hw4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "### DS 4420 - Homework 4\n",
    "Gavin Wainwright"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Question 1"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "outputs": [],
   "source": [
    "# Part 1\n",
    "X = np.genfromtxt('complex_distribution.csv')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gaussian_kernel(x, x_i, bandwidth):\n",
    "    return (1 / (bandwidth * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x - x_i) / bandwidth) ** 2)\n",
    "\n",
    "def kde(x, data, bandwidth):\n",
    "    return np.sum(gaussian_kernel(x, data[:, None], bandwidth), axis=0) / data.size\n",
    "\n",
    "# Compute KDE\n",
    "n_samples = 1000\n",
    "x = np.linspace(min(X), max(X), n_samples)\n",
    "bandwidth = 0.8\n",
    "density = kde(x, X, bandwidth)\n",
    "\n",
    "plt.plot(x, density, label='KDE')\n",
    "plt.title('Kernel Density Estimation')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "outputs": [],
   "source": [
    "# Part 2\n",
    "def rejection_sampling(kde_func, data, bandwidth, n_samples):\n",
    "    samples = []\n",
    "    max_density = max(kde_func(x, data, bandwidth))\n",
    "    while len(samples) < n_samples:\n",
    "        z = np.random.uniform(min(data), max(data))\n",
    "        u = np.random.uniform(0, max_density)\n",
    "        if u <= kde_func(z, data, bandwidth):\n",
    "            samples.append(z)\n",
    "\n",
    "    return np.array(samples)\n",
    "\n",
    "X_hat = rejection_sampling(kde, X, bandwidth, n_samples)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "outputs": [],
   "source": [
    "def kde_sampling(data, bandwidth, n_samples):\n",
    "    indices = np.random.choice(len(data), size=n_samples)\n",
    "    samples = data[indices]\n",
    "    noise = np.random.normal(0, bandwidth, size=n_samples)\n",
    "    return samples + noise\n",
    "\n",
    "X_bar = kde_sampling(X, bandwidth, n_samples)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1800x600 with 3 Axes>",
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(18, 6))\n",
    "\n",
    "# Original Data\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.hist(X, bins=30, alpha=0.7, label='Original X')\n",
    "plt.legend()\n",
    "\n",
    "# Rejection Sampling\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.hist(X_hat, bins=30, alpha=0.7, color='red', label='Rejection Samples X̂')\n",
    "plt.legend()\n",
    "\n",
    "# KDE Sampling\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.hist(X_bar, bins=30, alpha=0.7, color='green', label='KDE Samples X̄')\n",
    "plt.legend()\n",
    "\n",
    "plt.title('Comparison of X, X̂, and X̄')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original X\n",
      "\n",
      "E[x]: 10.814000119911924\n",
      "E[(x - μ^2)]: 49.40961360042826\n",
      "E[3x + 2]: 34.44200035973577\n",
      "E[x^2 - 5x]: 112.28221159432371\n",
      "E[2e^x + 1]: 258969297984.54385\n"
     ]
    }
   ],
   "source": [
    "# Part 3\n",
    "print('Original X\\n')\n",
    "print(f'E[x]: {np.mean(X)}')\n",
    "print(f'E[(x - μ^2)]: {np.var(X)}')\n",
    "print(f'E[3x + 2]: {np.mean(3*X + 2)}')\n",
    "print(f'E[x^2 - 5x]: {np.mean(X**2 - 5*X)}')\n",
    "print(f'E[2e^x + 1]: {np.mean(2 * np.exp(X) + 1)}')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rejection Samples X̂\n",
      "\n",
      "E[x]: 11.204183160158674\n",
      "E[(x - μ^2)]: 50.564186341849556\n",
      "E[3x + 2]: 35.61254948047603\n",
      "E[x^2 - 5x]: 120.07699082743942\n",
      "E[2e^x + 1]: 171185077499.10504\n"
     ]
    }
   ],
   "source": [
    "print('Rejection Samples X̂\\n')\n",
    "print(f'E[x]: {np.mean(X_bar)}')\n",
    "print(f'E[(x - μ^2)]: {np.var(X_bar)}')\n",
    "print(f'E[3x + 2]: {np.mean(3*X_bar + 2)}')\n",
    "print(f'E[x^2 - 5x]: {np.mean(X_bar**2 - 5*X_bar)}')\n",
    "print(f'E[2e^x + 1]: {np.mean(2 * np.exp(X_bar) + 1)}')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KDE Samples X̄\n",
      "\n",
      "E[x]: 10.449282595727611\n",
      "E[(x - μ^2)]: 54.06075268761185\n",
      "E[3x + 2]: 33.34784778718283\n",
      "E[x^2 - 5x]: 111.00184647434973\n",
      "E[2e^x + 1]: 16949254245.665464\n"
     ]
    }
   ],
   "source": [
    "print('KDE Samples X̄\\n')\n",
    "print(f'E[x]: {np.mean(X_hat)}')\n",
    "print(f'E[(x - μ^2)]: {np.var(X_hat)}')\n",
    "print(f'E[3x + 2]: {np.mean(3*X_hat + 2)}')\n",
    "print(f'E[x^2 - 5x]: {np.mean(X_hat**2 - 5*X_hat)}')\n",
    "print(f'E[2e^x + 1]: {np.mean(2 * np.exp(X_hat) + 1)}')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Question 2"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2975505554642717\n"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    return np.log(x + 1)\n",
    "\n",
    "x_samples = np.random.uniform(0, 2, 100000)\n",
    "\n",
    "f_values = f(x_samples)\n",
    "\n",
    "integral = 2 * np.mean(f_values)\n",
    "\n",
    "print(integral)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Question 3"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6669491526721298\n"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    return x**2 - x + 1\n",
    "\n",
    "x_samples = np.random.uniform(0, 1, 100000)\n",
    "\n",
    "f_values = f(x_samples)\n",
    "\n",
    "integral = 2 * np.mean(f_values)\n",
    "\n",
    "print(integral)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
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