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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Featured Recipe #4: Introduction to Machine Learning in Python with scikit-learn"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> This is a featured recipe from the [**IPython Cookbook**](http://ipython-books.github.io/), the definitive guide to **high-performance scientific computing** and **data science** in Python."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In **Statistical Data Analysis**, we are interested in getting insight into data, understanding complex phenomena through partial observations, and making informed decisions in the presence of uncertainty. In **Machine Learning**, we are still interested in analyzing and processing data using statistical tools. However, the goal is not necessarily to *understand* the data, but to *learn* from it."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Learning from data is close to what we do, as humans. From our experience, we intuitively learn general facts and relations about the world, even if we don't fully understand its complexity. The increasing computational power of computers makes them able to learn from data, too. That's the heart of [**machine learning**](http://en.wikipedia.org/wiki/Machine_learning), a modern and fascinating branch of artificial intelligence, computer science, statistics, and applied mathematics."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This featured recipe is a hands-on introduction to the most fundamental concepts in machine learning. These concepts are routinely used by data scientists. We will illustrate them with **scikit-learn**, a popular and user-friendly Python package for machine learning."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> This featured recipe is [Chapter 8](https://github.com/ipython-books/cookbook-code/blob/master/toc.md#chapter-8-machine-learning)'s introduction. In the [book](http://ipython-books.github.io/), the rest of the chapter illustrates many standard machine learning algorithms for classification, regression, feature selection, clustering, and dimension reduction."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Fundamental concepts in Machine Learning"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's describe the fundamental definitions and concepts of machine learning."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Learning from data\n",
      "\n",
      "In machine learning, most datasets can be represented as tables containing numerical values. Every row is called an **observation**, a **sample**, or a **data point**. Every column is called a **feature** or a **variable**."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's call $N$ the number of rows (or number of points), and $D$ the number of columns (or number of features). The number $D$ is also called the **dimensionality** of the data. The reason is that we can view this table as a set $E$ of vectors in a space with $D$ dimensions (or **vector space**). Here, a vector $x$ contains $D$ numbers $(x_1, ..., x_D)$, also called **components**. This mathematical point of view is very useful and we will use it throughout this recipe. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One generally makes the distinction between *supervised learning* and *unsupervised learning*."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* [**Supervised learning**](http://en.wikipedia.org/wiki/Supervised_learning) is when we have a label $y$ associated to every data point $x$. The goal is to learn the mapping from $x$ to $y$ from our data. The data gives us this mapping for a finite set of points, but what we want is to *generalize* this mapping. In other words, we want to find the label of any point $x$ that does not belong to our data.\n",
      "\n",
      "* [**Unsupervised learning**](http://en.wikipedia.org/wiki/Unsupervised_learning) is when we don't have any labels. What we want to do is discover some hidden structure in the data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Supervised learning\n",
      "\n",
      "Mathematically, supervised learning consists of finding a function $f$ that maps a set of points $E$ to a set of labels $F$, knowing a finite set of associations $(x, y)$ which is given by our data. This is what generalization is about: after observing the pairs $(x_i, y_i)$, given a new $x$, we are able to find the corresponding $y$ by applying the function $f$ to $x$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is a common practice to split the set of data points into two subsets: the **training set** and the **test set**. We learn the function $f$ on the training set, and test it on the test set. This is essential when assessing the predictive power of a model. By training and testing a model on the same set, our model may not be able to generalize well. This is the fundamental concept of **overfitting**, which we will detail later."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One generally makes the distinction between **classification** and **regression**, two particular instances of supervised learning."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* **Classification** is when our labels $y$ can only take a finite set of values (categories). Examples include:\n",
      "    * Handwritten digit recognition: $x$ is an image with a handwritten digit, $y$ is a digit between 0 and 9.\n",
      "    * Spam filtering: $x$ is an e-mail, and $y$ is 0 or 1 whether that e-mail is a spam or not."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* **Regression** is when our labels $y$ can take any real (continuous) value. Examples include:\n",
      "    * Predicting stock market.\n",
      "    * Predicting sales.\n",
      "    * Detecting the age of a person from a picture."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The figure below illustrates the difference between classification and regression."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Difference between classification and regression](images/ml.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Unsupervised learning\n",
      "\n",
      "Broadly speaking, unsupervised learning helps us discover systemic structures in our data. It is harder to grasp than supervised learning, in that there is no precise question and answer in general."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are a few important terms related to unsupervised learning: \n",
      "\n",
      "* **Clustering**: Grouping similar points together within clusters.\n",
      "* **Density estimation**: Estimating a probability density that can explain the distribution of the data points.\n",
      "* **Dimension reduction**: Getting a simple representation of high-dimensional data points by projecting them onto a lower-dimensional space. This technique is notably used for data visualization.\n",
      "* **Manifold learning** (or nonlinear dimension reduction): Finding a low-dimensional manifold containing the data points."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Feature selection and feature extraction\n",
      "\n",
      "In a supervised learning context, when our data contains many features, it is sometimes necessary to choose a subset of them. The features we want to keep are those that are most relevant to our question. This is the problem of **feature selection**."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Additionally, we may want to extract new features by applying complex transformations on our original dataset. This is **feature extraction**. For example, in computer vision, training a classifier directly on the pixels is not the most efficient method in general. We may want to extract the relevant points of interest or make appropriate mathematical transformations. These steps depend on our dataset and on the questions we want to answer."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example, it is often necessary to preprocess the data before learning models. **Feature scaling** (or **data normalization**) is a common preprocessing step where features are linearly rescaled to fit in the range $[-1,1]$ or $[0,1]$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Feature extraction and feature selection involve a balanced combination of domain expertise, intuition, and mathematical methods. These early steps are crucial, and they may be even more important than the learning steps themselves. The reason is that the few dimensions that are relevant to our problem are generally hidden in the high dimensionality of our dataset. We need to uncover the low-dimensional structure of interest to improve the efficiency of our learning models."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Chapter 8* illustrates a few feature selection and feature extraction methods. Methods that are specific to signals, images or sounds are covered in *Chapter 10* and *Chapter 11*. Here are a few further references:\n",
      "\n",
      "* [Feature selection in scikit-learn](http://scikit-learn.org/stable/modules/feature_selection.html)\n",
      "* [Feature selection on Wikipedia](http://en.wikipedia.org/wiki/Feature_selection)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Overfitting, underfitting, and the bias-variance tradeoff"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A central notion in machine learning is the trade-off between [**overfitting**](http://en.wikipedia.org/wiki/Overfitting) and [**underfitting**](http://en.wikipedia.org/wiki/Underfitting). A model may be able to represent our data accurately. However, if it is *too* accurate, it may not generalize well to unobserved data. For example, in face recognition, a too-accurate model would be unable to identity someone who styled their hair differently that day. The reason is that our model may learn irrelevant features in the training data. On the contrary, an insufficiently trained model would not generalize well either. For example, it would be unable to correctly recognize twins. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A popular solution to reduce overfitting consists of adding structure to the model, for example with [**regularization**](http://en.wikipedia.org/wiki/Regularization_%28mathematics%29). This method favors simpler models during training ([Occam's razor](http://en.wikipedia.org/wiki/Occam%27s_razor))."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The [**bias-variance dilemma**](http://en.wikipedia.org/wiki/Bias-variance_dilemma) is closely related. The **bias** of a model quantifies how precise a model is across training sets. The **variance** quantifies how sensitive the model is to small changes in the training set. A robust model is not overly sensitive to small changes. The dilemma involves minimizing both bias and variance; we want a precise and robust model. Simpler models tend to be less accurate but more robust. Complex models tend to be more accurate but less robust."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The importance of this trade-off cannot be overstated. This question pervades the entire discipline of machine learning. *Chapter 8* contains many examples."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Model selection"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we will see in *Chapter 8*, there are many supervised and unsupervised algorithms. For example, well-known classifiers that we will cover include logistic regression, nearest-neighbors, Naive Bayes, support vector machines. There are many others algorithms that we couldn't cover."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "No model performs uniformly better than the others. One model may perform well on one dataset and badly on another. This is the question of [**model selection**](http://en.wikipedia.org/wiki/Model_selection)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will see systematic methods for assessing the quality of a model on a particular dataset (notably cross-validation). In practice, machine learning is not an \"exact science\" in that it frequently involves trials and errors. We need to try different models and empirically choose the one that performs best."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That being said, understanding the details of the learning models allows us to gain intuition about which model is best adapted to our current problem."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are a few references on this question:\n",
      "\n",
      "* [Model evaluation in scikit-learn](http://scikit-learn.org/stable/modules/model_evaluation.html)\n",
      "* [How to choose a classifier?](http://blog.echen.me/2011/04/27/choosing-a-machine-learning-classifier/)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An important class of machine learning methods that we couldn't cover in *Chapter 8* include [**neural networks**](http://en.wikipedia.org/wiki/Artificial_neural_network) and [**deep learning**](http://en.wikipedia.org/wiki/Deep_learning). Deep learning is the subject of very active research in machine learning. Many state-of-the-art results are currently achieved by deep learning methods."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Getting started with scikit-learn"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's now introduce the basics of the machine learning package [**scikit-learn**](http://scikit-learn.org). This package is the main tool we are going to use throughout the chapter. Its clean API makes it really easy to define, train, and test models. Plus, scikit-learn is specifically designed for speed and (relatively) big data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will show here a very basic example of **linear regression** in the context of **curve fitting**. This toy example will allow us to illustrate key concepts such as linear models, overfitting, underfitting, regularization, and cross-validation."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> You will find all instructions to install scikit-learn on the [documentation](http://scikit-learn.org/stable/install.html)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## How to do it..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will generate a one-dimensional dataset with a simple model (including some noise), and we will try to fit a function to this data. With this function, we can predict values on new data points. This is a curve-fitting regression problem."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. First, let's make all the necessary imports."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.stats as st\n",
      "import sklearn.linear_model as lm\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2. We now define the deterministic function underlying our generative model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = lambda x: np.exp(3 * x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3. We generate the values along the curve on $[0, 2]$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_tr = np.linspace(0., 2, 200)\n",
      "y_tr = f(x_tr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4. Now, let's generate our data points within $[0, 1]$. We use the function $f$ and we add some Gaussian noise."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([0, .1, .2, .5, .8, .9, 1])\n",
      "y = f(x) + np.random.randn(len(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "5. Let's plot our data points on $[0, 1]$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(6,3));\n",
      "plt.plot(x_tr[:100], y_tr[:100], '--k');\n",
      "plt.plot(x, y, 'ok', ms=10);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9W3l5edq7d6/y8/NVUVFxwXWBgYGK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       "text": [
        "<matplotlib.figure.Figure at 0x7978470>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "6. Now, we use scikit-learn to fit a linear model to the data. There are three steps. First, we create the model (an instance of the `LinearRegression` class). Then we fit the model to our data. Finally, we predict values from our trained model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We create the model.\n",
      "lr = lm.LinearRegression()\n",
      "# We train the model on our training dataset.\n",
      "lr.fit(x[:, np.newaxis], y);\n",
      "# Now, we predict points with our trained model.\n",
      "y_lr = lr.predict(x_tr[:, np.newaxis])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "style": "tip"
     },
     "source": [
      "We need to convert `x` and `x_tr` to column vectors, as it is a general convention in scikit-learn that observations are rows, while features are columns. Here, we have 7 observations with 1 feature."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "7. We now plot the result of the trained linear model. We obtain a regression line, in green here."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(6,3));\n",
      "plt.plot(x_tr, y_tr, '--k');\n",
      "plt.plot(x_tr, y_lr, 'g');\n",
      "plt.plot(x, y, 'ok', ms=10);\n",
      "plt.xlim(0, 1);\n",
      "plt.ylim(y.min()-1, y.max()+1);\n",
      "plt.title(\"Linear regression\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JkiQpee0mM1IKmqYhcmSBJEmSJEmSJJWf/St9eiJHGEiSJEmSJEmSJNcwSNrR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\nUmJmzpzJTTfd1OZ+7733Hu+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k95ocfyBphAfj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\ntgCwArUFAMxBwwAAQlhzc7NKS0tVUVHR/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       "text": [
        "<matplotlib.figure.Figure at 0x82eae10>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "8. The linear fit is not well adapted here, since the data points are generated according to a nonlinear model (an exponential curve). Therefore, we are now going to fit a nonlinear model. More precisely, we will fit a polynomial function to our data points. We can still use linear regression for that, by pre-computing the exponents of our data points. This is done by generating a **Vandermonde matrix**, using the `np.vander` function. We will explain this trick in more detail in *How it works...*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lrp = lm.LinearRegression()\n",
      "plt.figure(figsize=(6,3));\n",
      "plt.plot(x_tr, y_tr, '--k');\n",
      "\n",
      "for deg, s in zip([2, 5], ['-', '.']):\n",
      "    lrp.fit(np.vander(x, deg + 1), y);\n",
      "    y_lrp = lrp.predict(np.vander(x_tr, deg + 1))\n",
      "    plt.plot(x_tr, y_lrp, s, label='degree ' + str(deg));\n",
      "    plt.legend(loc=2);\n",
      "    plt.xlim(0, 1.4);\n",
      "    plt.ylim(-10, 40);\n",
      "    # Print the model's coefficients.\n",
      "    print(' '.join(['%.2f' % c for c in lrp.coef_]))\n",
      "plt.plot(x, y, 'ok', ms=10);\n",
      "plt.title(\"Linear regression\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "22.03 -4.25 0.00\n",
        "-476.66 1286.40 -1171.56 419.94 -38.56 0.00\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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r9/0UYvkoru6+KdSVJEmSlLoXaT4RkcqjEvh2S34DkiRJkjYubYD/8fUfGQ/V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\n9KIGozPZryHVup999lmjsvnz5zcaNM9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ACkGn46Rc+U9KRaF+Y+KumBKK5tm2Q4Fcf9wxMXRoQ+AQAAAABAgu3YsSPZIURt587o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\n0oVGpqyPEhiRJma9T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sHprX/FzcjI0De/+U0tWrRIkmSapm699VZ9+9vf1rnn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SJEmSJEmRYeFCkiRJkiRJkiRFhoULSZIkSZIkSZIUGRYuJEmSJEmSJElSZFi4kCRJ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\nJ4b2nQFOKqL9dIIhdXLbn1vC+FT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       "text": [
        "<matplotlib.figure.Figure at 0x82d34a8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have fitted two polynomial models of degree 2 and 5. The degree 2 polynomial appears to fit the data points less precisely than the degree 5 polynomial. However, it seems more robust: the degree 5 polynomial seems really bad at predicting values outside the data points (look for example at the portion $x >= 1$). This is what we call overfitting: by using a too complex model, we obtain a better fit on the trained dataset, but a less robust model outside this set. Note the large coefficients of the degree 5 polynomial: this is generally a sign of overfitting."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "9. We will now use a different learning model, called **ridge regression**. It works like linear regression, except that it prevents the polynomial's coefficients to explode (which was what happened in the overfitting example above). By adding a **regularization term** in the **loss function**, ridge regression imposes some structure on the underlying model. We will see more details in the next section."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The ridge regression model has a meta-parameter which represents the weight of the regularization term. We could try different values with trials and errors, using the `Ridge` class. However, scikit-learn includes another model called `RidgeCV` which includes a parameter search with cross-validation. In practice, it means that we don't have to tweak this parameter by hand: scikit-learn does it for us. Since the models of scikit-learn always follow the `fit`-`predict` API, all we have to do is replace `lm.LinearRegression` by `lm.RidgeCV` in the code above. We will give more details in the next section."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ridge = lm.RidgeCV()\n",
      "plt.figure(figsize=(6,3));\n",
      "plt.plot(x_tr, y_tr, '--k');\n",
      "\n",
      "for deg, s in zip([2, 5], ['-', '.']):\n",
      "    ridge.fit(np.vander(x, deg + 1), y);\n",
      "    y_ridge = ridge.predict(np.vander(x_tr, deg + 1))\n",
      "    plt.plot(x_tr, y_ridge, s, label='degree ' + str(deg));\n",
      "    plt.legend(loc=2);\n",
      "    plt.xlim(0, 1.5);\n",
      "    plt.ylim(-5, 80);\n",
      "    # Print the model's coefficients.\n",
      "    print(' '.join(['%.2f' % c for c in ridge.coef_]))\n",
      "\n",
      "plt.plot(x, y, 'ok', ms=10);\n",
      "plt.title(\"Ridge regression\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "11.26 5.93 0.00\n",
        "4.39 3.80 3.32 3.27 3.97 0.00\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KZSNhxvYXgEVFbnsBYVHgTNYXuc91hM/7CUQvylvKvpOEUkRjiP5Obw+3EsZx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W3Dsri2+oWUDNaLJEqHP8AbNc28XN3I9ppm\nOuNQu76Xx2Vx2dwcrpifx4Wzs3E5Ii8lI7Hn9/vZu3fv4NMqmxOBjww6rmP4wD3AUwwM3t9CZMH7\nqxgYuD/JBAL3IiIiIiIiIiLxUre1kt0VG2MWuIdQyRwF7iUdtfkCbDvaxCvVjbxxrBlfwB77pnHK\nybBYM28aV8yfRlmxF6elgL2ETNbgfRbwL4POPT3K9Y8D3wF6CxldSSgw/+Io9xjAtwad+9lwF4qI\niIiIiIiIJFPdC9timnEPoQ1pSys2xKw9kVTX3NnNtqNNvFzdyM7jLfiD8QvY52U5KC+dxhWl01hR\n5MUyJ3OBFImXZAfvNwO/Ad6M4p584NfAef3O+YHvj3JPHfBDCJV56/ET4HJGztb/BnBFv+NG4N4o\nxikiIiIiIiIikhCHH3o0poF7y+um7Ed3DdmQVmSqqWvzUXm4iVePNPJWbStxjNcz3ePk8tJQhv35\nMzwK2MuYkh28/yBwB/A6oYD8C/RtMNufASwCPgF8BSgY9Pj3e+4bzWZCte5n9RzPByp72uuftT8H\n+Cbw+UH3/yuhAL6IiIiIiIiISMoI+vzUV+6KWXuGZYYC92vXxKxNkVRyrKmTVw438urhJqrq2uPa\n16xsVzhgv6jQjWkoYC+RS3bwvtfqni8AH3Cc0Ga0PkIb05YA3hHu/RnwvyPoowH4FPAckNlzbh7w\nB0JB+cPANGAuMLiw1O+Bf4ugDxERERERERGRuAv6/AT93aHv/X7sQGBc7RiWGc7YNyyL/PJVlFZs\nUMa9TCm2bXPwbAev9gTsjzR2xrW/ObkZXFE6jcvnT2NBQRaGAvYyTskO3g/3QRQXoaz4sTQRCto/\nHEV/LxPa6PYJQuV3ek0Dyka451fA56LoQ0REREREREQkLupe2Mbhhx6lvnJXX8DeHP/mllfteza8\nIa3pdGhzWpkyAkGb/afaePVII5WHmzjV6otrf6V5meEM+9K8TAXsJSaSHbzfAPwlcC1wMZBDqETO\nSILAXuA/gV8AZ8fR54vA+YQ2o70ZcA9zjQ3sAu4mlHUvIiIiIiIiIhJztm1HHOSr21o5/Ka0wfHV\nujcsC4cnSwF7mTJ8gSC7T7Tw6uEmKo800dTZHdf+FhRkccX8aVxeOo2SaZlj3yASpWQH7w/0fN1L\nKGh/HrCAUJmcHMAJtBDKsj8M7ARaY9DvaeBLwNeANcBiQtn3vSV7tgPvx6AfEREREREREZFhNTQ0\n8JWvfIX169fzsY99bNRr67ZWsrtiY0w3pc0vX6XAvUx67b4Abxxr5tXDjbxe00y7P3Y/I8NZXOgO\nB+yLcjLi2pdIsoP3/dnAuz1fidJJaJPcFxLYp4iIiIiIiIikuddff51bb72VY8eO8dJLL1FWVkZp\naemw19a9sG34jPsJMCyT0ooNMWtPJJGaOrvZdrSJV6ob2XmiBX9guMrcsWEAS2d5uKJ0GuWl05jh\ndcWtL5HBUil4LyIiIiIiIiIypQWDQR544AHuvvtuAj0161taWrjlllv405/+hMs1NDB4+KFHYxq4\nt7xuyn50lzallUnldKuPyiNNvHq4kb0nWwnGL16PacDKIi+X9wTs8936hIokh4L3IiIiIiIiIiIJ\nUFdXxxe/+EVeeGFoAYBdu3Zx1113cffddw84H/T5qa/cFbMxGJYZCtyvXROzNkXi5WhjJ68ebqTy\nSBNVde1x7ctlGVw4J4fyeblcOjeXnEyFTSX5tApFJC7a29u55pprAHj++edxu4fbG1pkctM6l3Sg\ndS7pQOtc0oHWefK9/PLLfOELX+DkyZMjXvPggw9y+WVrWPuBqwAwnQ6C/m7sngz9aBmWGc7YNyyL\n/PJVlFZsmLIZ91rnk59t27x3toNXqxt59UgTRxs749qf22ly6dxcykuncdGcbLKcVlz7iwWt8/Si\n4L2IxIVt21RVVYW/F5mKtM4lHWidSzrQOpd0oHWePH6/n3vuuYf7779/1P/3KwwP66x8Ard8m62E\nsu8NyyLvkhXj7vuqfc+GN6Q1nY4pvzmt1vnkFAja7D/VyiuHm6g80sjpVn9c+8vLcrBmXihgv7LI\ni9My49pfrGmdpxcF70VERERERERE4qC6upq/+Zu/YefOnaNeV2Z4+JpjDpZhDDhvBwLjLpljWBYO\nT9aUD9jL5NTVHWTXiRYqDzfx2tEmmjq749rfrGwX5fNyubx0GotneLBMY+ybRFKAgvciIiIiIiIi\nIjFk2za/+c1v+PrXv05ra+uo15YZHr7sKB4SuJ+o/PJVCtxLSmnu7GZ7TROvHWnijWMtdHXHbhPm\n4ZTmZfZsOJvLOflZGDH+GRNJBAXvRSQuMjIy+OlPfxr+XmQq0jqXdKB1LulA61zSgdZ54jQ3N3PH\nHXfw29/+dsxrV4yQcT9RhmVSWrEhpm1OBlrnqae2pYvXjoQC9ntPthKMc5WXJTPclJdOo3zeNGbn\nTs01oHWeXvSWU4Jt3bq1EDjd/9zy5ctxOvVuuIiIiIiIiMhktn37dr7whS9w9OjRiK7/R0cJy0xP\nTMdged2U/eguCteuiWm7IpGwbZuDZzuoPNLEa0caeb8+vhvOmgasLMqmvDSXNfNyme5xxbU/ST9+\nv5+9e/cOPj1j7dq1dYnoX5n3IiIiIiIiIiIT0N3dzX333ce9995LIBAY8ToLcPTkUdrYLDHcMR2H\nYZkK3EvCdQdt3qpt6QnYN1HXFt8NZ12WwUVzcigvzeWSklxyMhXelKlLq1tEREREREREZJyOHj3K\nF7/4RV577bURr1lheFhn5bPEcIdL5ASwscZZECG/fBUN2/Zg97xRYFgW+eWrKK3YQOHVl46rTZFo\ntPkCvHmsmcojTbxe00ybb+Q3rWLB47K4pCSHy0unceGcbLKcVlz7E0kVCt6LiIiIiIiIiETJtm0e\nf/xx/uEf/mHUTWnLRqhrP97APcCqR+7FdDoI+rsBMJ0ObU4rcXe2zc9rR5uoPNLInhOt+ONcwD4v\ny8GaebmUl05jZZEXp2XGtT+RVKTgvYiIiIiIiIhIFM6ePctXv/pVnnnmmVGvKzM8fNlRHNMNaQ3L\nCgfrFbCXeLJtmyONnbx2pInKI01U1bXHvc9Z2S4uL51G+bxcFs/wYJnarlPSm4L3IiIiIiIiIiIR\nam5u5oorruDkyZOjXrdihIz7icovX6WgvcRNIGjzzuk2KnsC9ieau+Le5zn5WT0Z9rmck5+FEeOf\nGZHJTMF7EREREREREZEI5eTk8NGPfpSHH3541OvWWfkxD9wblklpxYaYtinS2R1k1/EWKo80su1o\nM02d3XHtzzRg+Swva+blctm8XGZlZ8S1P5HJTMF7EREREREREZEobNy4kT//+c9UVVWFz1mAo6eO\nvY3NEsMd0z4tr5uyH92lDWklJpo6u9l+tIlXjzSx81gzXYH41q/PdJhcNCeHNfNyWV2SQ06mQpIi\nkdBPioiIiIiIiIhIFLKysnj44Ye59tprWdLtYp2VzxLDHc60D9h2jOvcm6HA/do1MWtT0s+J5i4q\njzTx2pEm9p9qJc77zZKX5eDSubmsmZfLBcXZuBzacFYkWgrei4hHiJQgAAAgAElEQVSIiIiIiIhE\nacWKFdz9yc9Q/JuXhgTqJxK4NywTOxDs+d4iv3wVpRUblHEvUQsEbarq2tl2tInXjjZxpKEz7n3O\nyc2gfF4ul82bxuIZbkzVrxeZEAXvRURERERERESiVLe1ktI/7SAQ0wx7i2uqnoOeNk2nQ5vTSlQ6\n/AF2HG9h+9GmhNSvN4AlMzzh+vUl0zLj2p9IulHwXkTiIhgMhus/Llq0CNPUx+Nk6tE6l3SgdS7p\nQOtc0oHWeWzVvbCNnTffGc6Qj5X88lU4vLGtlZ9O0nWd17X52HYkFKzfXduCP871652WwaribNbM\ny+XSubnkufUGUyKl6zpPVwrei0hcdHR0UF5eDkBNTQ0ejyfJIxKJPa1zSQda55IOtM4lHWidx9bh\nhx6NeeDesExKKzbEtM10ky7rPGjbHDzTwbajTWw72sTBsx1x7zM7w+KSkhzWzJvGhXOyyXJace9T\nhpcu61xCFLwXERERERERERlB0Ocn6A+VHjGdoTBKfeWumPZhed2hDWlV115G0NUdZNeJlnDAvr49\nvuVwAGZ6XayZF9pwdtksL5ap+vUiiabgvYiIiIiIiIjIIHUvbOPwQ49SX7kLOxAAQjXp8y5ZET6O\nBcMyQ4H7tWti1qZMDfXt/nDt+p3Hm+mKczkcgAUFWT0B+2nMz8/E0IazIkml4L2IiIiIiIiISD91\nWyuHrWlvBwITyro3LDPcpmFZ5JevorRigzLuBQDbtqmu7+S1nuz6qrr2uPdpGbCiKDu84ewMryvu\nfYpI5BS8F5G48Hg81NfXJ3sYInGldS7pQOtc0oHWuaQDrfPI1W2tZHfFxjjUtLe4puo56MlkNp0O\nTJc2+oylybjOfYEgb9W2hsvhnG71x73PLKfJ6jk5XDYvl9UlOXgzFB6cTCbjOpfx00+niIiIiIiI\niAihUjnDZdzHQn75Khxed8zblcmnqbOb12uaeO1IMzuON9Phj/16G6zQ4+SyeblcOjeXFUVeXJYZ\n9z5FZOIUvBcRERERERERAQ4/9GhcAveGZVJasSHm7crkYNs2NY1dbDvaxGtHm3jndBvB+JevZ1Gh\nm0vn5nLp3BzOyc9S/XqRSUjBexERERERERGZkt577z26u7tZsmTJsI8HfX6C/u7QgW1PqJ79SCyv\nO7Qhrerap5XuoM2+k33lcE40++LeZ4ZlcMHsbC6bm8vqubkUuFWWSWSyU/BeRERERERERKaU7u5u\nHnzwQb773e9y3nnn8fzzz+N09gUy617YxuGHHqW+chd2IBA6aZoQjHWdezMUuF+7JqbtSmpq7uzm\njWPNvF7TzBs1zbT6AnHvM9/t4JKS0GazZcXZZDpUDkdkKlHwXkRERERERESmjH379vH3f//37Nq1\nK3z8gx/8gDvuuAMIbUg7bF37CQTu88tX0bBtT/iNAMOyyC9fRWnFBmXcT2G2bVNd38n2miZer2lO\nWDmccwuyuHRuLpfNzWXB9CxMlcMRmbIUvBcRERERERGRSa+jo4N7772XBx54gEBgYMbzvffey3XX\nXUfhiUZ2V2yMaV17w7K46LHvA4RL8JhOB6ZLJUumos7uILtPtPD60Wa21zRR1+aPe59O02Blsben\nfn0uM7yuuPcpIqlBwXsRERERERERmdReeuklbr/9dt5///1hH/f7/dz32S/x8WN+iPGGtPnlq8KB\negXsp6ZTLb5wdv3uEy34AvFPr8/NdHBJSQ6Xzs1l1exs3C4r7n2KSOpR8F5EREREREREJqWGhgb+\n+Z//mUcffXTMaxdX14PpiWn/hmVSWrEhpm1K8gWCNm+fbuP1o01sq2nmSENnQvqdl5fZk12fw+JC\nD5apcjgi6U7BexERERERERGZVGzb5ne/+x3/+I//SF1d3bDXWICDUPDTxmaJ4Y7pGCyvO7QZrWra\nTwm9m81uP9rEjuMttHTFf7NZy4AVRX3lcIpyMuLep4hMLgrei4iIiIiIiMikcezYMe644w7+67/+\na9jHVxge1ln5LDHcWD0beQZsO/x9LBiWGQrcr10TszYlsfpvNrv9aDMH6hKz2Wx2hsXFc0LlcC6a\nk403Q6E5ERmZXiFEREREREREJOV1d3fz4x//mO9+97u0trYOe02Z4eFrjjlDAvUTCdwblhne4Naw\nLPLLV1FasUEZ95NQ72az24+G6tcnYrNZgNk5GVw2L1QOZ+lMr8rhiEjEFLwXkbjw+Xzcd999ANx+\n++24XK4kj0gk9rTOJR1onUs60DqXdDDZ1/mOHTu4/fbb2bt374jXlBkevuwojnGGvcU1Vc9BT5um\n06FNaVPYcOv8ZEsXr9c0s/1oM3tqE7PZrGnAspleVs/N4bK5uZRMy4x7n5I+JvvruURHb/Ul2Nat\nWwuB0/3PLV++HKdTv/xlamlra6OkpASAmpoaPJ7Ybgwlkgq0ziUdaJ1LOtA6l3QwWdd5U1MT3/72\nt/nZz36GbY8cdF1hePj6MBn3E1Vw5cVc/JsfxLRNiZ/+6/zu329nV113wjabzc10cHFJDpeU5HDh\nbJXDkfiZrK/nk5Xf7x/ujeMZa9euHX7DlRjTK4mIiIiIiIiIpJTeDWn/6Z/+idOnT495/TorP+aB\ne8MyKa3YENM2JT6aOrt5o6aZV947GT63ZV8dlisrrv0uKMhidUkOl8zNZeF0t8rhiEjMKXgvIiIi\nIiIiIinj0KFD3HHHHfzP//zPsI9bgKOnkEA3oWz8JYY7pmOwvO7QhrSqa5+SgrbNobMdvFHTzOs1\nfZvNBnwdce0302FywexsLinJYXVJDtM9KlciIvGl4L2IxIVlWVx//fXh70WmIq1zSQda55IOtM4l\nHUyWdf7AAw/wne98h66uriGPrTA8rLPyWWK4w1n2AdvmgN0e4zr3Zihwv3ZNzNqUiWvp6mbn8Rbe\nqGnmzWPN1Hd0D7nGMCzyll8Z/j4WirJdrC7J5ZK5OayY5cXlMGPSrsh4TZbXc4kNfZ4nwVTzXkRE\nRERERGR4Dz/8MN/4xjeGnC8zPHwtDjXtDcvEDgR7vrfIL19FacUGZdynALs3u/5YM2/UNPP26VB2\nfbxZBiyb5Q2XwynJzcCI8boTkclDNe9FRERERERERIBbb72Vxx9/nD179oTPlRkevuwojkPg3uKa\nquegp13T6cB0KbEumVp7s+t7AvbDZdfHQ+9ms5eW5HDhnBw8LmUzi0hqUPBeRERERERERFKCZVnc\nd999rF27Ftu2WRGnjHuA/PJVOLyxrZUv0bFtm/frO3i9JrHZ9RDabPaSubmsLslhUaEbU9n1IpKC\nFLwXERERERERkZQQ9PlZvnAxn7/5s/zk5z9lnZUfl8C9YZmUVmyIebsyttaubnaeCNWuf+NYM/Xt\nicmu791s9tKSHFaX5FLg0acsRCT1KXgvIiIiIiIiIklV98I2Dj/0KPWVu7ADAf4CuNy1CDMOWdiW\n1x3akFZ17RNiQHb9sWbePpW47PqibFc4u35FkReXpc1mRWRyUfBeREREREREZIoLBoP4fD4AXC4X\nppk6Qcy6rZXsvPnO8MaxvSwMiHHSvWGZocD92jWxbVgGaPMF2HE8VArnzWMtnG33J6Tf3s1mLynJ\nYbU2mxWRKUDBexEREREREZEpwrZtdu/ezZ49e9i/fz/79u3jnXfeobm5ecB1OTk5LFmyhGXLlrF0\n6VJWrlxJWVlZwgOddVsr2V2xcUjgfqLyy1fRsG0PdiAAhDanzS9fRWnFBmXcx0Fvdn1oo9kW9p9q\nTVh2fX6Wg4vm5LBam82KyBSk4L2IiIiIiIjIJHf27Fkee+wxHnnkEQ4ePDjm9c3NzWzfvp3t27eH\nzy1YsICbbrqJDRs2UFBQEM/hAqFSOcNl3E+UYVlc9Nj3AQj6Q/XUTacD06Ua57HU5guw83hf7fpE\nZdebBiyZ4WF1SQ4Xz8nhnIIsbTYrIlNWqgXvDaAUWA7MAaYBXUAD8C7wRs9xLGUCa4DFQB7gA2qA\n7UB1jPsSERERERERiZm6ujo2bdrEli1bwmVxxuvgwYNs3LiRu+++m/Xr17Np0yYKCwtjNNLQZrT9\ng+mHH3o05oF7CGXd9wbqFbCPHdu2qa7v5I1jzbxe08zbp1oJJDi7/uKSHFbNziY7I9XCWSIi8ZEK\nr3Z5wMeA/wVcDYz29r4f+CNwP/DSBPstBL4FfAZwj3DNDuDbwFMT7EtEREREREQkZmzb5sknn+TO\nO++kvr4+pm37fD4ee+wxnnvuOTZv3swNN9wwoXI6gzejBcA0IRj7wL1hmZRWbIh5u+mqubObncdb\n2HG8mR3HWjiT4Oz6i3sC9ucqu15E0lSyg/f/L3ArEOlb4U5Cgf6PAY8Afwe0jKPfDwBPMPobBQAX\nAr/v6etvCL15ICIiIiIiIpI0DQ0N3HbbbTz99NNx7ae+vp5bb72VP/zhD9x///3k5eVF3cZIm9HG\nI3Bved2hzWhV037cAkGbA3Vt7DjWwpvHmnn3THvCatfn9WbXzwll1+dkJjtkJSKSfMl+JbyE4QP3\n3UAtcKrn8XmESuj0dxOhUjfXAG1R9Hk58Cyhcjn9NRAqk5MHzAX673ByE+AFPh5FPyIiIiIiIiIx\nVVtby4033khVVVXC+nz66ad577332LJlC0VFRRHfF6/NaIdjWGYocL92Tdz7mmpOt/rYcayZN4+3\nsOt4C62+QEL6NQ1YXNhTu17Z9SIiw0p28L6/BuBRQmVxXmZgQN4ErgDu6vlvr9XAz4FPRNhHHvBr\nBgbuDwN/D/RPWZgNfBP4Qr9zNwJfBb4fYV8iaa29vZ1rrrkGgOeffx63e6TqVCKTl9a5pAOtc0kH\nWucyWdTW1rJu3TqqqxO/PduBAwdYt24dzzzzDG63m1/96ldUVFRgmuaw18drM1oIbUjbW37HsCzy\ny1dRWrFBGfcR6uoO8lZtK2/2lMI52tiZsL6nZTq4uCR+2fV6PZd0oHWeXpIdvLcJZbvfTShwP9Jm\ntEHgf4CrgAeBz/d7bD2hMjh/jqC/rwP90wTeJ5SJf3LQdceBLwJHgX/td34j8DOgMYK+RNKabdvh\nbCDbTtDnLEUSTOtc0oHWuaQDrXOZDBoaGrjxxhuTErjvVV1dzdVXX43P56OhoYHp06fzyU9+cthr\n47UZbcGVF3PhL783YONbbUo7Otu2OdLYyZvHWthxrJm9J1vxJWin2d7s+ot7susXxDm7Xq/nkg60\nztNLsoP33wL+i1CZnEgEgb8FVgEX9Tt/K2MH7wsJ1cjvZROqYz84cN/fd4EPAVf2HOcCdxDKyhcR\nERERERGJO9u2ue222xJaKmckp06dCn9/1113sW7dOjIdzgHBdID6yl0x77t3M1rT5VTAfgwtXd3s\nOt7Cm8daePN4M2faEreF37RMBxf1ZNdfqNr1IiITkuxX0GfHcU8Q2Az8pt+5D0Vw3/8FePodvwS8\nGMF9/wI83+/4cyh4LyIiIiIiIgny5JNPxn1z2vGYXtvEsx/YQPbx+gFlbPIuWRE+jhVtRju6QNDm\n3TPtvHmsmTePNVNVl7iNZnuz6y8qyWF1ArLrRUTSSbKD9+P18qDjfEJ17Ecr1PbRQcf/J8K+XiRU\n2md+z/Es4FJgW4T3i6SljIwMfvrTn4a/F5mKtM4lHWidSzrQOpdUVldXx5133pnsYQxhAZ+3ZuE9\nWkf/GLEdCMQ8616b0Q6vrs0XLoWz60QLLV2J2WgWILdf7fpUyq7X67mkA63z9DJZ3wrNADr6HdtA\nMXBq+MvxAvX0vVlhE6p9fzrC/h4mVGKn13cYZ/b91q1bCwf3u3z5cpxOfeRPREREREREBvrSl77E\nY489luxhDOtKM4cKR3FM29RmtCPzdQd562QrO4418+bxFo40JG6jWcuAJTM9XDQ7h4vm5LBgurLr\nRSQ9+P1+9u7dO/j0jLVr19Ylov/UeGs0erOHOXd2lOuXMnCu1UQeuAd4lYHB+7Io7hURERERERGJ\n2pkzZ9iyZUuyhzGiymALf2V3k2PEJrSgzWgHsm2bmsYu3jweKoXzVm3iNpoFmOl1hTLr52RTVpyN\nx2UlrG8REQmZrMH7KwYdH2H0TW+XDDp+O8r+3hmjPREREREREZGYevzxx/H5fMkexoi6sXk52MRH\nrIIJt6XNaEOaO7vZfaKFHcdbePNYM3UJ3Gg2w2FSVuTlwjk5XDQnm9k5GRjKrhcRSarJGrz/3KDj\nsTa+XTTouCbK/gZfPxdwAan7rygRERERERGZtGzb5pFHHkn2MMb0QqCJ68z8CQV503kzWl8gyNun\n2th5vIWdx1t470w7icuth3PyM7lwdg4XleSwdKYHl2UmsHcRERnLZAzeX8fAzHsb+PkY98wYdHws\nyj5PAQFCe/IAmEABUBtlOyIiIiIiIiJj2r17NwcPHkz2MMZUi49qu5NzjKxx3Z9um9Hats3hhs5w\nsP6tk610dQcT1n9OhsWFPZvMXjgnhwJ3+n7KQURkMphswft8QpvH9vd74M0x7vMOOm6Lsl+b0Aa5\n/dsZ3KaIiIiIiIhITOzZsyfZQ4hYtd3FOYwevM8vX0XDtj1puRnt2XY/u463sPN4MztPtFDfPlrV\n39gyDTh/hidcCmdBgRvLVCkcEZHJYjIF703glwzcrLYR+EoE9w4OtI9nS/b+wXtjmDZFRERERERE\nYmL//v3JHkLEjtqj/4ltWBYXPfZ9gLTYjLazO8je2tZQsP54C9UN4wlBjN9Mr4sL52Rz0ewcLpit\njWZFRCazyRS8vxf4X/2ObeALwPEI7s0cdDyeWvVdg47H95lAERERERERkTHs27cv2UOI2FF78J/L\nA+WXrwoH6qdiwD5o2xw808GOnmD926fa8AcTV7k+wzJYUZTNRXOyuWhODnNytdGsiMhUMVmC918B\nvjro3GbgiQjvH/w2t2scY8gYo00RERERERGRmHjnnXeSPYSI1YwSvDcsk9KKDQkcTWKcavGFM+t3\nnmihpSuQ0P7n52WGS+Esm+nF5dBGsyIiU9FkCN7/FXD/oHM/A74RRRutg44HZ+JHon+mvT1Mm+N2\n9uxZLMsiMzMT04z8F253dzcOR99TaBgGbrc7qr47OzsJBPr+keF0OnG5ontvo61t4BYCWVlZUc+j\nq6vvH3uah+YBmkcvzaOP5tFH8wjRPPpoHn00jxDNo4/m0UfzCJkM8wgGgzQ3N0fVXjK1E6QjGMAw\nDFwYmD1Z35bXHdqMdpSa9pPh+QBo8wXYfaIlvNHs8eaBb1jYgQDBQP8P+RtYruhCD0G/D9vum4dh\nOjAdoU8qZGdYrJodyqy/cHY20z3Dzy8dfj4ioXn00Tz6aB4h6TqPwf0BdHV1DZiHw+EYMo/u7sTt\nUzKcVH9rdh3wi0HntgC3RtnO4EC7J8r7DYaWyYlZ8P6yyy5j0aJFzJs3j5KSkoi/5s+fP+D4mmuu\nibrvioqKAW3cd999UbcxeFxVVVVR3f/MM89oHj00jz6aR4jm0Ufz6KN5hGgefTSPPppHiObRR/Po\no3mETIZ5+HzjqfSaXLd0v8fn/O9ywg6N3bDMUOB+7ZpR70vV5+PtA1XsO9nKIztque2pd1n/n2/x\nL1urefqdM0MC9wAN+19h1zfXhb/eeeBvox5D9ePfHdBG4PUnuGnVLP79+oX85q+X809Xz+dDCwtG\nDNwPN4+p+PMRCc2jj+bRR/MISdd5DO6vpKSEBQsWsGjRovDXueeeO+SasrKyqOcWS6mceX8VobI4\n/XdW+S9gA6HM92icGnQ8J8r7Zw4aRxA4E2UbImnLthNX71Ek0Xo/0r5o0aKosgREJotgMBj+h7TW\nuUxVWuciMWSZFFxxMaUVG0bNuE91X32qCmN6YqvlZjlNGvodf2hhAZ9eVZTQMUx2va/nx49Hsj2i\niEjqS9UdTC4BtjIwQ/5V4INAxzjau5lQqZ1ezxLK6o/UamBbv+P3gQXjGAdbt24tBE73P1dcXKyy\nOWn4cZ3hTKV5tLS0sGjRIgAOHTpEXl5eVG2kyjymyvOheYTEeh4dHR0sXLgQgJqaGjyesT/YlYrz\nmCrPh+YRn3m0tbVRUlICjL7OU30ekdI8+qTTPMZa55NlHmPRPEImwzyCwSDTp0+Pqr1ke//AuxiG\ngSfbiyNz8JZxI0vm89HQ4Wf3iVZ2Hm/m9fdPc6bdH37MdGRgRLGuxlM2JzfTwQXFXlbNzmHV7Gxy\nHEH9fPQY7zz6v55XVVWFxz7Z5tFrsj8fvTSPPrGYR11dXTjeUlVVRUFBwaScx2Qqm3Po0KHBt85Y\nu3ZtXcSDnYBUzLxfAfyJgYH7ncB1jC9wD3Bg0PH5Ud6/ZIz2JqSgoACn0xnLJiOWmTme8v8DRRKs\nGo3D4RjwJsR4aB59UmUe/V/8on0Bh9SZx0RpHiGaRx/No4/mEaJ59NE8+mgeIZpHH82jTzrMwzRN\ncnJyJk3d+5ycHKbNGN+bDYl8Ptp9Ad462cquEy3sPt5CdUP/zHoHlmv84zAsC8saXG13IKdlsGym\nhwt7gvXnFGSF9weIlXT4+YiU2+2eUDupMI+p8nxoHn1iMY/+AWq32x31JwZTZR6Jfj6G6y+SMfj9\n/jGviadUC94vAv4bmNbv3NvAh4CWCbT7NuAHeiPk84BZwMkI7y8fdLx7AmMRERERERERGdWSJUvY\nvn17socRkfPPjzY/LjF8gSDvnGoLBetPtHKgro1ggit6npOfxarZ2ayanc3yWV4yHCrLJSIikUul\n4P08QqVyCvudex+4Fjg7wbZbgJeA3p0LjJ52/zOCew1g7aBzT09wPCIiIiIiIiIjWrZs2aQJ3i9b\ntizZQwAgELQ5VN/B7uMt7DrRwr6TrXQFEhutL3A7WTU7mwtnZ3NBcTZ57uR8yl5ERKaGVAneFwHP\nA7P7nTtGKNheG6M+nqIveA9wC5EF768CSvsdnwQmx7+gRJLI4/FQX1+f7GGIxJXWuaQDrXNJB1rn\nkoqWLl2a7CFELFmZ97Ztc6ypqyezvoU9ta20dAXGvjGGMh0mK4u84ez6udMyMWJcCkcip9dzSQda\n5+klFYL3+YRK5ZzT79xpQpnxR2LYz+PAd+irpX8locD8i6PcYwDfGnTuZ8NdKCIiIiIiIhIrK1eu\nTPYQIpbIsZ5t87PrREv460xbYmsRmwacN93NhbOzWTU7hyUz3DgtlcIREZH4SHbwPhv4/xi4gWwD\n8EGgKsZ91QE/BP6h37mfAJczcnb/N4Ar+h03AvfGeFwiIiIiIiKS5qqrq5k/f374uKysjAULFnDw\n4MEkjmpsCxYsoKysLG7tt3R1s6e2ld0nWth1vIWapq649TWSomxXT2Z9DmXFXrIzkh1KERGRdJHs\n3zhPARcNOvd9YAZD68yP5U1CwfXRbAZuJrRZLcB8oBL4CgPr2M8Bvgl8ftD9/xpBHyIiIiIiIiJj\nsm2byspKvve97/Hyyy/z2muvcd555wFgGAY33XQTGzduTPIoR3fTTTfFtExMV3eQ/ada2XWilV3H\nWzh4tj3hm8x6XRZlxV5Wzc5h1exsinMyEjsAERGRHskO3v/FMOfuGmdbHyC0Ke1oGoBPAc8BmT3n\n5gF/IBSUPwxMA+YCgz/39nvg38Y5NhEREREREREgFLR/8cUX+d73vse2bdsAsID7/597+cEPfoDp\ndGC6nFw75zzuwqCbBEevI+RyudiwYcOE2ggEbd49086unk1m3z7dhj/Bm8w6TIPzZ3i4oKdu/cLp\nbixTdetFRCT5kh28T4aXgY8ATxCqt99rGjDSZ/1+BXwuzuMSERERERGRKcy2bZ577jm+973vsXPn\nTgBWGB7WWfksMdxYz+xj6zPXYFgW+WsuwFffxBozm5eCzUke+fDWr19PQUFBVPfYts2Rxs5wsP6t\n2lba/cE4jXB4BnBuQRYXFGdzwexsls3ykulQ3XoREUk9qRC8T0YKwYuE6ux/i1AZHfcw19jALuBu\nQln3IiIiIiIiIlELBoM89dRT3Hfffezbty98vszw8DXHHKxBZWfsQICzL78JwAZrBjuDbbQSSOiY\nx1JQUMCmTZvGvM62bWpbfOw50cLu2lb2nGihvqM7/gMcZE5uBmXF2VxQnM3KIi85makQDhERERld\nsn9bJfOt7dPAl4CvAWuAxYSy733AcWA78H7SRiciIiIiIiKTmt/v57e//S0/+MEPePfddwc8VmZ4\n+LKjeEjgfrBcw8FnrZk8EDgRz6FGbfPmzRQWFg772KkWH3tq+4L1dW3+BI8OCtxOLij2UlacTVlx\nNjO8roSPQUREZKKSHbxPBZ3ACz1fIiIiIiIiIhPS1tbGL3/5S374wx9y/PjxIY+vGCHjfiSXmtls\nD2bzut0S66GOy/XXX88NN9wQPj7T5mP3iVb21Lawp7aVky2+hI/J67JYUeQNlcIpzqZkWkZMN9IV\nERFJBgXvRURERERERGKgsbGRH//4x/zHf/wHZ8+eDZ+3AAehQHI3Nuus/IgD9wCGYXCrYxYnurs4\nZic+MN7f4sWL+da/bubFQw2hYP2JVo43dyV8HC7LYOlMLxfMDgXsFxRok1kREZl6FLwXERERERER\nmYDa2loefPBBfvGLX9Da2ho+P2Az2p5gfcC2x1U/1mtYfMNRwl3+o5wi8WVoAPKLSpj/uXv4wp+G\nfpog3kwDFk53hzeZPX+GB5c2mRURkSlOwXsRERERERGRcTh48CAPPPAAv/71r/H5BmbEj7QZbTQZ\n94PlGU42Oufy3e6ahGfgZ84sZc4tm6kjO2F9zsvLDJfBWVHkxeOyEta3iIhIKlDwXkTiwufzcd99\n9wFw++2343JpgyiZerTOJR1onUs60DqXaG3fvp0f/vCHPPvss9i2PeTxSDejHY88w8lGxzx+0n0y\nYTXw85Zfwbz1t+Nw58S1nxleZzhYX1acTb7bGdf+ZOrR67mkA63z9KKCcAm2devWQuB0/3PLly/H\n6dQ/SmRqaWtro6SkBICamho8Hk+SRyQSe1rnkg60ziUdaEt6N1oAACAASURBVJ1LNO655x42b94c\nPh5cz36p4eHrUWxGOxHbAs38LHCKFgJxad/hyWXux75C/soPxKX9nAyLsp5A/QXF2RTnuLTJrEyI\nXs8lHWidJ5bf72fv3r2DT89Yu3ZtXSL6V+a9iIiIiIiISIQ+/OEPs3nz5hHr2XcQjEvgPnvZQlz5\nudS/uhM7EArWX+bKo/ziNTxuNvLHypeGlO4ZL8Nykl92FXM+8nmc3ryYtAngdposn+VlZZGXC2Zn\nMz8/C1PBehERkREpeC8iIiIiIiISoZUrV/Lp5ZfwoQONw9az9xL7uuyGZbLwHysovPpSgj4/QX83\nAKbTgelyci1w9uxZHnvsMR555BEOHjw4rn4yps+h8JKPUHDRh3B6cic87kyHybJZHlYWZbOyyMt5\n091YpoL1IiIikVLwXkTiwrIsrr/++vD3IlOR1rmkA61zSQda5xKNuq2VXHekExKUMW553ZT96C4K\nr74UANPlxHQNLLva2R3kaJeLnMvWc8W8D5K1axfNR9+l/eT7dJw4RMfJagKdbQPbzfSQNWs+WcXn\n4p51Du7Z5+Ges3BCZWtclsHSmT3B+mIviwo9OBSslwTS67mkA63z9KLfogmmmvciIiIiIpLugsFg\nuMSLy+XCNM0kj2io4TLc617Yxs7/+w7sQDAhYzAsk1W/2Ezh2jUDznf4A+w/1cbe2lbeOtlKVV07\n3cGhG+f2Z9s2dsDf064zJrXlnabB4hkeVhZ5KSvOZvEMNy4r9Z5LERGR8VLNexEREREREZmSbNtm\n9+7d7Nmzh/3797Nv3z7eeecdmpubB1yXk5PDkiVLWLZsGUuXLmXlypWUlZUlZfPSuhe2cfihR6mv\n3BWuLW9YFvlrLsBX3xS3wL1hWQP7K19FacUGCq++lDZfgP2nWnmrNvT13pl2AqPH6oe2bxgYDteE\nxmgZsKjQw8piL2VF2Zw/00OGQ8F6ERGReFHwXkRERERERGIq2vrrzc3NbN++ne3bt4fPLViwgJtu\nuokNGzZQUFAQz+GG1W2tZOfNdw4J0NuBAGdffjNu/RZceTEX/vJ74Uz/tiC8Xe/jd7UtvPX7Axw6\n28EYifVxYRpw3nQ3ZUVeVhZns3SmhyynSjSIiIgkioL3IiIiIiIiEhN1dXVs2rSJLVu2hMvijNfB\ngwfZuHEjd999N+vXr2fTpk0UFhbGaKRD1W2tZHfFxoSVxOllWCaFn/sklcfbeOtkKLO+ur6DJMTq\nMYBzC7IoKw5tMLtslhePS8F6ERGRZFHwXkRERERERCbEtm2efPJJ7rzzTurr62Pats/n47HHHuO5\n555j8+bN3HDDDRMupzO4nv3ZV3YMm3Efb4GsLLZ95vP82zE3HKtOaN+9zsnPDG8wu3yWl+wMhQlE\nRERShX4ri4iIiIiIyLg1NDRw22238fTTT8e1n/r6em699Vb+8Ic/cP/995OXlxd1GyPVs3dkuxMe\nuA8aJk99/DNUz16Y0H7nTstkZZGXlcVeVszyMi3LmdD+RUREJHIK3ouIiIiIiMi41NbWcuONN1JV\nVZWwPp9++mnee+89tmzZQlFR0ZDH33zzTaqrq/nEJz4x4Pxo9ez9jS1xG2+X24OzswMzGOo3aJrU\nzF/IjvKrObxwadz67TU7J4OVxd5Qdn2Rl3y3gvUiIiKThYL3IiIiIiIiErXa2lrWrVtHdXXiy70c\nOHCAdevW8cwzz1BUVERXVxdPPvkkP/nJT9i5cyfZ2dl8+MMfxuv1AsmrZx80TP748Zs5es4izGAo\n0z9oWgQd8ftTfO60TFbM8rK8KJRZX+BRsF5ERGSyUvBeREREREREotLQ0MCNN96YlMB9r+rqaj76\n0Y9y7bXX8sQTT3DmzBkALMDX0soTv/wVN3/uc0mrZ9+Vkcmzn/xsOLs+GKc/v+fnZbKiKBSsXz7L\nS57K4IiIiEwZCt6LiIiIiIhIxGzb5rbbbktoqZyRHDx4kIMHDwKwwvCwzspnieHGMgzY9Av++9u/\njFs9exsYadvcoGHy7Cc/S/WiZTHt0wDOLcgKZ9Uvn+UlJ1N/1ouIiExV+i0vIiIiIiIiEXvyySfj\nvjlttOaRwdcdc0JB+37iWc/+dNEcOt1eSqrfjVs9e9OA86a7WT7Ly4oiL8tmevBm6M94ERGRdKHf\n+iIiIiIiIhKRuro67rzzzmQPY4iz+GklQG6C/sQNGiavXns9hxcuxezujlk9e8uARYWecGb90pke\n3C4rVsMWERGRSUbBexGJi/b2dq655hoAnn/+edxud5JHJBJ7WueSDrTOJR1onUdu06ZN1NfXJ3sY\nQ7QS5LHAaSocxXHva0gte4dj3PXsnabBohluVvRk1i+Z4SHLGZ9gvda5pAOtc0kHWufpRcF7EYkL\n27bDdVBt207yaETiQ+tc0oHWuaQDrfPInDlzhi1btiR7GCOqDLbwV3Y3OUb8/sydaC17l2WwZIaH\nFT2Z9YtneMhwmDEe5fC0ziUdaJ1LOtA6Ty8K3ouIiIiIiMiYHn/8cXw+X7KHMaJubF4ONvERq2DC\nbXVkucno6pxwLfsMh8nSmZ5wZv3CQjcuKzHBehEREZn8FLwXERERERGRUdm2zSOPPJLsYYzphUAT\n15n5GIM2ro1G0DD50yc+w9FzFkVdy97tNFk6MxSoX1Hk5bzpbhzm+MciIiIi6U3BexGJi4yMDH76\n05+GvxeZirTOJR1onUs60Dof2+7duzl48GCyhzGmWnxU252cY2SN6/4h9ezH+JM5N9PB8lkels70\nsnyWl3MLsrBSNFivdS7pQOtc0oHWeXpJzX9VTGFbt24tBE73P7d8+XKcTmeSRiQiIiIiIjK6n//8\n59x+++3JHkZEbrFmcY01Ler7gobJHz79hVHr2c/KdrFslpflMz0sm+VlTm7GhLL8RUREJLX5/X72\n7t07+PSMtWvX1iWif2Xei4iIiIiIyKj279+f7CFE7KjdOerjkdazN4DSvEyWzfKGAvazPEz3uOI5\ndBEREZEBFLwXERERERGRUe3bty/ZQ4jYUbtrxMdGq2fvMA3On+5m2axQVv3SmR6yM/Qns4iIiCSP\n/iUiIiIiIiIio3rnnXeSPYSI1YwQvB9czz7D6WLJDE+4DM6iGR4yHWYihyoiIiIyKgXvRURERERE\nZETBYJDm5uZkDyNi7QSxbXtALfqgYfLnT99K8Qcu5YOzUn9zWRERERFQ8F5ERERERERG4fP5kj2E\nqHVj48TANk24YDmlFRu4b90V2lxWREREJhUF70VERERERGRKWbnzKYqnZWM6HZguZ7KHIyIiIjIu\nCt6LiIiIiIjIEM3Nzdi2jSPTneyhRK2kuFBZ9iIiIjLpKXgvIiIiIiIiQKhEzh+2vsST/7ODA2c6\nOGf1VbQ6crAyPQQ625I9vIjk5OQocC8iIiJTgoL3IiIiIiIiacrXHaSqro3ndhxg23snqMeLI7sA\nc/7VzJoXoD0A2N1kzZpP6+F9yR5uRM4///xkD0FEREQkJhS8FxERERERSQO2bXO61c/bp9t453Qb\nO4+coaYlgG2YgAOy57Lg3f1c+MQvKTn8HmYwCEDQNHnI0cyryR1+xJYtW5bsIYiIiIjEhIL3IhIX\nwWCQqqoqABYtWoRpmkkekUjsaZ1LOtA6l3QwVde5rzvIe2faw8H6t0+3Ud/ePfAio2+u86v28dFf\nPoxpBwdcYgaDLO7wT5rgvTLvhzdV17lIf1rnkg60ztOLgvciEhcdHR2Ul5cDUFNTg8fjSfKIRGJP\n61zSgda5pIOpsM4HZ9W/c7qNQ2c76A7aQ641u7sxgwEAgqZF0OFgftU+rvvNz4YE7nvNNzLjOv5Y\nWrlyZbKHkJKmwjoXGYvWuaQDrfP0ouC9iIiIiIjIJBNRVv0gpe/u58JXnh9SEqduRjGFp45j2kMD\n/b3mG5kU4aIWX0znEWsLFiygrKws2cMQERERiQkF70VERERERFJYNFn1IxmtJM7Mk8fGvN8wDK62\ncvlVoC7q8SfSTTfdhGEYyR6GiIiISEwoeC8iIiIiIpJCxpNVD8OXwwHGLIkTqSvMXH4dOEM3kb9p\nkEgul4sNGzYkexgiIiIiMaPgvYjEhcfjob6+PtnDEIkrrXNJB1rnkg6Suc5jkVU/UjmcmtLzODb/\nPC574dkJB+4BcgwHa8xsXgo2T7iteFi/fj0FBQXJHkbK0uu5pAOtc0kHWufpRcF7ERERERGRBGnz\nBaiqa+PA6XYO1LVRVddOQ8fYWfUjGa0czrz3q5j7fhWxLCKzwZrBzmAbrQRi2OrEFRQUsGnTpmQP\nQ0RERCSmFLwXERERERGJg+6gTXV9BwdOt3Ggrp0Dp9uoaeoaV1vDlcSJpBxOrKu/5xoOPmvN5IHA\niRi3PDGbN2+msLAw2cMQERERiSkF70VERERERCbItm1OtfrCGfUHTrdz8Gw7vsDE6sOPVBKnbkYx\nhaeOY9qJrz9/qZnN9mA2r9stCe97ONdffz033HBDsochIiIiEnMK3ouIiIiIiESptaubqrp2qur6\ngvWNneMvfzOc0UrizDx5LKZ9RcOwTG5bUs6de1/kmD2+TxLEyuLFi/n+97+f1DGIiIiIxIuC9yIi\nIiIiIqPoDtq8X99BVQzK3wxnvCVxksHyuin70V0Url3D8qM1/OVHP8rhI4eTMpb58+ezZcsW8vLy\nktK/iIiISLwpeC8iIiIiItIjXuVvhpOKJXFGY1hmOHAPMHtuCX989o+sX7+eAwcOJHQsixcv5ne/\n+x2zZs1KaL8iIiIiiZTuwftMYA2wGMgDfEANsB2oTuK4REREREQkAXrL3/Rm1FfVxb78zXBStSQO\npkH2+efR+s4h7EDo0wCGZZFfvorSig0UXn3pgMuLior44x//yG233cbTTz+dkCH+5V/+Jffff78y\n7kVERGTKS7Xg/WxgNXBJz38vArz9Hj8CzI9BP4XAt4DPAO4RrtkBfBt4Kgb9iYiIiIhIkvkDQ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NDQ0cP36c/JPv84ehKSw1CgY2ig2aJjkrKlj4yY/T+NSPCXa7EzXFrBPdpx5UVZ9K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\nCprnzUNditEaVFVIMdetQVWlFHO8DGtQZWM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       "text": [
        "<matplotlib.figure.Figure at 0x81b99e8>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This time, the degree 5 polynomial seems more precise than the simpler degree 2 polynomial (which now causes underfitting). Ridge regression reduces the overfitting issue here. Observe how the degree 5 polynomial's coefficients are much smaller than in the previous example."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## How it works...\n",
      "\n",
      "In this section, we will explain all the aspects covered in the example above."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### scikit-learn API\n",
      "\n",
      "scikit-learn implements a clean and coherent API for supervised and unsupervised learning. Our data points should be in a $N \\times D$ matrix $\\mathbf{X}$, where $N$ is the number of observations, and $D$ is the number of features. In other words, each row is an observation. The first step in a machine learning task is to define what our matrix $\\mathbf{X}$ is exactly."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In a supervised learning setup, we also have a *target*, a $N$-long vector $\\mathbf{y}$ with a scalar value for each observations. This value is continuous or discrete, depending on whether we have a regression or classification problem, respectively."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In scikit-learn, models are implemented in classes that have `fit` and `predict` methods. The `fit` method accepts the data matrix `X` as input, and `y` as well for supervised learning models. This method *trains* the model on the given data.\n",
      "\n",
      "The `predict` method also takes data points as input (as a matrix $M \\times D$). It returns the labels or transformed points, according to the trained model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Ordinary Least Squares regression\n",
      "\n",
      "[Ordinary least squares regression](http://en.wikipedia.org/wiki/Ordinary_least_squares) is one of the simplest regression methods. It consists of modeling the output values $\\hat{y}_i$ as a linear combination of $X_{ij}$:\n",
      "\n",
      "$$\\forall i \\in \\{1, \\ldots, N\\}, \\quad \\hat{y}_i = \\sum_{j=1}^D w_j X_{ij}, \\quad \\textrm{or, in matrix form:} \\quad \\mathbf{\\hat{y}} = \\mathbf{X} \\mathbf{w}.$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here, $\\mathbf{w} = (w_1, \\ldots, w_D)$ is the (unknown) *parameter vector*. Also, $\\mathbf{\\hat{y}}$ represents the model's output. We want this vector to match the data points $\\mathbf{y}$ as closely as possible. Of course, the exact equality $\\mathbf{\\hat{y}} = \\mathbf{y}$ cannot hold in general (there is always some amount of noise in real-world data). Therefore, we want to *minimize* the difference between those two vectors. The ordinary least squares regression method consists of minimizing the following [**loss function**](http://en.wikipedia.org/wiki/Loss_function):\n",
      "\n",
      "$$\\min_{\\mathbf{w}} || \\mathbf{y} - \\mathbf{X} \\mathbf{w} ||_2^2 = \\min_{\\mathbf{w}} \\left( \\sum_{i=1}^N \\left(y_i - \\hat{y}_i\\right)^2 \\right)$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This sum of the components squared is called the [**$l_2$ norm**](http://en.wikipedia.org/wiki/Lp_space) (or [**Euclidean norm**](http://en.wikipedia.org/wiki/Euclidean_distance)). It is convenient because it leads to *differentiable* loss functions, so that gradients can be computed and common optimization procedures can be performed."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Polynomial interpolation with linear regression\n",
      "\n",
      "Ordinary Least Squares regression fits a linear model to the data. The model is linear both in the data points $X_i$ and in the parameters $w_j$. In our example, we obtained a poor fit because the data points were generated according to a nonlinear generative model (an exponential function)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, we can still use the linear regression method with a model that is linear in $w_j$, but nonlinear in $\\mathbf{x}_i$. To do this, we need to increase the number of dimensions in our dataset by using a basis of polynomial functions. In other words, we consider the following observations:\n",
      "\n",
      "$$\\mathbf{x}_i, \\mathbf{x}_i^2, \\ldots, \\mathbf{x}_i^D$$\n",
      "\n",
      "where $D$ is the maximum degree. The input matrix $\\mathbf{X}$ is therefore the [**Vandermonde matrix**](http://en.wikipedia.org/wiki/Vandermonde_matrix) associated to the original data points $\\mathbf{x}_i$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Ridge regression\n",
      "\n",
      "Polynomial interpolation with linear regression can lead to overfitting issues if the degree of the polynomials is too large. By capturing the random fluctuations (noise) instead of the general trend of the data, the model's predictive power decreases. This corresponds to an explosion of the polynomial's coefficients $w_j$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A solution to this problem is to prevent these coefficients from growing unboundedly. With [**ridge regression**](http://en.wikipedia.org/wiki/Tikhonov_regularization), this is done by adding a *regularization* term to the loss function:\n",
      "\n",
      "$$\\min_{\\mathbf{w}} || \\mathbf{y} - \\mathbf{X} \\mathbf{w} ||_2^2 + \\alpha ||\\mathbf{w}||_2^2$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "By minimizing this loss function, we not only minimize the error between the model and the data (first term, related to the bias), but also the size of the model's coefficients (second term, related to the variance). The bias-variance trade-off is quantified by the hyperparameter $\\alpha$, which precises the relative weight between the two terms in the loss function.\n",
      "\n",
      "Here, ridge regression led to a polynomial with smaller coefficients, and thus a better fit."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Cross-validation and grid search\n",
      "\n",
      "A drawback of the ridge regression model compared to the ordinary least squares model is the presence of an extra hyperparameter $\\alpha$. The quality of the prediction depends on the choice of this parameter. One possibility would be to fine-tune this parameter manually, but this procedure can be tedious and can also lead to overfitting."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can use a [**grid search**](http://en.wikipedia.org/wiki/Hyperparameter_optimization) for this: we loop over many possible values for $\\alpha$, and we evaluate the performance of the model for each possible value. Then, we choose the parameter that yields the best performance."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How to assess the performance of a model with a given $\\alpha$ value? A common solution is to use [**cross-validation**](http://en.wikipedia.org/wiki/Cross-validation_%28statistics%29). This procedure consists of splitting the dataset into a *train set* and a *test set*. We fit the model on the train set, and test its predictive performance on the *test set*. By testing the model on a different dataset than the one used for training, we avoid overfitting."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are many ways to split the initial dataset into two parts like this. One possibility is to remove *one* sample to form the train set, and to put this one sample into the test set. This is called **Leave-One-Out** cross-validation. With $N$ samples, we obtain $N$ sets of train and test sets. The cross-validated performance is the average performance on all these set decompositions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we will see in *Chapter 8*, scikit-learn implements several easy-to-use functions to do cross-validation and grid search. Here, we used a special estimator called `RidgeCV` that implements a cross-validation and grid search procedure that is specific to the ridge regression model. Using this model ensures that the best hyperparameter $\\alpha$ is found automatically for us."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> In the book, the [rest of the chapter](https://github.com/ipython-books/cookbook-code/blob/master/toc.md#chapter-8-machine-learning) introduces many standard algorithms in machine learning."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## There's more\u2026"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are a few references about cross-validation and grid search:\n",
      "\n",
      "* [Cross validation in scikit-learn](http://scikit-learn.org/stable/modules/cross_validation.html).\n",
      "* [Grid search in sciki-learn](http://scikit-learn.org/stable/modules/grid_search.html)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are a few references about scikit-learn:\n",
      "\n",
      "* [scikit-learn basic tutorial](http://scikit-learn.org/stable/tutorial/basic/tutorial.html).\n",
      "* [scikit-learn tutorial given at the SciPy 2013 conference](http://github.com/jakevdp/sklearn_scipy2013)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Books\n",
      "\n",
      "Here are a few excellent, math-heavy textbooks on machine learning:\n",
      "\n",
      "* Bishop, C. M. (2006). [*Pattern recognition and machine learning*](http://research.microsoft.com/en-us/um/people/cmbishop/prml/). Springer.\n",
      "* Murphy, K. P. (2012). [*Machine learning: a probabilistic perspective*](http://www.cs.ubc.ca/~murphyk/MLbook/). MIT Press.\n",
      "* Hastie, T., Tibshirani, R., Friedman, J., Hastie, T., Friedman, J., & Tibshirani, R. (2009). [*The Elements of Statistical Learning*](http://statweb.stanford.edu/~tibs/ElemStatLearn/). Springer.\n",
      "\n",
      "Here are a few books targetting programmers without necessarily a strong mathematical background:\n",
      "\n",
      "* Conway, D., & White, J. (2012). [*Machine Learning for Hackers*](http://shop.oreilly.com/product/0636920018483.do). O'Reilly Media, Inc.\n",
      "* Harrington, P. (2012). [*Machine Learning in Action*](http://www.manning.com/pharrington/). Manning Publications Co.\n",
      "\n",
      "You will find many other references online."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> This was a featured recipe from the [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}