Bhargav_Solanki_assignment_07.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please fill in your name and that of your teammate.\n",
    "\n",
    "You: Bhargav Solanki\n",
    "\n",
    "Teammate: Carmen Sangro Prieto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Welcome to the seventh lab. After learning about SVMs last week, we finally introduce the _kernel trick_ and make them capable of tackling nonlinear data. We also introduced more generally the concept of _function mapping_ and learned a bit about word embeddings."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How to pass the lab?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below you find the exercise questions. Each question awarding points is numbered and states the number of points like this: **[0pt]**. To answer a question, fill the cell below with your answer (markdown for text, code for implementation). Incorrect or incomplete answers are in principle worth 0 points: to assign partial reward is only up to teacher discretion. Over-complete answers do not award extra points (though they are appreciated and will be kept under consideration). Save your work frequently! (`ctrl+s`)\n",
    "\n",
    "**You need at least 16 points (out of 24 available) to pass** (66%)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Function Mappings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1 **[3pt]** Give an _original_ example for each of the following concepts (i.e. not one that you find in the slides!):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Mapping from an example data type to a decision space\n",
    "2. Inverse mapping\n",
    "3. Mapping from the example data to two destination feature spaces\n",
    "4. Mapping from the two feature spaces above to a decision space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example (here is what we presented in the slides):\n",
    "\n",
    "1. Given a picture, decide if it represents an apple or an orange. Original space: \n",
    "$64\\times64\\times3$ images; destination space: $\\{$apple, orange$\\}$.\n",
    "2. Given the label apple, map it to a $64\\times64\\times3$ picture of the fruit.\n",
    "3. Map $\\Phi_1 $ goes from the picture to an estimate of average color; map $\\Phi_2$ goes from the picture to a fruit width measured in pixels.\n",
    "4. Map $\\Phi_3$ goes from the two features of estimated color and fruit width, to the decision space of classifying the fruit as apple or orange."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Mapping from an example data type to a decision space\n",
    "Given an input json we need to find if they fall in income group,decision space {\"High\", \"Low\"} \n",
    "```json\n",
    "[\n",
    "    {\n",
    "    \"id\" : 1234,\n",
    "    \"fname\" : \"Michael\",\n",
    "    \"lname\" : \"Scott\",\n",
    "    \"title\" : \"Regional Manager\"\n",
    "    \"Income\": \"45000\"\n",
    "    },\n",
    "    {\n",
    "    \"id\" : 1235,\n",
    "    \"fname\" : \"Dwight\",\n",
    "    \"lname\" : \"Schrute\",\n",
    "    \"title\" : \"Assistant to the Regional Manager\",\n",
    "    \"Income\": \"35000\"\n",
    "    }    \n",
    "]\n",
    "```\n",
    "\n",
    "##### 2. Inverse mapping\n",
    "Given a Income group of \"High, \"medium\" or \"low\" identify the salary of the person\n",
    "\n",
    "##### 3. Mapping from the example data to two destination feature spaces\n",
    "Map  $\\Phi_1$ gives the title of the person and map $\\Phi_2$ gives the income range\n",
    "\n",
    "##### 4. Mapping from the two feature spaces above to a decision space\n",
    "\n",
    "Map $\\Phi_3\\$  goes from two features above of title and salary range and gives the name of the employee"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2 **[1pt]** Explain advantages and disadvantages of Bag Of Words versus Word Embedding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### <u>Bag Of words</u>\n",
    "\n",
    "It is a special case of n- gram model, where n is 1. Here we simply keep a dictionary of a word and the number of occurances of that word in a sentance/paragraph/book etc. The order does not matter and nor does the position of the word in the text.  \n",
    "**Advantage** : Its easier and less complex to build. You can perform easy unions and can be used in computervision. Human readable.  \n",
    "**Disadvantage** : Order is not tracked. Grammar is ignored. Relationship between words is not maintained. High dimensionality.\n",
    "Cant calculate similarities between words. \n",
    "\n",
    "##### <u>Word Embedding<u>\n",
    "\n",
    "It means, word mapping. here we represent words as vectors in vectorial space. Reduce the dimensionality.  \n",
    "**Advantage** :  \n",
    "Order of words can be tracked. Grammar rules can be retained. Similarities between words can be found using simple cosine rules.  \n",
    "**Disadvantage** :  \n",
    "Difficult for humans to understand, but easier for computers. Unable to handle unknown words. Scaling to new language is harder.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3 **[2pt]** Refer to the graph exemplifying Word Embedding in the slides, and its explanation. (i) What does it mean that the point representing Paris is close to the point representing Berlin? (ii) Why is the point for Paris closer to the point for France than to the point representing Italy?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(i) While embedding texts, city names are closer to each other and county names are closer to each other.  Hence, Paris and Berlin are close. That is the distance between these two words is less.  \n",
    "(ii) Also, in embedded texts, City and Country are often mentioned together, so when one speaks of Paris, they also mention france more often. Hence word distance between these two is closer than Paris and berlin."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Kernels theory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1 **[1pt]** Write the definition of kernel function (use latex)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\\\\n",
    "k(x,y) = \\langle \\phi(x), \\phi(y) \\rangle \\\\\n",
    "\\forall x,y \\in X \\\\\n",
    "k(x,y) = \\langle \\phi(x), \\phi(y) \\rangle  = \\langle k(\\cdot,x), k(\\cdot,y) \\rangle\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2 **[1pt]** Explain the Representer property in English."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You represent a each data point as a kernal function (mapping) in hilbert space. That data point with real values represented by kernal function is now a **representation** in hilbert space. This is the representer property"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3 **[2pt]** Explain the kernel trick in English."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Its easier to work with n dimensional data in n+1th dimension for doing math operations. Once we do that, we can get our classifiers or regressors much easier. However, using kernal trick, we get the same results without actually computing the points in n+1th dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.4 **[1pt]** Explain in English the required properties of a Mercer kernel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Properties**:  \n",
    "<u>Symmetry</u> :  \n",
    "A kernal function of $x_1$ and  $x_2$ is the same as kernal function of $x_2$ and  $x_1$  for all $x_1$ and $x_2$ in $X$.  \n",
    "<u>Positive definiteness:</u>  \n",
    "The result value of a kernal function cannot be negative and the thus the vector matrix generated will have only non negative values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.5 **[1pt]** Calculate by hand the linear kernel on points $\\{[2,4], [1, -2]\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let linear kernal be represented as $z$\n",
    "$ \\\\\n",
    "z = \\left[\n",
    "        2,4\\right] . \\begin{bmatrix}\n",
    "           1 \\\\\n",
    "           -2\n",
    "         \\end{bmatrix}          \n",
    "$  \n",
    "z =  (2 x 1) + (4 x -2)  \n",
    "z = 2 - 8   \n",
    "z = -6  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.6 **[1pt]** How do you compute the entry of the Gram matrix for row $i$ and column $j$ for a Gaussian kernel?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\\\\n",
    "K(x_i, x_j) = e^{- \\gamma . {|| x_i - x_j ||}^2} \\\\\n",
    "for \\\\\n",
    "\\gamma > 0\n",
    "$  \n",
    "or \n",
    "$ \\\\ \n",
    " = e^{-({x_i - x_j})^T . C . {(x_i - x_j)}}\n",
    "$  \n",
    "for a symmetric, positive definite matrix C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.7 **[2pt]** Explain why does the Perceptron work with non-linearly separable data using Kernelization. Do you think Linear Regression would work with Kernelization? Explain your reasoning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we kernalize, we hope to see the non linearly sperated date in n dimension,s to be (hyperplane)linearly seperable in n +1 th dimension. For that reason, Perceptron with kernalization works for non-linearly separable data.\n",
    "Also, it is possible to use Linear regression with kernalization, for example using kernal ridge regression.  It is for the same reasons above, If we want to find the value given oter set of values, kernalization can help predict that value. \n",
    "By representing our data in higher dimension"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.8 **[1pt]** Explain the Universal Consistency of SVMs (in English)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as the number of the samples increase, the predicted value converges to the true value. SVMs are consistent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Kernels in practice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity, let's use once again a two-species adaptation of the Iris dataset. You can copy the code from the last assignment. This time though, to make it harder for linear classifiers let's separate the \"central\" species from the other two. This means that you should set label `versicolor` rather than `setosa` as class `-1`. I suggest you un-comment the `pairplot`s to verify it works.  \n",
    "NOTE: all recommendation on how to handle and prepare the data from the past assignment(s) still hold. As do the warnings that using the wrong data sets will **invalidate the whole answer**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "sns.set(rc={'figure.figsize':(8,6)}, style=\"whitegrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sepal_length    float64\n",
      "sepal_width     float64\n",
      "petal_length    float64\n",
      "petal_width     float64\n",
      "species           int64\n",
      "dtype: object\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x7faaa2db6790>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 769.55x720 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "df = sns.load_dataset('iris')\n",
    "# sns.pairplot(df, hue='species')\n",
    "\n",
    "df.loc[df['species'] == 'versicolor', 'species'] = -1\n",
    "df.loc[df['species'] != -1, 'species'] = 1\n",
    "df['species'] = pd.to_numeric(df['species'])\n",
    "print(df.dtypes)\n",
    "# sns.pairplot(df, hue='species')\n",
    "\n",
    "train, test = train_test_split(df, test_size=0.2)\n",
    "sns.pairplot(test, hue='species')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### 3.1 **[1pt]** Train an SVM with linear kernel on the Iris data using Scikit-learn (this time you are required to use class `SVC`). Then do the same using a Gaussian kernel (still `SVC`) and compare the performance using its method `score()`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Remember to prepare inputs/labels for Scikit-learn; again the last assignment should help.\n",
    "- Calling the method `score()` on the trained model just does the prediction and returns the percentage of correct answers. It is a useful function to learn to quickly check if your model is working.\n",
    "- You expect the linear kernel to perform poorly. If the performance is close to the Gaussian kernel, it is possible that the test set was by chance not homogeneous. You can verify that by doing a pairplot on the test set, and if so just run the data loading and preparation again.\n",
    "- No need to find an optimal value for `C` but pass it explicitly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score for linear on Trained data--> 73.33\n",
      "Score for Gaussian on Trained data--> 94.17\n",
      "Score for linear on Test data--> 83.33\n",
      "Score for Gaussian on Test data--> 100.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "def helper_get_x_and_label(data):\n",
    "    x = data[data.columns[:-1]].values.tolist()\n",
    "    label = data[data.columns[-1]].values.tolist()\n",
    "    return x, label\n",
    "lin_clf = SVC(C=1.0, kernel = 'linear')\n",
    "gaus_clf = SVC(C=1.0, kernel='rbf') \n",
    "x_train, labels = helper_get_x_and_label(train)\n",
    "x_test, labels_test = helper_get_x_and_label(test)\n",
    "#x_train = train[train.columns[:-1]].values.tolist()\n",
    "#labels = train[train.columns[-1]].values.tolist()\n",
    "#x_train\n",
    "lin_clf.fit(x_train, labels)\n",
    "gaus_clf.fit(x_train, labels)   \n",
    "print(\"Score for linear on Trained data-->\",round(lin_clf.score(x_train, labels)*100,2))\n",
    "print(\"Score for Gaussian on Trained data-->\",round(gaus_clf.score(x_train, labels)*100,2))\n",
    "# Now testing performance on test\n",
    "print(\"Score for linear on Test data-->\",round(lin_clf.score(x_test, labels_test)*100,2))\n",
    "print(\"Score for Gaussian on Test data-->\",round(gaus_clf.score(x_test, labels_test)*100,2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.2 **[1pt]** Write a Python function that takes two data points and a value for `gamma` as input, and returns the Gaussian kernel of the points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36787944117144233"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_gauss_kernal(point1, point2, gamma):\n",
    "    x1 = np.array(point1[:-1]) # removing labels \n",
    "    x2 = np.array(point2[:-1])\n",
    "    return np.exp(-1 * gamma*(\n",
    "        np.absolute(\n",
    "            np.linalg.norm(x1-x2)\n",
    "        )**2\n",
    "    )\n",
    "                 )\n",
    "get_gauss_kernal([1,-2], [2,-4], 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3 **[3pt]** Write a Python function that takes two dataset (and a gamma) and returns their Gram matrix for a Gaussian kernel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- You need two datasets because you need to compute the *train* matrix between the train and itself, but the *test* matrix between the test and the train.\n",
    "- Simplest method:\n",
    "    - Create a return matrix, initially empty, shaped size_of_A times size_of_B, with dtype 'float64'\n",
    "    - Run two loops with indices (i, j) in ranges up to size_of_A and size_of_B\n",
    "    - Compute the kernel between row i in A and row j in B, and place it in the return matrix at row i column j\n",
    "- Careful with Pandas' `iterrows()`, as the \"index\" it returns is the DataFrame index (i.e. for use with `loc[]`), not the ordinal index (i.e. for `iloc[`). \n",
    "- Generating the matrix automatically is harder, as there is no straightforward way to compute an `outer` in numpy or pandas with a custom function.\n",
    "- One way is to use `column_stack` https://stackoverflow.com/a/21759340 then apply the kernel defined above.\n",
    "- Another is to use `ufunc.outer` http://folk.uio.no/inf3330/scripting/doc/python/NumPy/Numeric/numpy-7.html which is only defined for Universal Functions (`ufuncs`). Look at the examples for `outer`, you can re-implement the function above starting with `np.subtract.outer(A, B)`, which generates the matrix (but check the shape!), then you can run the other operations using broadcast. Both outers and universal functions are super useful, it's worth the effort of learning them, more [[here]](https://docs.scipy.org/doc/numpy/reference/ufuncs.html).\n",
    "- `pandas.apply()` along rows is also an option you should be able to consider with by now. The function name for `-` is `np.subtract` (which is an `ufunc`, see above).\n",
    "\n",
    "Above all, remember the first rule of a good BDD engineer: red, green, refactor! First make it work, then make it better ;) complex solutions are as good as bonus questions here.\n",
    "\n",
    "Also, know that a common default value for gamma is one over the number of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(120, 120)\n",
      "[[1.         0.09926125 0.97044553 ... 0.17033299 0.83945702 0.08629359]\n",
      " [0.09926125 1.         0.12745397 ... 0.83527021 0.10487354 0.86935824]\n",
      " [0.97044553 0.12745397 1.         ... 0.22313016 0.8824969  0.11765484]\n",
      " ...\n",
      " [0.17033299 0.83527021 0.22313016 ... 1.         0.23107799 0.69767633]\n",
      " [0.83945702 0.10487354 0.8824969  ... 0.23107799 1.         0.08332555]\n",
      " [0.08629359 0.86935824 0.11765484 ... 0.69767633 0.08332555 1.        ]]\n"
     ]
    }
   ],
   "source": [
    "def get_gram_matrix(df1, df2, gamma = None):\n",
    "    if not gamma:\n",
    "        gamma = df1.shape[1]\n",
    "    #print(df1.shape[0])\n",
    "    #print(df1.iloc[0])\n",
    "    n1 = df1.shape[0]\n",
    "    n2 = df2.shape[0]\n",
    "    res = []\n",
    "    for i in range(0, n1):\n",
    "        temp = []\n",
    "        for j in range(0, n2):\n",
    "            temp.append(get_gauss_kernal(df1.iloc[i], df2.iloc[j], gamma))\n",
    "        res.append(temp)\n",
    "    return np.array(res)\n",
    "res = get_gram_matrix(train, train, .25)\n",
    "print(res.shape)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.4 **[2pt]** Compute the Gram matrix on the inputs of your datasets. Then train a new SVM, same settings as before with linear kernel, but this time using the Gram matrix('s rows) as the inputs. Print the `score` performance of this new SVM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- With an 80-20 split you are looking at a $120 \\times 120$ shape for the train, and $30 \\times 120$ for the test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(30, 120)\n",
      "Score for Gaussian matrix and then linear on Test data--> 100.0\n",
      "Score for Gaussian matrix and then linear on Train data--> 97.5\n"
     ]
    }
   ],
   "source": [
    "train_matrix_df = pd.DataFrame(data=get_gram_matrix(train, train, 0.25))\n",
    "test_matrix_df = pd.DataFrame(data=get_gram_matrix(test, train, 0.25))\n",
    "print(test_matrix_df.shape)\n",
    "gram_lin_clf = SVC(C=1.0, kernel = 'linear')\n",
    "gram_lin_clf.fit(train_matrix_df, labels)\n",
    "print(\"Score for Gaussian matrix and then linear on Test data-->\",round(gram_lin_clf.score(test_matrix_df, labels_test)*100,2))\n",
    "print(\"Score for Gaussian matrix and then linear on Train data-->\",round(gram_lin_clf.score(train_matrix_df, labels)*100,2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.5 **[1pt]** Plot the confusion matrix for the three SVMs you trained in the past questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Let's learn a convenient and easy function for this common, very useful metric: `ConfusionMatrixDisplay.from_estimator` [[link here]](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.ConfusionMatrixDisplay.html#sklearn.metrics.ConfusionMatrixDisplay.from_estimator).\n",
    "- So far we saw explicitly 4 cells: true and false positives, true and false negatives. More generally the confusion matrix can be scaled to any number of classes by having the correct labels on the rows, and the predictions on the columns. Errors will be outside the diagonal.\n",
    "- You can use the `normalize` option to get percentages if you like. Which setting do you find most informative?\n",
    "- It's easier if you write a `for` loop over the three models you trained in the previous questions -- just make sure you gave them different names. Also careful as one takes a Gram matrix as input ;)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion matrix for linear \n",
      "Confusion matrix for Gaussian \n",
      "Confusion matrix for gram matrix and then linear \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x7f9e392add30>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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t697v2LGjfvOb30iSjh49qszMTA0aNKhOu8jISD322GNat26dOnTooLlz53r8TnRjAgAaVVZWloKDg03HIiIiLrp9aWmpxowZo/vuu0/9+vWrc37x4sXun8eMGaPBgwd7/EySHQDAxJC1FxicaxMdHa2wsDBL9/7mm280ZswYjRo1SqNHj65zvqqqSm+99ZZ7HM8wjDqJtT50YwIATAxZ7Ma8xMeFVVdX6w9/+IMmT55cb6KTpJYtW+rll19Wfn6+JGnVqlVUdgAACy61tLNozZo1qqio0CuvvKJXXnlFknTnnXdq8uTJmjVrlu68804NGjRICxcu1Jw5c3Ty5El17dpVGRkZHj+bZAcA8KlNmzZJkh5++OE6ywzOSU9Pd//ct29f5eTkNOgeJDsAgJkNHxdGsgMAmPDWAwCA7dnxTeUkOwCAmSFrXZJ+XNmx9AAAYHtUdgAAE8bsAAD256N1dpcTyQ4AYHLuCSpW2vkrkh0AwMyGlR0TVAAAtnfByu6777772YZt27Zt5FAAAP6gSa2zu+WWW+RwOGTUM73G4XDoiy++uKyBAQB8xIbdmBdMdl9++aU34wAA+A3HD5uVdv7J45idy+XS8uXLNWPGDFVXV2vp0qVyOp3eiA0AgEbhcTZmRkaGjh49qp07d8owDH344YcqLy9XamqqN+IDAHibDbsxPVZ2W7du1bx58xQWFqbWrVtrxYoV+vjjj70RGwDAF4xL2PyUx8ouJCREQUE/5sTQ0FCFhLA8DwBsy3BYfBC0/47Zecxa3bt3V2ZmppxOp7799lu9+uqr6tGjhzdiAwD4gB2fjemxG3PWrFnatWuXjhw5oqSkJNXU1CglJcUbsQEA0Cg8Vnbh4eF69tlnvRELAMBf+HGVZoXHyu7IkSN64okn1K9fP912221KSUlRZWWlN2IDAPjCuTE7K5uf8pjsUlNT1blzZ61Zs0arVq1SmzZtNHv2bG/EBgDwAYdhffNXHrsxDx06pJdeesm9P336dMXHx1/WoAAAPtQU19lFRUXp4MGD7v2SkhJFRkZe1qAAAGhMF6zs/vjHP0qSjh49qmHDhunWW29VUFCQPvnkE1177bVeCxAA4GVNaZ1dTExMvcdvv/32yxULAMAf2LAb84LJ7t577633uGEY2r9//2ULCADgY00p2Z3zxhtvKCMjQydOnHAfa9++Pc/HBAAEDI/J7u9//7teeeUVvfTSS5oyZYr+8Y9/qKSkxBuxAQB8wYaVncfZmG3btlXv3r3Vs2dPHTlyROPGjdO2bdu8ERsAwCesLij33wkqHpNdSEiIjh8/ri5duujzzz+XJF7eCgA2ZsdF5R6T3QMPPKBHH31Ut99+u1avXq3ExERdddVV3ogNAOALXnyfXXV1teLi4lRUVCRJ2rJli+Lj43XXXXdpwYIF9bYpLi7WyJEjNWTIEI0bN041NTUe7+Mx2Q0fPlwrVqxQ27ZttXr1aj322GNauHBhw74NAAA/kZ+fr6SkJBUWFkqSTp48qZSUFC1ZskTr169XQUGBNm/eXKfd008/reTkZOXl5alXr15asmSJx3tdcILKK6+8csFGWVlZeuSRRy7iqwAAUL/s7GylpaVp2rRpkqTPP/9cXbp0UefOnSVJ8fHxysvL08CBA91tamtrtW3bNi1evFiSlJiYqAcffFBTp0792XtdMNl99dVXl/xFGlOL9/6lloeP+zqMwJVyh1rmfOLrKALee8X/8nUIAe+zQ3fow8VLfR1GQDt1JlK7S/tfts+3Ov52rk1JSYmCg4NN5yIiIhQREWE6lp6ebtovKyszPY4yKipKpaWlpmuOHTum8PBwhYScTV+RkZF1rqnPBZPdc88957ExAMCGDFl8XNjZfyUnJ6uiosJ0asKECZo4ceLPNne5XHI4fryvYRim/Qsd++l+fTyuswMANDGXuM4uKyur3srOk+joaJWXl7v3y8vLFRUVZbqmffv2qqqqktPpVHBwcL3X1MfjBBUAABoiOjpanTp1Mm0Xk+x69+6tffv2af/+/XI6nXr33Xc1YMAA0zXNmjVT3759tX79eklSbm5unWvqQ7IDAJh5cenB+cLCwjRv3jxNnDhRQ4cO1VVXXaUhQ4ZIkmbNmqWNGzdKktLS0pSdna2hQ4dq+/btmjJlisfP9tiN6XK5tGLFCu3du1dPPfWUMjMzNWbMmDolKgDAHi51gkpDbdq0yf1z//79tW7dujrXnD+ZpWPHjlq5cmWD7uEx2WVkZOjo0aPauXOnJOnDDz9UeXm5UlNTG3QjAEAA8eOnoVjhsRtz69atmjdvnsLCwhQeHq4VK1bwxgMAQEDxWNmFhIQoKOjHnBgaGupe3wAAsCEbvvXAY9bq3r27MjMz5XQ69e233+rVV19Vjx49vBEbAMAHvD1m5w0euzFnzZqlXbt26ciRI0pKSlJNTY1SUlK8ERsAwBesvN7H/Zof/+SxsgsPD9ezzz7rjVgAAP6gKXZj/vnPf673OLMxAQCB4qLeVH5ua9WqlT799FNvxAUA8BE7vrzVY2U3YcIE0/7YsWM1bty4yxYQAMDHmmI35k+Fh4errKzscsQCAPAHVqu0QE52zzzzjPv1CYZhaNeuXbrqqqsue2AAADQWj8muXbt2pv177rlH99xzz2ULCADgB/y4SrPCY7I7cOCAMjIyvBELAMAfNMUxuy+//LLeN8MCAOzJjk9Q8ZjsIiMjFRsbq969e6tVq1bu46yzAwAEigsmu9OnTys0NFR9+vRRnz59vBkTAACN6oLJ7ne/+51ycnLqrLMDANhcUxqzMww/jhoAcNk0qTG7U6dOaffu3RdMetddd91lCwoA4ENNqbI7ePCgJk6cWG+yczgc2rhx42UNDADgI00p2V199dXKzc31YigAAFweDX42JgDA3prUmF3fvn29GQcAwJ/4ceKy4oLJjkXjANA02bGy8/jyVgAAAh1jdgAAs6Y0GxMA0ESR7AAAdmfHMTuSHQDAzIaVHRNUAAC2R2UHADCzYWVHsgMAmDBmBwBoGi5z4nrzzTe1atUq935RUZESEhI0e/Zs97EXX3xRb731liIiIiRJDzzwgEaOHGnpfiQ7AICJNyq7+++/X/fff78kae/evRo/fnydl4UXFBRo/vz56tOnT8OD+QmSHQDAp+bMmaPHH39c7du3Nx0vKCjQ0qVLdejQId18882aPn26wsLCLN2D2ZgAADPjEjZJJSUlKioqMm2VlZX13mrLli06efKk7r77btPxmpoa9ezZU1OnTlVOTo4qKyu1ZMkSy1+JZAcAMLvEZJecnKxBgwaZttdee63eW73xxht65JFH6hxv1aqVli1bpm7duikkJESjR4/W5s2bLX8lujEBAHU4LqFtVlaWgoODTcfOTTI53+nTp7Vt2zbNmzevzrni4mJt2bJFw4cPlyQZhqGQEOspi2QHAGhU0dHRFzW2tmfPHnXt2lUtW7asc6558+Z6/vnn1a9fP3Xq1EmZmZkaPHiw5ZjoxgQAmF1iN+bFOnjwoKKjo03Hxo4dq507d6p9+/aaO3euxo0bpyFDhsgwjHq7Oy8WlR0AwMRbi8qHDh2qoUOHmo4tW7bM/XNMTIxiYmIaHkg9SHYAADMeFwYAsD0bJjvG7AAAtkdlBwAwccjimF2jR9J4SHYAADMbdmOS7AAAJrziBwBgfzas7JigAgCwPSo7AIAJ3ZgAAPuzYTcmyQ4AYGbDZMeYHQDA9qjsAAAmjNkBAJoGP05cVpDsAAAmDsOQw2h4trPSxltIdgAAMyaoAAAQeKjsAAAmTFABANifDbsxSXYAADOLlR3JDgAQOGxY2TFBBQBge1R2AAATJqgAAJoGP05cVpDsAAAmdqzsGLMDANgelR0AwMyQZOU5l35c2ZHsAAAmduzGJNkBAMxsuM6OZAcAMHG4zm5W2vkrJqgAAGyPys7m/u+gSj0y87CuiHpCs5Z+rwV/6qzvq4N9HRaaiI1vtdObL0XJISmshUuP/blIrnYuvTS7o7b/o7WcToeG/7FMcQ8d8XWoOJ8NuzG9WtlVV1crLi5ORUVF3rxtk9Wm/Rn9acFBPTO2q74om6+SA6EanXLY12GhiTj4dZhefuYKpWd+o5f+e4+Sp5Ro7h+u1Cdv/0uHvg3T3//xpRat/0o5yyL15WctfR0uzuPQj5NUGrQ18D6jRo1SbGysEhISlJCQoPz8fNP5L774QomJiYqJidGsWbN05swZy9/Ja8kuPz9fSUlJKiws9NYtm7xfD6zSnn+1UPG+MEnSu6/9UncmHpNf//ULttEszNCUvxzUL3519g+o7r1P6Fh5iHZu/FJ3/e6IgkOk1m2duj3hO216q52Po4WJYVjfLvoWhgoLC7V27Vr31rt3b9M1U6dO1ezZs/Xee+/JMAxlZ2db/kpeS3bZ2dlKS0tTVFSUt27Z5EV2PK2K4lD3fvnhZmoV4VLLcD8eRYZtRHc+rX6/rZR09s/ApXOu0C13VaqqolqRV9S6r/tlh9OqONzMV2GiHpaqugYuV/j2228lSaNHj9Y999yjVatWmc4fOnRIJ0+e1I033ihJSkxMVF5enuXv5LUxu/T0dG/dCj8IctT/Fy2n0/uxoOk6+X2Q/jLl/6i8uJnSM7/VozFXynFef5chKYhhZFspKSlRcLD5f9SIiAhFRES49ysrK9W/f3899dRTqq2t1UMPPaQrr7xSv/nNbyRJZWVlioyMdF8fGRmp0tJSyzEFzASV6evG+TqEgNOuxYdq2+ITdfztk5Kk57eN0RnXTD39P7N8HFng+uyQryMILN+VHNerT6xRVNdfauTfhmpvdTO1/dXr2rZ7uk786lpJ0q69H8nV+qQ+O/RbH0cLt0ucoJKcnKyKigrTqQkTJmjixInu/T59+qhPnz7u/eHDh2vz5s3uZOdyueQ4729FhmGY9hsqYJLdf9zzko4dPu7rMAJKm1/Uaummr/TCA09rUnaaCt78s4qjQvXXx+f5OrSA9V7xv3wdQsD4vjpI4+67VoPvP6oH/1Qq6XVJUs+BT2rv+68qecQ+nagJ1uJN12jSfxzUDR1f9m3AAeTUmUjtLl102T7/Up+gkpWVVW9ld77t27ertrZW/fv3l3Q2mYWE/JiSoqOjVV5e7t6vqKi4pGGwgEl2aLjjR5rpr4931lN/L9QVUX/S6R4n9Pzk/+PrsNBErHvllyorCtXHG9rq4w1t3ceT5vfUru9O64+/vVZnaoM09MEK3dC/xneBoq4GTjYxtdPZRBUWFvazl1ZVVemFF17QG2+8odraWuXk5Ojpp592n+/YsaPCwsK0Y8cO3XTTTVq7dq0GDBjQ8Jh+QLKzuW2bIrRtU4TmbZuh2b+nooP3jJhYphETy+oc/+xQK42bS39wU3fHHXcoPz9fw4YNk8vlUnJysvr06aOxY8dq0qRJuv766/WXv/xFqampqq6u1nXXXaeHHnrI8v28nuw2bdrk7VsCABrCYjdmQ8f5pkyZoilTppiOLVu2zP1zjx49tGbNGguB1EVlBwAws+ETVEh2AACTc09QsdLOX5HsAABmLuPsZqWdn+KtBwAA26OyAwCYMWYHALC7S11U7o9IdgAAs0tcVO6PGLMDANgelR0AwIRuTACA/TFBBQBgdw4ZclgYf3P4cbYj2QEAzFw/bFba+SkmqAAAbI/KDgBg4jAsdmP68dIDkh0AwIwJKgAA27PhonKSHQDAxI7r7JigAgCwPSo7AICZIYvdmI0eSaMh2QEATByG5LCwZs6fuzFJdgAAMxtOUGHMDgBge1R2AAAz1tkBAGzP4hNU/Lkbk2QHADCz4ZgdyQ4AYMZbDwAACDxUdgAAE17eCgCwP8bsAAC2R7IDANgeE1QAAAg8VHYAABOHxUXlDW3z4osvasOGDZKkgQMHatq0aXXOv/XWW4qIiJAkPfDAAxo5cmSD45JIdgCAn/LCK362bNmijz76SDk5OXI4HBozZow++OADDR482H1NQUGB5s+frz59+jQ8lp8g2QEAzLwwQSUyMlIzZsxQaGioJKlbt24qLi42XVNQUKClS5fq0KFDuvnmmzV9+nSFhYU1PC4xZgcAaGQlJSUqKioybZWVlaZrrrnmGt14442SpMLCQm3YsEEDBw50n6+pqVHPnj01depU5eTkqLKyUkuWLLEcE8kOAPATxo/VXUO2H/oxk5OTNWjQINP22muv1XunvXv3avTo0Zo2bZq6du3qPt6qVSstW7ZM3bp1U0hIiEaPHq3Nmzdb/kZ0YwIAzC5x6UFWVpaCg4NNp85NMjnfjh07NGnSJKWkpCg2NtZ0rri4WFu2bNHw4cMlSYZhKCTEesoi2QEATC51NmZ0dLTHsbXDhw9r/PjxWrBggfr371/nfPPmzfX888+rX79+6tSpkzIzM02TVxqKZAcAMPPCBJXly5fr1KlTmjdvnvvYiBEjtGnTJk2aNEnXX3+95s6dq3Hjxqm2tla//vWv9cgjjzQ8ph+Q7AAAXpeamqrU1NQ6x5OSktw/x8TEKCYmplHuR7IDAJi5jLOblXZ+imQHADDjQdAAAPuzmOx4nx0AIGB44XFh3saicgCA7VHZAQDMmKACALA9w3V2s9LOT5HsAABmNpyNyZgdAMD2qOwAAGaM2QEA7I91dgAAu7PhmB3JDgBgxqJyAAACD5UdAMDM5Tq7WWnnp0h2AAAzxuwAALZHsgMA2J5hcZ2dHyc7JqgAAGyPyg4AYGIYLhkWHupspY23kOwAAGYuWXxcWKNH0mhIdgAAMxtOUGHMDgBge1R2AAAzFpUDAGzPht2YJDsAgIlhuGRYqNKYjQkACBw2rOyYoAIAsD0qOwCAGevsAAC2Z7jOblba+SmSHQDAxHAZMixUdlbaeAtjdgCAn3D9WN01ZGtgP+Y777yjoUOH6q677lJmZmad81988YUSExMVExOjWbNm6cyZM5a/EckOAOB1paWlWrBggbKyspSbm6vVq1fr66+/Nl0zdepUzZ49W++9954Mw1B2drbl+5HsAABmP3RjNnRryKSWLVu26JZbblHbtm3VsmVLxcTEKC8vz33+0KFDOnnypG688UZJUmJioul8Q/n9mJ3xw7qNiKjWPo4k8LXr0MbXIQS8U2cifR2CLfDf8dKcdraX9OOfj40tIjLc0pq5iMhwSVJJSYmCg4PN5yIiFBER4d4vKytTZOSPvwdRUVH6/PPPL3g+MjJSpaWlDY7pHL9PdrW1tZKkcS8/6ONIAt/0deN8HULA2239/2s4z+7SRb4OwRZqa2vVvHnzRvu84OBgBQcHX9Kft7W1tbr33ntVU1NjOj5hwgRNnDjRve9yueRwONz7hmGY9j2dbyi/T3atWrVS9+7d1axZs0v6ogBgF4ZhqLa2Vq1atWrUzw0JCVGvXr3kdDotf8b333+vdevW1Tl+flUnSdHR0dq+fbt7v7y8XFFRUabz5eXl7v2KigrT+Yby+2QXFBSk1q3pwgSA8zVmRXe+kJAQhYRYTw1hYWFq166dx+tuvfVWLVq0SEePHlWLFi30/vvv65lnnnGf79ixo8LCwrRjxw7ddNNNWrt2rQYMGGA5LodxuTp9AQD4Ge+8846WLl2q2tpaDR8+XGPHjtXYsWM1adIkXX/99fryyy+Vmpqq6upqXXfddXruuecUGhpq6V4kOwCA7bH0AABgeyQ7AIDtkewAALZHsgMA2B7JDgBgeyS7JmTPnj2KjY31dRhowqqrqxUXF6eioiJfh4ImhmTXROTm5mrMmDE6ceKEr0NBE5Wfn6+kpCQVFhb6OhQ0QSS7JqCqqkobN27U/PnzfR0KmrDs7GylpaVd0iOfAKv8/nFhuHStW7fWokWL6DqCT6Wnp/s6BDRhVHYAANsj2dnU3/72NyUkJCghIUEbN270dTgA4FN0Y9rU5MmTNXnyZF+HAQB+gcoOAGB7vPUAAGB7VHYAANsj2QEAbI9kBwCwPZIdAMD2SHYAANsj2cGvFBUVqWfPnu4F8QkJCbrnnnu0Zs2aS/7sRx99VG+//bYkKSEhQZWVlRe8tqqqSg899FCD75GXl6dRo0bVOf7JJ58oLi7OY/trr71WR48ebdA9Z8yYoeXLlzeoDdDUsKgcfqd58+Zau3ate7+0tFRxcXHq1auXevTo0Sj3OP/z63P8+HHt3LmzUe4FwPdIdvB7v/rVr9SlSxcVFhZq9+7dWrNmjU6cOKHw8HCtXLlSb775pl5//XW5XC61bdtWTz31lLp166bS0lLNmDFDZWVluuKKK3TkyBH3Z1577bXaunWr2rdvr6VLlyonJ0chISHq0qWL5s2bp5kzZ+rkyZNKSEjQ22+/rcLCQqWnp+u7776T0+nUqFGjNHz4cElnH832zjvvqG3bturSpYvH77Nv3z7NnTtXNTU1Ki8vV48ePbRw4UKFhYVJkhYuXKidO3fK5XJpypQpuuOOOyTpgt8TgGckO/i9zz77TAcOHFDv3r21detWff3119q0aZPCw8P16aefKjc3V5mZmWrRooU++ugjTZgwQRs2bNDcuXPVu3dvTZkyRfv379ewYcPqfPbGjRv19ttvKzs7W23atNFzzz2nVatW6bnnnlN8fLzWrl2rM2fOaNKkScrIyNB1112nqqoq/e53v9PVV1+tiooKvf/++8rNzVXz5s01fvx4j98nOztbw4YNU0JCgmpra5WYmKh//vOfiomJkSR16tRJc+fO1VdffaVRo0Zpw4YN+vrrry/4PQF4RrKD3zlXUUmS0+lUu3bt9Pzzz6tDhw6SzlZl4eHhkqR//vOf2r9/v0aMGOFuX1lZqe+++05btmzR9OnTJUldunRRv3796txr69atGjJkiNq0aSNJmjlzpiSZXodUWFioAwcOKCUlxRTj7t279c0332jw4MHueO677z6tXLnyZ7/f1KlT9fHHH2vZsmUqLCxUWVmZvv/+e/f5pKQkSVL37t3VrVs3ffbZZ9qxY8cFvycAz0h28Ds/HbP7qZYtW7p/drlcSkhI0NSpU937ZWVlatOmjRwOh85/Gl5ISN1f9+DgYDkcDvd+ZWVlnYkrTqdTrVu3NsVUUVGh1q1bKyMjw3SP4OBgj9/viSeekNPp1N13363bb79dhw8fNn1GUNCP88ZcLpdCQkJ+9nsC8IzZmAhot912m/7rv/5LZWVlkqTXX39dv//97yVJ//Zv/6bVq1dLkoqLi/XJJ5/UaX/rrbfqgw8+UHV1tSRp0aJFevXVVxUSEiKn0ynDMHTllVeaEvDhw4cVFxengoICDRgwQHl5eaqsrJTL5fI48UWSPvroI40fP15Dhw6VJOXn58vpdLrP5+TkSJJ27drl7r79ue8JwDMqOwS02267TWPHjtXo0aPlcDgUHh6uF198UQ6HQ2lpaZo5c6buvvtuRUdH1zuTc+DAgfr666/dXYdXX321nnnmGbVo0UI33HCDYmNjlZmZqSVLlig9PV0vv/yyzpw5o8mTJ+umm26SJO3Zs0f33XefIiIi1KNHDx07duxnY3788cc1fvx4tWzZUuHh4br55pt14MAB9/mDBw9q2LBhcjgcmj9/vtq2bfuz3xOAZ7z1AABge3RjAgBsj2QHALA9kh0AwPZIdgAA2yPZAQBsj2QHALA9kh0AwPZIdgAA2/v/Hp72KbNxlHAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import ConfusionMatrixDisplay\n",
    "print(\"Confusion matrix for linear \")\n",
    "ConfusionMatrixDisplay.from_estimator(lin_clf, x_test, labels_test)\n",
    "print(\"Confusion matrix for Gaussian \")\n",
    "ConfusionMatrixDisplay.from_estimator(gaus_clf, x_test, labels_test)\n",
    "print(\"Confusion matrix for gram matrix and then linear \")\n",
    "ConfusionMatrixDisplay.from_estimator(gram_lin_clf, test_matrix_df, labels_test)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# At the end of the exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bonus question with no points! Answering this will have no influence on your scoring, not at the assignment and not towards the exam score -- really feel free to ignore it with no consequence. But solving it will reward you with skills that will make the next lectures easier, give you real applications, and will be good practice towards the exam.\n",
    "\n",
    "The solution for this questions will not be included in the regular lab solutions pdf, but you are welcome to open a discussion on the Moodle: we will support your addressing it, and you may meet other students that choose to solve this, and find a teammate for the next assignment that is willing to do things for fun and not only for score :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BONUS **[ZERO pt]** Use a contour plot to show the classification boundaries of your SVMs. [[link here]](https://scikit-learn.org/stable/auto_examples/svm/plot_iris_svc.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BONUS **[ZERO pt]** Learn to search for the best values for `gamma` and `C` [[link here]](https://scikit-learn.org/stable/auto_examples/svm/plot_rbf_parameters.html) . NOTE: this is extremely valuable experience for when (not even if!) you will need a SVM for a real application."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BONUS **[ZERO pt]** Generate points to run through with a regression algorithm like Linear Regression from our earlier exercises. This time start from a nonlinear equation (e.g. $x^2$), and add noise as usual. Then try your hand with SVR with a (linear or) nonlinear kernel, which is equivalent to running Linear Regression on the Gram matrix (yet another name: Kernel Ridge Regression) [[link here]](https://scikit-learn.org/stable/modules/kernel_ridge.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Final considerations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- I once read a quote that restricting calculus to linear functions is like restricting biology to the study of great apes (help tracking its origin would be welcome). We start from linearity because it's easier to study; the real world is rarely so kind, so learning adaptations such as the kernel trick is simply invaluable.\n",
    "- Trying (scikit-learn) Naïve Bayes or Linear Discriminant Analysis on the Gram matrices would take you just a minute and be invaluable experience. For example, I wouldn't be surprised if LDA performed better than NB (think: why?). But if we had a very large dataset, the Gram matrix would become too large for LDA to handle (remember it does not scale well on the number of features).\n",
    "- **[IMPORTANT]** If you want to gain first-hand experience in tools you can actually use in the real world, consider submitting on the bonus questions from this point on, as I am switching the topic from \"topics for curiosity\" to \"actual deployed value\"."
   ]
  }
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