bit with your code by changing the degree of the polynomial. What happens?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Write your code for In-class Exercise:\n",
    "\n",
    "# until here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Go back to the previous cell and try to keep increasing the polynomial degree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* You see the prediction getting worse!\n",
    "\n",
    "This is called **overfitting**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Overfitting is a natural consequence of having a model that is more complex than it should be!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- As we know, the mean of the data that originates from the car stopping distance problem is generated with a quadratic model: $y = z_1 x + z_2 x^2$\n",
    "    * Therefore, we don't need additional complexity to describe the *mean* of the data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Also, the fit is better **within the domain** that we used for training ($x\\in [3, 83]$) than away from it.\n",
    "\n",
    "In other words, we **interpolate** better than we **extrapolate**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Nevertheless, overfitting is also an issue when we are interpolating...\n",
    "    - See this by making the degree very high, e.g. 30, and plot for $x\\in [5, 80]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It might be surprising, but this is an important issue in ML.\n",
    "\n",
    "It is very common to use models that are complicated (have many parameters) and that perform poorly even when interpolating, but especially when extrapolating!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "## Solution for In-class Exercise\n",
    "\n",
    "```python\n",
    "degree = 2\n",
    "poly_model = make_pipeline(PolynomialFeatures(degree),LinearRegression()) # model\n",
    "poly_model.fit(np.reshape(Data_x, (-1, 1)),Data_y) # training (fitting)\n",
    "y_pred = poly_model.predict(Data_X) # predict y for Data_x\n",
    "x_plot = np.linspace(0, 90, 200) # 200 points uniformly spaced\n",
    "y_plot = poly_model.predict(np.reshape(x_plot, (-1, 1))) # prediction for those points\n",
    "fig_poly, ax_poly = plt.subplots() # create a plot\n",
    "ax_poly.plot(Data_x, Data_y, 'b.', markersize=12,label=\"Data\") # Markers locating data points)\n",
    "ax_poly.plot(Data_x, y_pred, 'm*', markersize=12,label=\"Predictions\") # Markers locating prediction points)\n",
    "legend_str = \"Linear regression with Polynomial of degree \" + str(degree)\n",
    "ax_poly.plot(x_plot, y_plot, 'm-', linewidth=2,label=legend_str) # polynomial interpolation plotted\n",
    "ax_poly.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "ax_poly.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "ax_poly.set_title(\"Car stopping distance problem\", fontsize=20) # create title with font size 20\n",
    "ax_poly.legend(loc='upper left') # replot legend\n",
    "```"
   ]
  }
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