Lab7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Instance Based Learning\n",
    "\n",
    "Reminder on Voronoi diagrams: https://youtu.be/j2c3kumwoAk\n",
    "\n",
    "Key ideas:\n",
    "* training: simply store all training examples\n",
    "* classification: compute only locally the target function\n",
    "* Inductive bias: the classification of query/test instance $x_q$ will be most similar to the classification of training instances that are nearby\n",
    "\n",
    "Advantages:\n",
    "* can learn very complex target functions\n",
    "* training is very fast\n",
    "* don't lose information\n",
    "* robust to noisy training\n",
    "\n",
    "Disadvantages:\n",
    "* slow at query time\n",
    "* easily fooled by irrelevant attributes (the curse of dimensionality)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-Nearest Neighbour\n",
    "\n",
    "## Algorithm\n",
    "\n",
    "Training:\n",
    "* Store all training examples\n",
    "\n",
    "Classification:\n",
    "* Given a query/test instance $x_q$, first locate the $k$ nearest training examples $x_1,...,x_k$, then estimate $\\hat{f}(x_q)$:\n",
    " * in case of *discrete-valued* $f=\\mathbb{R}^n \\rightarrow V$, take a vote among its k nearest neighbours\n",
    " $$\\hat{f}(x_q) \\leftarrow \\bbox{argmax}_{v\\in V}\\sum_{i=1}^{k} \\delta(v, f(x_i))$$\n",
    " where $\\delta(a,b)=1$ if $a=b$, and $\\delta(a,b)=0$ if $a \\neq b$\n",
    " * in case of *continuous-valued* $f$, take the mean of the $f$ values of its $k$ nearest neighbours\n",
    " $$\\hat{f}(x_q) \\leftarrow \\frac{\\sum_{i=1}^kf(x_i)}{k}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification\n",
    "\n",
    "Given a dataset like the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "d = pd.DataFrame({\n",
    "    'X1': [-1, 0, 0, 1, 1, 1, 2, 2],\n",
    "    'X2': [1, 1, 2, -1, 0, 2, 2, 3],\n",
    "    'Y': [0, 1, 0, 0, 1, 1, 0, 1]\n",
    "})\n",
    "X, Y = d[['X1', 'X2']], d['Y']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which we can plot using `matplotlib` with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "c= ['green' if l == 0 else 'red' for l in Y]\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "plt.scatter(X['X1'], X['X2'], color=c)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use `KNeighborsClassifier` from `sklearn.neighbors` to classify the point at (0, 0) for $k=3$ neighbours:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn = KNeighborsClassifier(n_neighbors=3)\n",
    "knn.fit(X.values, Y)\n",
    "knn.predict([[0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Very similar to the previous algorithms, the `predict_proba` give us the probability for each instance to be in each class. In the example above, for one point in class 0 and two points in class 1, the probabilities will be 1/3 and 2/3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.33333333, 0.66666667]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn.predict_proba([[0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualise the decision surface using `matplotlib`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tools.plots import plot_decision_surface_knn\n",
    "knn = KNeighborsClassifier(n_neighbors=3).fit(X, Y)\n",
    "plot_decision_surface_knn(knn, X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the point (0, 0) falls in the red area."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the particular case of $k=1$, the resulting decision boundaries correspond to a _Voronoi diagram_, which splits the surface into zones based on the closest point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "knn = KNeighborsClassifier(n_neighbors=1).fit(X, Y)\n",
    "plot_decision_surface_knn(knn, X, Y, voronoi=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Give it a try!**\n",
    "\n",
    "`KNeighborsClassifier` can work with Manhattan distance instead of Euclidean distance by changing the value of the `p` paramater from 2 to 1.\n",
    "\n",
    "Plot the decision surface of 1-NN using Manhattan distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "d = pd.DataFrame({\n",
    "    'X1': [-1, 0, 0, 1, 1, 1, 2, 2],\n",
    "    'X2': [1, 1, 2, -1, 0, 2, 2, 3],\n",
    "    'Y': [0, 0, 1, 0, 0, 0, 0, 0]\n",
    "})\n",
    "X, Y = d[['X1', 'X2']], d['Y']\n",
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying weights\n",
    "\n",
    "By default, all points in each neighborhood are weighted equally, meaning that for 3-NN the classification will always be the majority, regardless of how far each training point is from the predicted one. An alternative to this is to take into consideration the distances by switching the `weights` parameter from `\"uniform\"` to `\"distance\"` which weights training points by the inverse of their distance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**Give it a try!**\n",
    "\n",
    "Create a dataset and train that `KNeighborsClassifier` with the two types of weighing to illustrates the difference between `\"uniform\"` and `\"distance\"`. In the simplest case, you can create a triangle and plot the decision surface for 3-NN in the two cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression\n",
    "\n",
    "On the same dataset as before, we can use `KNeighborsRegressor` to predict the numeric value of point (0, 0), considering Y as being a number rather than a class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "knn = KNeighborsRegressor(n_neighbors=3).fit(X, Y)\n",
    "knn.fit(X.values, Y)\n",
    "knn.predict([[0, 0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measuring accuracy\n",
    "\n",
    "### Training accuracy\n",
    "\n",
    "For the classifier, the `score` function returns the accuracy on the given dataset and labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.875"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn = KNeighborsClassifier(n_neighbors=3)\n",
    "knn.fit(X, Y)\n",
    "knn.score(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can quickly check this number by having a look at the visualisation above for 3-NN and counting how many points end up in the zone of the same colour. We can see that only 2 red points and 1 green point are correctly classified, which means that the accuracy is $\\frac{3}{8}=0.375$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the regressor, the `score` function returns the coefficient of determination $R^2$ for the prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11111111111111094"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn = KNeighborsRegressor(n_neighbors=3)\n",
    "knn.fit(X, Y)\n",
    "knn.score(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-validation accuracy\n",
    "\n",
    "Cross-validation works with the usual functions `cross_val_score` and `LeaveOneOut`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CVLOO scores: [1. 1. 0. 1. 1. 1. 1. 1.]\n",
      "Mean CVLOO score:  0.875\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import LeaveOneOut, cross_val_score\n",
    "from statistics import mean\n",
    "loo = LeaveOneOut()\n",
    "knn = KNeighborsClassifier(n_neighbors=3)\n",
    "scores = cross_val_score(knn, X, Y, cv=loo)\n",
    "print(\"CVLOO scores:\", scores)\n",
    "print(\"Mean CVLOO score: \", mean(scores))"
   ]
  }
 ],
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