Solutions to Chapter 1 The Learning Problem.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Function Definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import sklearn\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "import math\n",
    "from sklearn.preprocessing import normalize\n",
    "from functools import partial\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "#target = -1 + 2*x1 + 2*x2 #np.array([2,2,-1])\n",
    "df = pd.DataFrame({'x1':[0,1,0,-0.5,-1,2,1,3,0.5,-1,0,-2,-3,1,2,-4,-3,3,-0.5,-2],\n",
    "                   'x2':[0,1,1,0,-1,4,-1,-5,-2,1,3,0,-1,6,8,2,3,10,2,1], \n",
    "                   'y':[1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]})\n",
    "df['x0'] = 1\n",
    "df = df[['x0','x1', 'x2', 'y']]\n",
    "\n",
    "def perceptron(points, dim, max_it=100, use_adaline=False, \n",
    "               eta = 1, randomize=False, print_out = True):\n",
    "    w = np.zeros(dim+1)\n",
    "    xs, ys = points[:,:dim+1], points[:,dim+1]\n",
    "    num_points = points.shape[0]\n",
    "    for it in range(max_it):\n",
    "        correctly_predicted_ids=  set()\n",
    "        idxs = np.arange(num_points)\n",
    "        if randomize:\n",
    "            idxs = np.random.choice(np.arange(num_points), num_points, replace=False)\n",
    "        for idx in idxs:\n",
    "            x, y = xs[idx], ys[idx]\n",
    "            st = np.dot(w.T, x)\n",
    "            prod = st*y #np.dot(w.T, x)*y\n",
    "            if prod < -100: #avoid out of bound error\n",
    "                st = -100\n",
    "            threshold = 1 if use_adaline else 0\n",
    "            st = st if use_adaline else 0\n",
    "            if prod <= threshold:\n",
    "                w = w + eta *(y-st)*x\n",
    "                break #PLA picks one example at each iteration\n",
    "            else:\n",
    "                correctly_predicted_ids.add(idx)\n",
    "        if len(correctly_predicted_ids) == num_points:\n",
    "            break\n",
    "    \n",
    "    c = 0\n",
    "    for x, y in zip(xs, ys):\n",
    "        prod = np.dot(w.T, x)*y\n",
    "        if prod > 0:\n",
    "            c +=1\n",
    "    w = w/w[-1]\n",
    "    if print_out:\n",
    "        print('final correctness: ', c, '. Total iteration: ', it)\n",
    "        print('final normalized w:', w)\n",
    "    return w, it\n",
    "    \n",
    "def flip_coins(total_coins):\n",
    "    \"\"\"Flip all coins once, return their head/tail status\n",
    "    \"\"\"\n",
    "    \n",
    "    hts = np.zeros(total_coins) #head: 1, tail: 0\n",
    "    probs = np.random.uniform(size=total_coins)\n",
    "    hts[probs > 0.5] = 1\n",
    "    return hts\n",
    "\n",
    "def run_once(total_coins, total_flips, print_freq = False):\n",
    "    v1, vrand, vmin = None, None, None\n",
    "    crand = np.random.choice(total_coins)\n",
    "    hts_sum = np.zeros(total_coins) # store the sum of heads in total_flips\n",
    "    \n",
    "    for flip in range(total_flips):\n",
    "        hts_sum = hts_sum + flip_coins(total_coins)\n",
    "    \n",
    "    hts_freq = hts_sum/total_flips\n",
    "    \n",
    "    v1 = hts_freq[0]\n",
    "    vrand = hts_freq[crand]\n",
    "    cmin = np.argmin(hts_sum)\n",
    "    vmin = hts_freq[cmin]\n",
    "    \n",
    "    if print_freq:\n",
    "        print('Frequency of first coin: {}'.format(v1))\n",
    "        print('Frequency of a random coin: id({})-freq({})'.format(crand, vrand))\n",
    "        print('Frequency of the coin with minimum frequency: id({})-freq({})'.format(cmin, vmin))\n",
    "    return v1,vrand,vmin\n",
    "\n",
    "def hoeffding_bound(epsilon, n):\n",
    "    return 2.0*np.exp(-2.0*n*epsilon**2)\n",
    "\n",
    "\n",
    "def generate_random_numbers01(N, dim, num_grid_points):\n",
    "    random_ints = np.random.randint(num_grid_points, size=(N, dim))\n",
    "    init_lb = 0\n",
    "    return (random_ints - init_lb)/(num_grid_points - 1 - init_lb)\n",
    "\n",
    "def generate_random_numbers(N, dim, num_grid_points, lb, ub):\n",
    "    zero_to_one_points = generate_random_numbers01(N, dim, num_grid_points)\n",
    "    res = lb + (ub - lb)*zero_to_one_points\n",
    "    return res\n",
    "\n",
    "def generate_random_coeffs(dim):\n",
    "    rn = generate_random_numbers(1, dim, 1000, -10, 10)\n",
    "    return rn\n",
    "\n",
    "def true_f(x, coeffs):\n",
    "    return coeffs.flatten()[0] + np.dot(coeffs.flatten()[1:], x.flatten())\n",
    "\n",
    "def generate_two_classes(N, dim, true_func, rn_func):\n",
    "    cls1, cls2 = [], []\n",
    "    while True:\n",
    "        rn = rn_func(1, dim).flatten()\n",
    "        if true_func(rn) > 0 and len(cls1) < N:\n",
    "            cls1.append(rn)\n",
    "        elif true_func(rn) < 0 and len(cls2) < N:\n",
    "            cls2.append(rn)\n",
    "        if len(cls1) == N and len(cls2) == N:\n",
    "            break\n",
    "    return np.asarray(cls1), np.asarray(cls2)    \n",
    "\n",
    "def generate_df(N, dim,true_func, rn_func):\n",
    "    cls1, cls2 = generate_two_classes(N/2, dim, true_func, rn_func)\n",
    "    cols = ['x' + str(i) for i in range(1, dim+1)]\n",
    "    df1 = pd.DataFrame(cls1, columns=cols)\n",
    "    df1['y'] = 1\n",
    "    df2 = pd.DataFrame(cls2, columns=cols)\n",
    "    df2['y'] = -1\n",
    "    df = pd.concat([df1, df2])\n",
    "    df['x0'] = 1\n",
    "    df = df[['x0'] + cols + ['y']]\n",
    "    return df\n",
    "\n",
    "def plot_data(x1, df, norm_coeffs, norm_g, lb, ub):\n",
    "        figsize = plt.figaspect(1)\n",
    "        f, ax = plt.subplots(1, 1, figsize=figsize)\n",
    "        cls1_df = df.loc[df['y']==1]\n",
    "        cls2_df = df.loc[df['y']==-1]\n",
    "        line = ax.plot(x1, -(norm_coeffs[0]+norm_coeffs[1]*x1), label='True Function')\n",
    "        pluses = ax.scatter(cls1_df[['x1']].values, cls1_df[['x2']].values, marker='+', c= 'r', label='+1 labels')\n",
    "        minuses = ax.scatter(cls2_df[['x1']].values, cls2_df[['x2']].values, marker=r'$-$', c= 'b', label='-1 labels')\n",
    "        if norm_g is not None:\n",
    "            hypothesis = ax.plot(x1, -(norm_g[0]+norm_g[1]*x1), c = 'r', label='Final Hypothesis')\n",
    "\n",
    "        ax.set_ylabel(r\"$x_2$\", fontsize=11)\n",
    "        ax.set_xlabel(r\"$x_1$\", fontsize=11)\n",
    "        ax.set_title('Data set size = %s'%N, fontsize=9)\n",
    "        ax.axis('tight')\n",
    "        legend_x = 2.0\n",
    "        legend_y = 0.5\n",
    "        ax.legend(['True Function', 'Final Hypothesis', \n",
    "                   '+1 labels', '-1 labels', ], \n",
    "                  loc='center right', bbox_to_anchor=(legend_x, legend_y))\n",
    "        #ax.legend(handles=[pluses, minuses], fontsize=9)\n",
    "        ax.set_ylim(bottom=lb, top=ub)\n",
    "        plt.show()\n",
    "        \n",
    "def run_perceptron_experiment(N, dim, lb, ub, num_grid_points, coeff_lb, coeff_ub, \n",
    "                              eta, maxit, use_adaline=False, randomize=False,\n",
    "                              show_plot=True, test_N = 10000):\n",
    "    \n",
    "    rns = generate_random_numbers(N, dim, num_grid_points, lb, ub)\n",
    "    rn_func = partial(generate_random_numbers, num_grid_points = num_grid_points, lb = lb, ub = ub)\n",
    "    coeffs = generate_random_numbers(1, dim+1, num_grid_points, coeff_lb, coeff_ub)\n",
    "    norm_coeffs = coeffs.flatten()/coeffs.flatten()[-1]\n",
    "    true_func = partial(true_f, coeffs = norm_coeffs)\n",
    "    \n",
    "    df = generate_df(N, dim, true_func, rn_func)\n",
    "    test_df = generate_df(test_N, dim, true_func, rn_func)\n",
    "    \n",
    "    x1 = np.arange(lb, ub, 0.01)\n",
    "    norm_g, num_its = perceptron(df.values, dim, maxit, use_adaline, \n",
    "                                 eta, randomize, show_plot)\n",
    "    \n",
    "    if show_plot:\n",
    "        print('True coeffs: ', norm_coeffs)\n",
    "        plot_data(x1, df, norm_coeffs, norm_g, lb, ub)\n",
    "    return num_its, norm_g, test_df"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1 The Learning Problem\n",
    "\n",
    "## Exercises\n",
    "\n",
    "#### Exercise 1.1\n",
    "\n",
    "1. (a) \n",
    "  * Input space $\\mathcal{X}$: patient's medical history, symptoms, personal health information etc.\n",
    "  * Output space $\\mathcal{Y}$: all possible diseases\n",
    "  * target function $f: \\mathcal{X} \\to \\mathcal{Y}$: ideal formula to identify a patient's problem\n",
    "  * Data set: All available patients' information and their corresponding correct problem diagnostic.\n",
    "2. (b)\n",
    "  * Input space $\\mathcal{X}$: handwritten digits (digitalized)\n",
    "  * Output space $\\mathcal{Y}$: 0-9 digits\n",
    "  * target function $f: \\mathcal{X} \\to \\mathcal{Y}$: ideal formula match a handwritten digit to a correct digit\n",
    "  * Data set: handwritten digits and their corresponding correct matches\n",
    "3. (c)\n",
    "  * Input space $\\mathcal{X}$: every information of an email, e.g. words\n",
    "  * Output space $\\mathcal{Y}$: yes/no \n",
    "  * target function $f: \\mathcal{X} \\to \\mathcal{Y}$: ideal formula to identify whether an email is spam or not\n",
    "  * Data set: Spam and non-spam emails that have been identified by human\n",
    "4. (d)\n",
    "  * Input space $\\mathcal{X}$: price of electric, temperature, day of the week\n",
    "  * Output space $\\mathcal{Y}$: electric load\n",
    "  * target function $f: \\mathcal{X} \\to \\mathcal{Y}$: ideal function that gives exact electric load for a given price, temperature and day of the week.\n",
    "  * Data set: historical electric load along with corresponding price, temperature and day of the week information.\n",
    "5. (e) \n",
    "  * Input space $\\mathcal{X}$: cat images \n",
    "  * Output space $\\mathcal{Y}$: types of cats\n",
    "  * target function $f: \\mathcal{X} \\to \\mathcal{Y}$: ideal function that gives cat type according to the picture\n",
    "  * Data set: picutres with cats that have been categorized to various types\n",
    "\n",
    "#### Exercise 1.2\n",
    "1. (a) Keywords with a large positive weight: free, cheap, earn, !\n",
    "1. (b) Keywords with a negative weight: person name, hi, the\n",
    "1. (c) The parameter $b$ in perceptron directly affects how many borderline messages end up being classified as spam. This is because $b$ is the threshold used to classify the emails into spam and non-spam categories.\n",
    "\n",
    "#### Exercise 1.3\n",
    "1. (a) If $x(t)$ is misclassified by $w(t)$, then $w^T(t)x(t)$ has different signs of $y(t)$, thus $y(t)w^T(t)x(t) \\gt 0$.\n",
    "2. (b)\n",
    "\n",
    "\\begin{align*}\n",
    "y(t)w^T(t+1)x(t) &= y(t) \\left(w(t)+y(t)x(t)\\right)^Tx(t) \\\\\n",
    "&= y(t)\\left(w^T(t) + y(t)x^T(t)\\right)x(t) \\\\\n",
    "&= y(t)w^T(t)x(t) + y(t)y(t)x^T(t)x(t)\\\\\n",
    "&\\gt y(t)w^T(t)x(t) \\;\\;\\;\\text{because the last term is } \\ge \\text{ than } 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "3. (c) \n",
    "\n",
    "From previous problem, we see that $y(t)w^T(t)x(t)$ is increasing with each update. \n",
    "\n",
    "If $y(t)$ is positive, but $w^T(t)x(t)$ is negative, we move $w^T(t)x(t)$ toward positive by increasing it. \n",
    "\n",
    "If however $y(t)$ is negative, but $w^T(t)x(t)$ is positive, $y(t)w^T(t)x(t)$ increases means $w^T(t)x(t)$ is decreasing, i.e. moving toward negative region. \n",
    "\n",
    "So the move from $w(t)$ to $w(t+1)$ is a move \"in the right direction\" as far as classifying $x(t)$ is concerned."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.4\n",
    "Implement the perceptron learning algorithm and check\n",
    "* Convergence speed: The convergence is fast, it depends on the data, but usually it only takes about 10 iterations to find a solution.\n",
    "* How well the final hypothesis $g$ matches your target $f$: The final hypothesis $g$ doesn't match my target $f$ very closely in terms of their coefficients. But from picture, they are largely in line with each other in the range of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final correctness:  20 . Total iteration:  2\n",
      "final normalized w: [0.02354535 0.26266196 1.        ]\n",
      "True coeffs:  [2.16057234 0.3672496  1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#perceptron(df.values, 2)\n",
    "\n",
    "lb, ub = -100, 100\n",
    "N, dim = 20, 2 \n",
    "num_grid_points = 2000\n",
    "coeff_lb, coeff_ub = -10, 10\n",
    "eta = 1\n",
    "maxit = 100\n",
    "use_adaline, randomize = False, False\n",
    "_, _, _ = run_perceptron_experiment(N, dim, lb, ub, num_grid_points,\n",
    "                             coeff_lb, coeff_ub, eta, maxit, use_adaline, randomize)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.5\n",
    "1. (a) Learning\n",
    "1. (b) Design\n",
    "1. (c) Learning\n",
    "1. (d) Design\n",
    "1. (e) Learning\n",
    "\n",
    "#### Exercise 1.6\n",
    "1. (a) Supervised Learning\n",
    "1. (b) Reinforcement Learning\n",
    "1. (c) Unsupervised Learning\n",
    "1. (d) Learning to play music\n",
    "  * If learn by yourself, it's unsupervised learning\n",
    "  * If learn from a teacher, it's supervised learning\n",
    "  * If learn by yourself but with someone to tell you if your music is good or not, it's reinforcement learning. \n",
    "1. (e) Supervised Learning\n",
    "\n",
    "#### Exercise 1.7\n",
    "1. (a) The learning algorithm will pick the final hypothesis that always returns 1. \n",
    "  * 1 out of 8 $f$ agrees with $g$ on all three points; 3 $f$ agree with $g$ on two of the points; 3 $f$ agree with $g$ on one of the points, 1 $f$ agrees with none of the points. \n",
    "1. (b) The learning algorithm will pick the final hypothesis that always returns 0. \n",
    "  * 1 out of 8 $f$ agrees with $g$ on all three points; 3 $f$ agree with $g$ on two of the points; 3 $f$ agree with $g$ on one of the points, 1 $f$ agrees with none of the points.\n",
    "1. (c) The learning algorithm will pick the final hypothesis $XOR$. \n",
    "  * 1 out of 8 $f$ agrees with $g$ on all three points; 3 $f$ agree with $g$ on two of the points; 3 $f$ agree with $g$ on one of the points, 1 $f$ agrees with none of the points.\n",
    "1. (d) The learning algorithm will pick the final hypothesis $f_7$. \n",
    "  * 1 out of 8 $f$ agrees with $g$ on all three points; 3 $f$ agree with $g$ on two of the points; 3 $f$ agree with $g$ on one of the points, 1 $f$ agrees with none of the points.\n",
    "  \n",
    "#### Exercise 1.8\n",
    "\n",
    "In a sample of 10 marbles, for the fraction $\\nu$ of red marbles to be $\\nu \\le 0.1$, we must have at most one red marbles. \n",
    "\n",
    "\\begin{align*}\n",
    "P(number\\;of\\;red \\le 1) &= P(red = 0) + P(red = 1) \\\\\n",
    "&= (1-\\mu)^{10} + \\mu (1-\\mu)^9\\\\\n",
    "&= (1-\\mu)^9\\\\\n",
    "&= 1.0e-9\n",
    "\\end{align*}\n",
    "\n",
    "#### Exercise 1.9\n",
    "We have $\\mu=0.9$, $N=10$, and want $\\nu \\le 0.1$, i.e. $|\\mu - \\nu| = \\mu - \\nu \\ge 0.9 - 0.1 = 0.8$. Let's pick $\\epsilon = 0.7$, then according to Hoeffding Inequity, we have\n",
    "\n",
    "\\begin{align*}\n",
    "P(\\nu \\le 0.1) &= P(\\mu - \\nu \\ge 0.8)\\\\\n",
    "&= P(|\\mu - \\nu| \\ge 0.8) \\\\\n",
    "&\\le P(|\\mu - \\nu| \\gt 0.7) \\\\\n",
    "&= P(|\\mu - \\nu| \\gt \\epsilon) \\\\\n",
    "&\\le 2e^{-2\\epsilon^2N}\\\\\n",
    "&\\approx 0.0001109032\n",
    "\\end{align*}\n",
    "\n",
    "This is an upper bound of the probability from pervious problem and is much larger than the calculated probability.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.10\n",
    "1. (a) The $\\mu$ for the three coins are all $0.5$ since the coins are fair."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frequency of first coin: 0.5\n",
      "Frequency of a random coin: id(83)-freq(0.3)\n",
      "Frequency of the coin with minimum frequency: id(7)-freq(0.0)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.5, 0.3, 0.0)"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exercise 1.10 (a) \n",
    "total_coins = 1000\n",
    "total_flips = 10\n",
    "run_once(total_coins, total_flips, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([6.23941e+05, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00,\n",
       "        3.76049e+05, 0.00000e+00, 0.00000e+00, 0.00000e+00, 1.00000e+01]),\n",
       " array([0.  , 0.02, 0.04, 0.06, 0.08, 0.1 , 0.12, 0.14, 0.16, 0.18, 0.2 ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\figure.py:2369: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
      "  warnings.warn(\"This figure includes Axes that are not compatible \"\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise 1.10 (b) \n",
    "total_coins = 1000\n",
    "total_flips = 10\n",
    "total_runs = 1000000\n",
    "v1s, vrands, vmins = [],[],[]\n",
    "for run in range(total_runs):\n",
    "    v1,vrand,vmin = run_once(total_coins, total_flips)\n",
    "    v1s.append(v1)\n",
    "    vrands.append(vrand)\n",
    "    vmins.append(vmin)\n",
    "\n",
    "fig, axs = plt.subplots(1,3,sharey=True, tight_layout=True)\n",
    "n_bins = 10\n",
    "axs[0].hist(v1s,bins=n_bins)\n",
    "axs[1].hist(vrands,bins=n_bins)\n",
    "axs[2].hist(vmins,bins=n_bins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x230e84aef98>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise 1.10 (c)\n",
    "eps = np.arange(0.0,0.5,0.05)\n",
    "bounds = hoeffding_bound(eps, total_flips)\n",
    "v1s, vrands, vmins = np.array(v1s), np.array(vrands), np.array(vmins)\n",
    "v1d = np.abs(v1s-0.5)\n",
    "vrandd = np.abs(vrands-0.5)\n",
    "vmind = np.abs(vmins-0.5)\n",
    "\n",
    "p1, prand, pmin = np.zeros(len(eps)),np.zeros(len(eps)),np.zeros(len(eps))\n",
    "\n",
    "for idx in range(eps.shape[0]):\n",
    "    ep = eps[idx]\n",
    "    p1[idx] = np.sum(v1d > ep)/total_runs\n",
    "    prand[idx] = np.sum(vrandd > ep)/total_runs\n",
    "    pmin[idx] = np.sum(vmind > ep)/total_runs\n",
    "\n",
    "#plt.ylim((0,0.01))    \n",
    "plt.plot(eps, bounds, marker='o', markerfacecolor='blue', markersize=8, color='skyblue', label='Hoeffding Bound')\n",
    "plt.plot(eps, p1, marker='', color='r', linewidth=1, label='First Coin')\n",
    "plt.plot(eps, prand, marker='', color='g', linewidth=1, linestyle='dashed', label='Random Coin')\n",
    "plt.plot(eps, pmin, marker='', color='y', linewidth=1, linestyle='dashed', label='Coin with Minimum Freq')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.10\n",
    "1. (d) The first and random coins follow the Hoeffding bound. The coin with minimum frequency doesn't obey Hoeffding bound. This is because that for the first two coins, the coins were chosen before the experiment. While for the last one, we have to flip all the coins first, and use the data to compute out which is the coin with minimum frequency of heads. This violates the Hoeffding inequality condition which says the hypothesis $h$ has been fixed before samples were drawn.\n",
    "\n",
    "1. (e) When we choose the coin having the minimum frequency of heads. We are like choosing the bin from 1000 bins (our hypothesis space). But we choose bin after we finish sampling the data.  This is akin to learning algorithm for the final hypothesis. The other two coins were chosen before the sampling, which is choosing bin beforehand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1.11\n",
    "\n",
    "1. (a) $S$ can not produce a hypothesis that is guaranteed to perform better than random on any point outside $\\mathcal{D}$. \n",
    "If $f$ has 25 $+1$ on $\\mathcal{D}$ but $-1$ on all other points in $\\mathcal{X}$, $S$ will choose the hypothesis $h_1$, which will not match $f$ outside of $\\mathcal{D}$ at all. On the other hand, a random function will have $+1$ and $-1$ 50/50, and it matches $f$ half of time, which is better than the function produced by $S$.\n",
    "\n",
    "1. (b) It is possible that $C$ produces a better hypothesis than $S$ produces. See the example above.\n",
    "1. (c) If every point in $\\mathcal{D}$ has 1, then $S$ will choose $h_1$ and $C$ will choose $h_2$. So outside of $\\mathcal{D}$, $h_1$ will have 90% chance to match with $f$, while $h_2$ will have only 10% chance. $S$ will always produce a better hypothesis than $C$. \n",
    "\n",
    "1. (d) From previous problem, we can see that when $p \\lt 0.5$, $C$ will produce a better hypothesis than $S$. Since $C$ always produce $h_2$, which will match $f$ better than $h_1$ if $p \\lt 0.5$.\n",
    "\n",
    "#### Exercise 1.12\n",
    "\n",
    "I think the best I can promise is (c). \n",
    "* The unknown target $f$ can be very complex that we can't learn at all.\n",
    "* If we can learn and produce a hypothesis $g$, since there are many data points (4000), the probability that $g$ matches $f$ is high according to Hoeffding inequality, and the error on $g$ might be small since we have a large data set.\n",
    "\n",
    "#### Exercise 1.13\n",
    "\n",
    "1. (a) The probability of error that $h$ makes in approximating $y$ is\n",
    "\n",
    "\\begin{align*}\n",
    "P(h \\ne y) &= P(h \\ne y| y = f(x))P(y=f(x)) + P(h\\ne y| y \\ne f(x))P(y\\ne f(x))\\\\\n",
    "&= \\mu \\lambda + (1-\\mu)(1-\\lambda)\\\\\n",
    "&= \\mu (2 \\lambda - 1) + (1-\\lambda)\\\\\n",
    "\\end{align*}\n",
    "\n",
    "1. (b) It can be seen from previous problem, that when $\\lambda = 0.5$, $P(h\\ne y) = 1-\\lambda = 0.5$, is independent of $\\mu$.\n",
    "\n",
    "## Problems\n",
    "\n",
    "#### Problem 1.1\n",
    "\n",
    "\\begin{align*}\n",
    "P(\\text{1st ball is black}) &= P(\\text{1st ball is black}|\\text{picked black,black  bag})P(\\text{picked black,black bag}) \\\\\n",
    "&+ P(\\text{1st ball is black}|\\text{picked black,white  bag})P(\\text{picked black,white bag})\\\\\n",
    "&= 1.0*0.5 + 0.5 * 0.5\\\\\n",
    "&= 0.75\\\\\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "P(\\text{picked black,black bag}|\\text{1st ball is black}) &= \\frac{P(\\text{picked  black,black bag and 1st ball is black})}{P(\\text{1st ball is black})} \\\\\n",
    "&= \\frac{P(\\text{1st ball is black}|\\text{picked black,black bag})P(\\text{picked black,black bag})}{P(\\text{1st ball is black})}\\\\\n",
    "&= \\frac{1.0*0.5}{0.75}\\\\\n",
    "&= \\frac{2}{3}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "P(\\text{picked black,white bag}|\\text{1st ball is black}) &= \\frac{1}{3}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Now we can compute the probability that the second ball is also black:\n",
    "\n",
    "\\begin{align*}\n",
    "P(\\text{2nd ball is black}) &= P(\\text{2nd ball is black}|\\text{picked b-b bag}|\\text{1st ball is black})*P(\\text{picked b-b bag}|\\text{1st ball is black}) \\\\\n",
    "&+ P(\\text{2nd ball is black}|\\text{picked b-w bag}|\\text{1st ball is black})*P(\\text{picked b-w bag}|\\text{1st ball is black})\\\\\n",
    "&= 1.0*\\frac{2}{3} + 0*\\frac{1}{3}\\\\\n",
    "&= \\frac{2}{3}\n",
    "\\end{align*}\n",
    "\n",
    "#### Problem 1.2\n",
    "\n",
    "1. (a)\n",
    "\n",
    "for $h(x) =1$, we need to have $w^Tx \\gt 0$, and for $h(x) = -1$, we need to have $w^Tx \\lt 0$. The line separate the two regions has $w^Tx = w_0 + w_1 x_1 + w_2 x_2 = 0$, compare with $x_2 = ax_1 + b$, we have $ a = -\\frac{w_1}{w_2}$ and $b =  -\\frac{w_0}{w_2}$.\n",
    "\n",
    "1. (b) The pictures for the cases $w=[1,2,3]^T$ and $w=-[1,2,3]^T$ should be be same according to the formula above.\n",
    "\n",
    "#### Problem 1.3\n",
    "\n",
    "\n",
    "1. (a) If $w^{*}$ is the optimal set of weights that separate the data, then for every $x_n$ in the data set $\\mathcal{D}$, $w^{*T}x_n$ has the same sign as $y_n$, which means $y_n(w^{*T}x_n) \\gt 0$. This implies $\\rho = min_{1\\le n\\le N}y_n(w^{*T}x_n) \\gt 0$.\n",
    "\n",
    "\n",
    "1. (a) Let's use induction to prove this.\n",
    "  * When $t=1$, we have $w^T(t-1)w^* + \\rho = w^T(0)w^* + \\rho = \\rho$, while $w(t)=w(1) = w(0) + y_ix_i = y_ix_i$ for some $i$. \n",
    "  \n",
    "  So $w^T(t)w^* = (y_ix_i)^Tw^* = y_ix_i^Tw^* = y_iw^{*T}x_i$. Here we use the fact that $y_i \\in {-1,1}$ and $x_i^Tw^*$ is a scalar. By definition of $\\rho$, we have $y_iw^{*T}x_i \\ge \\rho$. Thus the inequation is valid at $t=1$.\n",
    "  \n",
    "  \n",
    "  * Suppose the inequation is valid at $t$, let's prove that it's still valid at $t+1$. And $w(t+1)=w(t)+y_ix_i$ for some $i$. Then\n",
    "  \n",
    "\\begin{align*}\n",
    "w^T (t+1)w^* &= w^T(t)w^* + y_ix_i^Tw^* \\\\\n",
    "&\\ge w^T(t-1)w^* + \\rho + y_ix_i^Tw^*  \\\\\n",
    "&= \\left(w^T(t-1) + y_ix_i^T\\right)w^* + \\rho \\\\\n",
    "&= w^T(t)w^* + \\rho\\\\\n",
    "\\end{align*}\n",
    "  \n",
    "  This finishes the proof.\n",
    "  \n",
    "  It's easy to see that $w^T(t)w^* \\ge w^T(t-1)w^* + \\rho \\ge w^T(t-2)w^* + 2\\rho \\ge \\dots \\ge t\\rho$.\n",
    "  \n",
    "  \n",
    "1. (c) $w(t) = w(t-1) + y(t-1)x(t-1)$, take squared norm on $w(t)$ we have \n",
    "\n",
    "\\begin{align*}\n",
    "||w(t)||^2 &= \\left(w(t-1) + y(t-1)x(t-1)\\right)^T\\left(w(t-1) + y(t-1)x(t-1)\\right)\\\\\n",
    "&= ||w(t-1)||^2 + ||y(t-1)||^2||x(t-1)||^2 + 2y(t-1)w^T(t-1)x(t-1) \\\\\n",
    "&= ||w(t-1)||^2 + ||x(t-1)||^2 + 2y(t-1)w^T(t-1)x(t-1) \\\\\n",
    "&\\le ||w(t-1)||^2 + ||x(t-1)||^2\n",
    "\\end{align*}\n",
    "\n",
    "since $y(t-1)w^T(t-1)x(t-1) \\le 0$ because $x(t-1)$ was misclassified by $w(t-1)$.\n",
    "\n",
    "1. (d) Let's use induction.\n",
    "  * When $t=0$, it's obvious that $||w(0)||^2 = 0 \\le tR^2 = 0$.\n",
    "  * Assume at $t$, we have $||w(t)||^2 \\le tR^2$, then at $t+1$, we have $||w(t)||^2 \\le ||w(t-1)||^2 + ||x(t-1)||^2 $ from previous problem. Then we have\n",
    "  \n",
    "  $||w(t)||^2 \\le ||w(t-1)||^2 + ||x(t-1)||^2 \\le (t-1)R^2 + R^2 = tR^2$ \n",
    "  \n",
    "  where we used the fact that $||x(t-1)||^2 \\le R^2$ by definition of $R$.\n",
    "  \n",
    "1. (e) Apply the results from (b) and (d) we have \n",
    "\n",
    "$\\frac{w^T(t)}{||w(t)||} w^* \\ge \\frac{t\\rho}{||w(t)||} \\ge  \\frac{t\\rho}{\\sqrt{t}R} = \\sqrt{t}\\frac{\\rho}{R}$.\n",
    "\n",
    "\n",
    "Reverse the inequality and square, we have \n",
    "\n",
    "\\begin{align*}\n",
    "t &\\le \\frac{R^2}{\\rho^2} \\frac{\\left(w^T(t)w^*\\right)^T\\left(w^T(t)w^*\\right)}{||w(t)||^2} \\\\\n",
    "&= \\frac{R^2}{\\rho^2} \\frac{w^{*T}w(t)w^T(t)w^*}{||w(t)||^2} \\\\\n",
    "&= \\frac{R^2}{\\rho^2} ||w^*||^2\n",
    "\\end{align*}\n",
    "\n",
    "Or we can use the hint, where \n",
    "$\\frac{w^{*T}w^*}{||w(t)||||w^*||} \\le 1$ because $||w^T(t)w^*|| \\le ||w^T(t)||\\cdot||w^*||$ \n",
    "\n",
    "according to the Cauchy-Schwarz inequality. Then we have \n",
    "\n",
    "$\\sqrt{t}\\frac{\\rho}{R} \\le \\frac{w^{*T}w^*}{||w(t)||} \\le ||w^*||$\n",
    "\n",
    "Move $t$ to the right and square, we obtain the desired inequality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 1.4\n",
    "\n",
    "1. (a) See plot below\n",
    "1. (b) It takes about tens of iterations to find a line that can separate the data, very fast. But the final hypothesis $g$ is not necessarily close the target functio $f$.\n",
    "1. (c) Repeat the experiment in (b) shows similar results\n",
    "1. (d) When $N=100$, the PLA still finds a solution fast in about 100 iterations. It can be much slower on some data.\n",
    "1. (e) $N=1000$, it now takes more about 1000 iterations to find a solution\n",
    "1. (f) $N=1000$ and $d=10$, it usually takes thousands of iterations to find a solution. \n",
    "1. (g) See graph below.\n",
    "1. (h) As $N$ or $d$ increases, it takes more time to find a solution. The maximum number of updates are approximately on the order of $Nd$. As long as the data are separable, it can always find a solution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final correctness:  20 . Total iteration:  15\n",
      "final normalized w: [0.54617486 2.47176685 1.        ]\n",
      "True coeffs:  [2.94108527 2.57829457 1.        ]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### problem 1.4 (a)-(c)\n",
    "lb, ub = -100, 100\n",
    "N, dim = 20, 2 \n",
    "num_grid_points = 2000\n",
    "coeff_lb, coeff_ub = -10, 10\n",
    "eta = 1\n",
    "maxit = 100\n",
    "use_adaline, randomize =False, False\n",
    "_, _, _ = run_perceptron_experiment(N, dim, lb, ub, num_grid_points,\n",
    "                             coeff_lb, coeff_ub, eta, maxit, use_adaline, randomize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final correctness:  1000 . Total iteration:  744\n",
      "final normalized w: [  8.08664678 -12.27446301   1.        ]\n",
      "True coeffs:  [  7.27067669 -12.38345865   1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### problem 1.4 (d)(e)\n",
    "lb, ub = -100, 100\n",
    "N, dim = 1000, 2\n",
    "num_grid_points = 2000\n",
    "coeff_lb, coeff_ub = -10, 10\n",
    "eta = 1\n",
    "maxit = 2000\n",
    "use_adaline, randomize =False, False\n",
    "_, _, _ = run_perceptron_experiment(N, dim, lb, ub, num_grid_points,\n",
    "                             coeff_lb, coeff_ub, eta, maxit, use_adaline, randomize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final correctness:  1000 . Total iteration:  10259\n",
      "final normalized w: [ 1.09458111  1.54263841  0.80743205  1.31244049  1.48918964 -0.82812599\n",
      " -0.76109284 -1.93628042 -0.46584229  1.69249813  1.        ]\n",
      "True coeffs:  [ 0.27029805  1.52209661  0.76978417  1.28982528  1.42754368 -0.78828366\n",
      " -0.7368962  -1.90236382 -0.44707091  1.69270298  1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### problem 1.4 (f)\n",
    "lb, ub = -100, 100\n",
    "N, dim = 1000, 10 \n",
    "num_grid_points = 2000\n",
    "coeff_lb, coeff_ub = -10, 10\n",
    "eta = 1\n",
    "maxit = 50000\n",
    "use_adaline, randomize =False, False\n",
    "_, _, _ = run_perceptron_experiment(N, dim, lb, ub, num_grid_points,\n",
    "                                 coeff_lb, coeff_ub, eta, maxit, use_adaline, randomize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([67., 22.,  7.,  2.,  1.,  0.,  0.,  0.,  0.,  1.]),\n",
       " array([ 1150. ,  6034.9, 10919.8, 15804.7, 20689.6, 25574.5, 30459.4,\n",
       "        35344.3, 40229.2, 45114.1, 49999. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### problem 1.4 (g)\n",
    "lb, ub = -100, 100\n",
    "N, dim = 1000, 10 \n",
    "num_grid_points = 2000\n",
    "coeff_lb, coeff_ub = -10, 10\n",
    "eta = 1\n",
    "maxit = 50000\n",
    "use_adaline, randomize =False, True\n",
    "show_plot = False\n",
    "num_iterations = []\n",
    "for it in range(100):\n",
    "    #print('Working on experiment: ', it)\n",
    "    num_it, _, _ = run_perceptron_experiment(N, dim, lb, ub, num_grid_points,\n",
    "                                     coeff_lb, coeff_ub, eta, maxit, use_adaline, randomize,\n",
    "                                      show_plot)\n",
    "    num_iterations.append(num_it)\n",
    "    \n",
    "plt.hist(num_iterations)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 1.5\n",
    "\n",
    "1. (e) When $\\eta$ is large, with the same number of updates, the Adaline algorithm may have difficulty finding a solution (overshoot), and thus have lower accuracy. When $\\eta$ is small, the algorithm can find a solution and have much better accuracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final correctness:  21 . Total iteration:  999\n",
      "final normalized w: [-0.14994332  0.94531305  1.        ]\n",
      "True coeffs:  [0.6691135  0.08187465 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eta =  100  Accuracy =  78.81\n",
      "final correctness:  23 . Total iteration:  999\n",
      "final normalized w: [-0.14342911  0.99469809  1.        ]\n",
      "True coeffs:  [0.6691135  0.08187465 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eta =  1  Accuracy =  77.53\n",
      "final correctness:  21 . Total iteration:  999\n",
      "final normalized w: [-0.15667765  0.95975058  1.        ]\n",
      "True coeffs:  [0.6691135  0.08187465 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eta =  0.01  Accuracy =  78.42\n",
      "final correctness:  97 . Total iteration:  999\n",
      "final normalized w: [0.08152881 0.04400447 1.        ]\n",
      "True coeffs:  [0.6691135  0.08187465 1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eta =  0.0001  Accuracy =  98.94\n"
     ]
    }
   ],
   "source": [
    "#### problem 1.5 (a)-(d)\n",
    "lb, ub = -100, 100\n",
    "N, dim = 100, 2 \n",
    "num_grid_points = 2000\n",
    "coeff_lb, coeff_ub = -10, 10\n",
    "maxit = 1000\n",
    "use_adaline, randomize = True, True\n",
    "show_plot = True\n",
    "test_N = 10000\n",
    "\n",
    "rns = generate_random_numbers(N, dim, num_grid_points, lb, ub)\n",
    "rn_func = partial(generate_random_numbers, num_grid_points = num_grid_points, lb = lb, ub = ub)\n",
    "coeffs = generate_random_numbers(1, dim+1, num_grid_points, coeff_lb, coeff_ub)\n",
    "norm_coeffs = coeffs.flatten()/coeffs.flatten()[-1]\n",
    "true_func = partial(true_f, coeffs = norm_coeffs)\n",
    "\n",
    "df = generate_df(N, dim, true_func, rn_func)\n",
    "test_df = generate_df(test_N, dim, true_func, rn_func)\n",
    "\n",
    "x1 = np.arange(lb, ub, 0.01)\n",
    "\n",
    "for eta in [100, 1, 0.01, 0.0001]:\n",
    "    norm_g, num_its = perceptron(df.values, dim, maxit, use_adaline, \n",
    "                                 eta, randomize, show_plot)\n",
    "\n",
    "    if show_plot:\n",
    "        print('True coeffs: ', norm_coeffs)\n",
    "        plot_data(x1, df, norm_coeffs, norm_g, lb, ub)\n",
    "\n",
    "    xs = test_df[['x0', 'x1', 'x2']].values\n",
    "    ys = test_df['y'].values\n",
    "    accuracy = 0\n",
    "    for x, y in zip(xs, ys):\n",
    "        prod = np.dot(norm_g.T, x)*y\n",
    "        if prod > 0:\n",
    "            accuracy +=1\n",
    "    print('Eta = ', eta, ' Accuracy = ', accuracy/100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 1.6\n",
    "\n",
    "1. (a) $P(\\nu=0) = (1-\\mu)^{10}$, so \n",
    "  * $P(\\nu = 0) =  0.5987369392383787$ when $\\mu = 0.05$\n",
    "  * $P(\\nu = 0) =  0.0009765625$ when $\\mu = 0.5$\n",
    "  * $P(\\nu = 0) =  1.0239999999999978e-07$ when $\\mu = 0.8$\n",
    "\n",
    "\n",
    "1. (b) We compute the probability that none of the 1000 samples have $\\nu = 0$, i.e. all samples have $\\nu \\gt 0$. For a given sample, we have $P(\\nu \\gt 0) = 1-P(\\nu = 0) = 1-(1-\\mu)^{10}$.  \n",
    "For all 1000 samples to have $\\nu \\gt 0$, the probability is \n",
    "\n",
    "$P(\\cap_{i=1}^{1000} \\nu_{i} \\gt 0) = \\prod_{i=1}^{1000}P(\\nu_i \\gt 0) = \\prod_{i=1}^{1000}[1-(1-\\mu)^{10}] =[1-(1-\\mu)^{10}]^{1000}$\n",
    "\n",
    "So the probability that at least one of the samples has $\\nu = 0$ is: $1-P(\\cap_{i=1}^{1000} \\nu_{i} \\gt 0) = 1-[1-(1-\\mu)^{10}]^{1000}$\n",
    "\n",
    "  * $P = 1$ when $\\mu = 0.05$\n",
    "  * $P = 0.623576201943276$ when $\\mu = 0.5$\n",
    "  * $P = 0.00010239476257623004$ when $\\mu = 0.8$\n",
    "\n",
    "1. (c) For 1000000 samples, we have the probability: $1-P(\\cap_{i=1}^{1000000} \\nu_{i} \\gt 0) = 1-[1-(1-\\mu)^{10}]^{1000000}$\n",
    "\n",
    "  * $P = 1$ when $\\mu = 0.05$\n",
    "  * $P = 1$ when $\\mu = 0.5$\n",
    "  * $P = 0.09733159268316072$ when $\\mu = 0.8$\n",
    "\n",
    "According to Hoeffding inequality, for given tolerance, the upper bound decreases with the number of samples. The probability of the deviation between $\\mu$ and $\\nu'$ (proportion of red marbles in samples) becomes smaller and smaller. So $\\nu'$ is closer to $\\mu$.\n",
    "\n",
    "#### Problem 1.7\n",
    "\n",
    "1. (a) Suppose there are $m$ coins, we compute the probability that none of the coins have $\\nu = 0$, i.e. all coins have $\\nu \\gt 0$. For a given coin, we have $P(\\nu \\gt 0) = 1-P(\\nu = 0) = 1-P[0|N,\\mu] = 1-(1-\\mu)^N$.  \n",
    "For all $m$ coins to have $\\nu \\gt 0$, the probability is \n",
    "\n",
    "$P(\\cap_{i=1}^{m} \\nu_{i} \\gt 0) = \\prod_{i=1}^{m}P(\\nu_i \\gt 0) = \\prod_{i=1}^{m}[1-(1-\\mu)^{N}] =[1-(1-\\mu)^{N}]^{m}$\n",
    "\n",
    "So the probability that at least one of the coins has $\\nu = 0$ is: $1-P(\\cap_{i=1}^{m} \\nu_{i} \\gt 0) = 1-[1-(1-\\mu)^{N}]^{m}$\n",
    "\n",
    "  * $P= 0.5987369392383787$ when $\\mu = 0.05, m = 1$\n",
    "  * $P= 1$ when $\\mu = 0.05, m = 1000$\n",
    "  * $P= 1$ when $\\mu = 0.05, m = 1000000$\n",
    "  \n",
    "  * $P= 1.02400000034919e-07$ when $\\mu = 0.8, m = 1$\n",
    "  * $P= 0.00010239476257623004$ when $\\mu = 0.8, m = 1000$\n",
    "  * $P= 0.09733159268316072$ when $\\mu = 0.8, m = 1000000$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. (b) TODO\n",
    "\n",
    "For $N=6$ and 2 coins with $\\mu = 0.5$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "P[max_{i}|\\nu_i - \\mu| \\gt \\epsilon] &= 1 - P[max_{i}|\\nu_i - \\mu| \\le \\epsilon]\\\\\n",
    "&= 1 - P[|\\nu_1 - \\mu| \\le \\epsilon\\;and\\;|\\nu_2 - \\mu| \\le \\epsilon\\;\\dots\\;and\\;|\\nu_N - \\mu| \\le \\epsilon]\\\\\n",
    "&= 1 - \\prod_{i=1}^{N}P[|\\nu_i - \\mu| \\le \\epsilon]\\\\\n",
    "&= 1 - P[|\\nu_1 - \\mu| \\le \\epsilon]^N\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 1.8 \n",
    "\n",
    "1. (a) Consider random variable $I(t\\ge \\alpha)$, which equals to $1$ when $t\\ge \\alpha$, else $0$. It's clear that for $\\alpha \\gt 0$ and $t$ a non-negative random variable, we have $\\alpha I(t \\ge \\alpha) \\le t$, take expectation on both sides, and since expectation is a monotonically increasing function here $(t \\ge 0)$ , we have \n",
    "\n",
    "\\begin{align*}\n",
    "E[\\alpha I(t \\ge \\alpha)] &\\le E[t]\\\\\n",
    "\\alpha E[I(t \\ge \\alpha)] &\\le E[t]\\\\\n",
    "E[I(t \\ge \\alpha)] &\\le \\frac{E[t]}{\\alpha}\\\\\n",
    "P[t \\ge \\alpha] &\\le \\frac{E[t]}{\\alpha}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "1. (b) Since $(u-\\mu)^2 \\ge 0$, according to problem (a) above, for any $\\alpha \\gt 0$, we have $P[(u - \\mu)^2 \\ge \\alpha] \\le \\frac{E[(u-\\mu)^2]}{\\alpha} = \\frac{\\sigma^2}{\\alpha}$.\n",
    "\n",
    "1. (c) $u = \\frac{1}{N}\\sum_{n=1}^{N}$, this random variable has mean $\\mu$ and variance $\\frac{\\sigma^2}{N}$. Take this into problem (b)'s inequation, we have $P[(u-\\mu)^2 \\ge \\alpha] \\le \\frac{\\sigma^2}{N\\alpha}$.\n",
    "\n",
    "This is the Chebyshev Inequality. Notice that the RHS goes down linearly in $N$, while the counterpart in Hoeffding's Inequality goes down exponentially. \n",
    "\n",
    "#### Problem 1.9\n",
    "\n",
    "1. (a) Consider random variable $I(t\\ge \\alpha)$, which equals to $1$ when $t\\ge \\alpha$, else $0$. It's clear that $e^{st}$ is monotonically increasing in $t$.We have $e^{\\alpha t} I(t \\ge \\alpha) \\le e^{st}$, take expectation on both sides, and since expectation is a monotonically increasing function here $(e^{st} \\ge 0)$ , we have \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "E[e^{\\alpha t} I(t \\ge \\alpha)] &\\le E[e^{st}]\\\\\n",
    "e^{\\alpha t} E[I(t \\ge \\alpha)] &\\le E[e^{st}]\\\\\n",
    "E[I(t \\ge \\alpha)] &\\le e^{-\\alpha t}E[e^{st}]\\\\\n",
    "P[t \\ge \\alpha] &\\le e^{-\\alpha t}T(s)\\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "1. (b) Choose $t = uN$, and use $N\\alpha$ to replace $\\alpha$, according the previous problem, we have\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "P[uN \\ge N\\alpha] &\\le e^{-sN\\alpha}E[e^{suN}]\\\\\n",
    "P[u \\ge \\alpha] &\\le e^{-sN\\alpha}E[e^{s\\sum_{n=1}^{N}u_n}]\\\\\n",
    "P[u \\ge \\alpha] &\\le e^{-sN\\alpha}E[\\prod_{n=1}^{N}e^{su_n}]\\\\\n",
    "P[u \\ge \\alpha] &\\le e^{-sN\\alpha}\\prod_{n=1}^{N}E[e^{su_n}]\\\\\n",
    "P[u \\ge \\alpha] &\\le e^{-sN\\alpha}E[e^{su_n}]^N\\\\\n",
    "P[u \\ge \\alpha] &\\le \\left(e^{-s\\alpha}U(s)\\right)^N\\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "1. (c) $U(s) = E(e^{su_n}) = P(u_n=0)e^0 + P(u_n=1)e^s = \\frac{1}{2}(1+e^s)$, let's minimize $e^{-s\\alpha}U(s)$ by taking its derivative w.r.t. $s$ and let it equal to $0$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "-\\alpha e^{-s\\alpha}\\frac{1}{2}(1+e^s) + e^{-s\\alpha}\\frac{1}{2}e^s &= 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "we conclude that $s = ln{\\frac{\\alpha}{1-\\alpha}}$ since $0 \\lt \\alpha \\lt 1$.\n",
    "\n",
    "1. (d) It's easy to see that $E[u] = \\frac{1}{2}$. Let $\\alpha = E(u) + \\epsilon = \\frac{1}{2} + \\epsilon$, then we have $P[u \\ge E(u) + \\epsilon] \\le (e^{-s\\alpha}U(s))^N$ from previous problem. Since this inequality holds for every $s \\gt 0$, it also holds for $s = ln{\\frac{\\alpha}{1-\\alpha}}$. Take this $s$ into the RHS of the inequality, we have\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "e^{-s\\alpha}U(s) &= e^{-s\\alpha} \\frac{1}{2}(1+e^s)\\\\\n",
    "&= \\frac{1}{2} e^{-\\alpha ln{\\frac{\\alpha}{1-\\alpha}}} (1+e^ {ln{\\frac{\\alpha}{1-\\alpha}}})\\\\\n",
    "&= \\frac{1}{2} \\left(\\frac{1-\\alpha}{\\alpha}\\right)^{\\alpha} (1+\\frac{\\alpha}{1-\\alpha})\\\\\n",
    "&= \\frac{1}{2} \\left(\\frac{1-\\alpha}{\\alpha}\\right)^{\\alpha} \\frac{1}{1-\\alpha}\\\\\n",
    "&= \\frac{1}{2} \\frac{(1-\\alpha)^{\\alpha -1}}{\\alpha^{\\alpha}}\\\\\n",
    "&= \\frac{1}{2} \\frac{(\\frac{1}{2}-\\epsilon)^{\\epsilon -\\frac{1}{2}}}{(\\frac{1}{2}+\\epsilon)^{\\frac{1}{2}+\\epsilon}}\\\\\n",
    "&= \\frac{1}{2}(\\frac{1}{2}-\\epsilon)^{-(\\frac{1}{2}-\\epsilon)}(\\frac{1}{2}+\\epsilon)^{-(\\frac{1}{2}+\\epsilon)}\\\\\n",
    "&= 2^{-\\beta}\\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "where $\\beta = 1 + (\\frac{1}{2}+\\epsilon)log_2{(\\frac{1}{2}+\\epsilon)}+ (\\frac{1}{2}-\\epsilon)log_2{(\\frac{1}{2}-\\epsilon)}$\n",
    "\n",
    "This proves that $P[u \\ge E(u) + \\epsilon] \\le 2^{-\\beta N}$.\n",
    "\n",
    "We now prove that $\\beta \\gt 0$. To prove that $\\beta \\gt 0$, we first prove that $\\beta$ is mononically increasing, then we find its minimum at $\\epsilon = 0$. \n",
    "\n",
    "Take derivative of $\\beta$ with respect to $\\epsilon$, we have \n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial{\\beta}}{\\partial{\\epsilon}} &= log_2{(\\frac{1}{2}+\\epsilon)} + 1 - log_2{(\\frac{1}{2}-\\epsilon)} - 1\\\\\n",
    "&= log_2{(\\frac{1}{2}+\\epsilon)} - log_2{(\\frac{1}{2}-\\epsilon)}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "The derivative is always larger or equal to zero, so $\\beta$ is mononically increasing function. It thus achieves minimum at left point, $\\epsilon=0$, where $\\beta=0$. \n",
    "So we have proved that $\\beta \\gt 0$, since $0 \\lt \\epsilon \\lt \\frac{1}{2}$. hence the bound is exponentially decreasing in $N$.\n",
    "\n",
    "#### Problem 1.10\n",
    "\n",
    "1. (a) $E_{off}(h,f)$ equals to the fraction of odd numbers between $N+1$ and $N+M$ in total $M$ numbers.\n",
    "\n",
    "1. (b) For a function $f$ to generate $\\mathcal{D}$ in a noiseless setting, it means $f(x_i)=y_i$ for $i=1,2,\\dots, N$. They only have freedom to assign various values on the rest points in $\\mathcal{X}$, i.e. $x_{N+1},\\dots,x_{N+M}$. So there are total $2^M$ $f$ that can generate $\\mathcal{D}$.\n",
    "\n",
    "1. (c) Among those $f$ in(b), if they agree with a given $h$ on $M-k$ points, i.e. $E_{off}(h,f)=\\frac{k}{M}$, then each of them need to choose $k$ points from $M$ $x_{N+1},\\dots,x_{N+M}$ to match with $y$, and other $M-k$ points to mismatch with $y$.\n",
    "This has ${M \\choose k}$ combinations.\n",
    "\n",
    "1. (d) The expectation is w.r.t. $f$. Given a hypothesis $h$, for an integer $k$ between $0$ and $M$, from previous problem (c), we know that there are ${M \\choose k}$ number of functions $f$ that satisfy $E_{off}(h,f)=\\frac{k}{M}$. So the probability to get $E_{off}(h,f)=\\frac{k}{M}$ is $\\frac{M \\choose k }{2^M}$. So the expectation is $E_{f}[E_{off}(h,f)] = \\frac{1}{2^M} \\sum_{k=0}^{M} {M \\choose k} \\frac{k}{M}$.\n",
    "\n",
    "1. (e) The above expectation in problem (d) depends on $M$ only, and doesn't depend on $h$ at all (each term in the expectation depends on the number of mismatches between $h$ and $f$, but they are consumed in the expectation). So for any two deterministic algorithms $A_1$ and $A_2$, the expectations will be the same.  \n",
    "\n",
    "We thus proved that in a noiseless setting, for a fixed $\\mathcal{D}$, if all possible $f$ are equally likely, any two deterministic algorithms are equivalent in terms of the expected off-training-set error. \n",
    "\n",
    "#### Problem 1.11\n",
    "\n",
    "* Let the risk to be $r_{1}$ when $y_n=1$ and $r_{-1}$ when $y_n = -1$. The in-sample error $E_{in} = \\sum_{i=1}^{N} max\\left( -h(x_i)y_i,0\\right)r(y_i) = \\sum_{i=1}^{N} max\\left( -h(x_i)y_i,0\\right) [max(y_i,0), max(-y_i,0)] \\cdot [r_1, r_{-1}]^T $\n",
    "\n",
    "#### Problem 1.12\n",
    "\n",
    "1. (a) Take derivative of $E_{in}(h)$ w.r.t. $h$, and let it equal to $0$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial{E_{in}(h)}}{\\partial{h}} &= \\sum_{n=1}^{N}2(h-y_n) \\\\\n",
    "h_{mean} &= \\frac{1}{N} \\sum_{n=1}^{N}y_n\\\\\n",
    "\\end{align*}\n",
    "\n",
    "1. (b) Take derivative of $E_{in}(h)$ w.r.t. $h$, and let it equal to $0$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial{E_{in}(h)}}{\\partial{h}} &= \\sum_{n=1}^{N}sign(h - y_n) \\\\\n",
    "\\end{align*}\n",
    "\n",
    "It's clear, that $h_{med}$ (which is any value for which half the data points are at most $h_{med}$ and half the data points are at least $h_{med}$) will make the derivative to zero, thus minimize the in-sample error.\n",
    "\n",
    "1. (c) If $y_N$ is perturbed to $y_N + \\epsilon$, where $\\epsilon \\to \\infty$, we can see that $h_{mean}$ will increase a lot since $y_N$ contributes to its calculation, but $h_{med}$ can stay the same, because it only requires $h_{med} \\lt y_N$."
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