mlearn

Mathematics of Machine Learning
git clone git://popovic.xyz/mlearn.git
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lecture.ipynb (86753B)


      1 {
      2  "cells": [
      3   {
      4    "cell_type": "code",
      5    "execution_count": 1,
      6    "id": "59c78675",
      7    "metadata": {},
      8    "outputs": [],
      9    "source": [
     10     "import numpy as np\n",
     11     "import matplotlib.pyplot as plt\n",
     12     "import warnings\n",
     13     "warnings.simplefilter('ignore', np.RankWarning)"
     14    ]
     15   },
     16   {
     17    "cell_type": "code",
     18    "execution_count": 19,
     19    "id": "1aad8b4c",
     20    "metadata": {},
     21    "outputs": [],
     22    "source": [
     23     "iterations = 50\n",
     24     "degrees = [3, 4, 7, 20]\n",
     25     "largeNumber = 1000\n",
     26     "\n",
     27     "RademacherPoly = np.ones([iterations, len(degrees)])\n",
     28     "EmpErrorsPoly = np.zeros([iterations, len(degrees)])\n",
     29     "ErrorsPoly = np.ones([iterations, len(degrees)])\n",
     30     "\n",
     31     "#test data\n",
     32     "x_test = np.arange(-1, 1, 1/largeNumber)\n",
     33     "y_test = (x_test - 0.3) * (x_test + 0.15) * x_test * (x_test + 0.75) * (x_test - 0.8)\n",
     34     "\n",
     35     "#precompute training data\n",
     36     "x = np.random.uniform(-1, 1, iterations)\n",
     37     "y = (x - 0.3) * (x + 0.15) * x * (x + 0.75) * (x - 0.8)"
     38    ]
     39   },
     40   {
     41    "cell_type": "code",
     42    "execution_count": 61,
     43    "id": "83c3bea1",
     44    "metadata": {},
     45    "outputs": [],
     46    "source": [
     47     "for m in range(1, iterations):\n",
     48     "    x_short = x[0:m]\n",
     49     "    y_short = y[0:m]\n",
     50     "    \n",
     51     "    for k in range(len(degrees)):\n",
     52     "        # fit polynomials to data\n",
     53     "        p = np.poly1d(np.polyfit(x_short, y_short, degrees[k]))\n",
     54     "        \n",
     55     "        #compute errors\n",
     56     "        y_exp = p(x_test) - y_test\n",
     57     "        y_emp = p(x_short) - y_short\n",
     58     "        EmpErrorsPoly[m, k] = abs(y_emp).mean()\n",
     59     "        ErrorsPoly[m, k] = abs(y_exp).mean()\n",
     60     "        \n",
     61     "        #estimate empirical Rademacher complexities\n",
     62     "        err = 0\n",
     63     "        for it in range(largeNumber):\n",
     64     "            rdm = 2*np.round(np.random.uniform(0, 1, m))-1\n",
     65     "            p = np.poly1d(np.polyfit(x_short, rdm, degrees[k]))\n",
     66     "            err = err + np.dot(p(x_short), rdm)/m\n",
     67     "            \n",
     68     "        RademacherPoly[m, k] = err/largeNumber"
     69    ]
     70   },
     71   {
     72    "cell_type": "code",
     73    "execution_count": 85,
     74    "id": "493d868e",
     75    "metadata": {},
     76    "outputs": [
     77     {
     78      "data": {
     79       "text/plain": [
     80        "Text(0.5, 1.0, 'Expected errors')"
     81       ]
     82      },
     83      "execution_count": 85,
     84      "metadata": {},
     85      "output_type": "execute_result"
     86     },
     87     {
     88      "data": {
     89       "image/png": 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\n",
     90       "text/plain": [
     91        "<Figure size 1296x360 with 3 Axes>"
     92       ]
     93      },
     94      "metadata": {
     95       "needs_background": "light"
     96      },
     97      "output_type": "display_data"
     98     }
     99    ],
    100    "source": [
    101     "fig, ax = plt.subplots(1, 3, figsize= [18, 5])\n",
    102     "\n",
    103     "ax[0].plot(np.arange(iterations), RademacherPoly)\n",
    104     "ax[0].legend([f'Degree {s}' for s in degrees], loc='best')\n",
    105     "ax[0].set_title('Rademacher Complexities', c='white')\n",
    106     "\n",
    107     "ax[1].semilogy(np.arange(iterations), EmpErrorsPoly)\n",
    108     "ax[1].legend([f'Degree {s}' for s in degrees], loc='best')\n",
    109     "ax[1].set_title('Empirical Erros', c='white')\n",
    110     "\n",
    111     "ax[2].semilogy(np.arange(iterations), ErrorsPoly)\n",
    112     "ax[2].legend([f'Degree {s}' for s in degrees], loc='best')\n",
    113     "ax[2].set_title('Expected errors', c='white')"
    114    ]
    115   },
    116   {
    117    "cell_type": "code",
    118    "execution_count": 31,
    119    "id": "fcc108f0",
    120    "metadata": {},
    121    "outputs": [],
    122    "source": [
    123     "n = 10\n",
    124     "d = 4 \n",
    125     "ω = lambda i, j : np.exp(-2*np.pi *1j/n * (i-1) * (j-1))\n",
    126     "H = np.zeros([n, d], dtype='complex')\n",
    127     "for i in range(n):\n",
    128     "    for j in range(d):\n",
    129     "        H[i, j] = 1/np.sqrt(n) * ω(i, j)"
    130    ]
    131   },
    132   {
    133    "cell_type": "code",
    134    "execution_count": 33,
    135    "id": "1de22922",
    136    "metadata": {},
    137    "outputs": [
    138     {
    139      "data": {
    140       "text/plain": [
    141        "array([[ 1.+0.j, -0.-0.j,  0.-0.j,  0.-0.j],\n",
    142        "       [-0.+0.j,  1.+0.j, -0.-0.j, -0.-0.j],\n",
    143        "       [ 0.+0.j, -0.+0.j,  1.+0.j, -0.-0.j],\n",
    144        "       [ 0.+0.j, -0.+0.j, -0.+0.j,  1.+0.j]])"
    145       ]
    146      },
    147      "execution_count": 33,
    148      "metadata": {},
    149      "output_type": "execute_result"
    150     }
    151    ],
    152    "source": [
    153     "np.round((np.conjugate(H).T @ H), 1)"
    154    ]
    155   },
    156   {
    157    "cell_type": "code",
    158    "execution_count": null,
    159    "id": "87ef752d",
    160    "metadata": {},
    161    "outputs": [],
    162    "source": []
    163   },
    164   {
    165    "cell_type": "code",
    166    "execution_count": null,
    167    "id": "3797e92d",
    168    "metadata": {},
    169    "outputs": [],
    170    "source": []
    171   }
    172  ],
    173  "metadata": {
    174   "kernelspec": {
    175    "display_name": "Python 3 (ipykernel)",
    176    "language": "python",
    177    "name": "python3"
    178   },
    179   "language_info": {
    180    "codemirror_mode": {
    181     "name": "ipython",
    182     "version": 3
    183    },
    184    "file_extension": ".py",
    185    "mimetype": "text/x-python",
    186    "name": "python",
    187    "nbconvert_exporter": "python",
    188    "pygments_lexer": "ipython3",
    189    "version": "3.10.4"
    190   }
    191  },
    192  "nbformat": 4,
    193  "nbformat_minor": 5
    194 }