W02_KiK_zrodla_kanaly.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mrospond/kik/blob/main/W02_KiK_zrodla_kanaly.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Potrzebne biblioteki...\n",
        "\n",
        "# Obliczenia matematyczne, dla nas głównie logarytm\n",
        "import math\n",
        "\n",
        "# Generowanie liczb losowych\n",
        "import random\n",
        "\n",
        "# Praca z wektorami i macierzami\n",
        "import numpy as np\n",
        "\n",
        "# Rysowanie standardowych wykresów\n",
        "import matplotlib.pyplot as plt\n",
        "# Obróbka statystyczna przy rysowaniu wykresów i formatowaniu ich wyglądu\n",
        "import seaborn as sns\n",
        "sns.set()\n",
        "\n",
        "# Obliczenia probabilistyczne\n",
        "## Dowolny rozkład dyskretny\n",
        "from scipy.stats import rv_discrete\n",
        "## Entropia Shannona i dywergencja Kullbacka-Leiblera\n",
        "from scipy.stats import entropy\n",
        "## Estymacja jądrowa (ang. kernel density estimation) rozkładu prawdopodobieństwa z próbek\n",
        "from scipy.stats import gaussian_kde\n",
        "\n",
        "# Obsługa plików\n",
        "## Pobieranie\n",
        "import requests\n",
        "## Rozpakowywanie\n",
        "import zipfile\n",
        "\n",
        "# Obróbka języka naturalnego: generowanie n-gramów i rozkładów warunkowych\n",
        "import string\n",
        "## Zliczanie statystyk językowych\n",
        "import nltk\n",
        "from nltk import ConditionalFreqDist"
      ],
      "metadata": {
        "id": "e9_HTJHJfmD2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Badanie języka z użyciem entropii"
      ],
      "metadata": {
        "id": "UKAinhr_mZEW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Użyjemy korpusu języka angielskiego (przykładowy tekst)\n",
        "#@markdown Alice = Alicja w Krainie Czarów\n",
        "\n",
        "url = 'http://corpus.canterbury.ac.nz/resources/cantrbry.zip'\n",
        "r = requests.get(url, allow_redirects=True)\n",
        "\n",
        "open('cantrbry.zip', 'wb').write(r.content)\n",
        "with zipfile.ZipFile('cantrbry.zip', 'r') as zip_ref:\n",
        "    zip_ref.extractall('cantrbry')\n",
        "\n",
        "with open('cantrbry/alice29.txt', encoding='utf8') as f:\n",
        "    text = f.read()\n",
        "f.close()\n",
        "\n",
        "text = text.upper()\n",
        "print(text[:1000])"
      ],
      "metadata": {
        "id": "wDFvC3Wh38YG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b58c1de1-c8b6-46d2-b5cb-f8dfe3cb6f0d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\n",
            "\n",
            "                ALICE'S ADVENTURES IN WONDERLAND\n",
            "\n",
            "                          LEWIS CARROLL\n",
            "\n",
            "               THE MILLENNIUM FULCRUM EDITION 2.9\n",
            "\n",
            "\n",
            "\n",
            "\n",
            "                            CHAPTER I\n",
            "\n",
            "                      DOWN THE RABBIT-HOLE\n",
            "\n",
            "\n",
            "  ALICE WAS BEGINNING TO GET VERY TIRED OF SITTING BY HER SISTER\n",
            "ON THE BANK, AND OF HAVING NOTHING TO DO:  ONCE OR TWICE SHE HAD\n",
            "PEEPED INTO THE BOOK HER SISTER WAS READING, BUT IT HAD NO\n",
            "PICTURES OR CONVERSATIONS IN IT, `AND WHAT IS THE USE OF A BOOK,'\n",
            "THOUGHT ALICE `WITHOUT PICTURES OR CONVERSATION?'\n",
            "\n",
            "  SO SHE WAS CONSIDERING IN HER OWN MIND (AS WELL AS SHE COULD,\n",
            "FOR THE HOT DAY MADE HER FEEL VERY SLEEPY AND STUPID), WHETHER\n",
            "THE PLEASURE OF MAKING A DAISY-CHAIN WOULD BE WORTH THE TROUBLE\n",
            "OF GETTING UP AND PICKING THE DAISIES, WHEN SUDDENLY A WHITE\n",
            "RABBIT WITH PINK EYES RAN CLOSE BY HER.\n",
            "\n",
            "  THERE WAS NOTHING SO VERY REMARKABLE IN THAT; NOR DID ALICE\n",
            "THINK IT SO VERY MUCH OUT OF THE WAY TO HEAR THE RABBIT SAY TO\n",
            "ITSELF, `OH DEAR!  OH DEAR!  I SHALL BE LAT\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@markdown Policzymy na tej książce statystkę liter w języku angielskim\n",
        "\n",
        "# Ograniczamy się do liter, bo w tekście występują też jakieś kropki, spacje itd.\n",
        "Vocabulary = list(string.ascii_uppercase) \n",
        "print(Vocabulary)\n",
        "\n",
        "# Słownik częstotliwości występowania liter w języku angielskim\n",
        "freq = dict(zip(Vocabulary,[0 for _ in range(len(Vocabulary))]))\n",
        "how_many = 0\n",
        "\n",
        "for char in text:\n",
        "  if char in freq:\n",
        "    how_many += 1\n",
        "    freq[char] += 1\n",
        "\n",
        "for elem in freq:\n",
        "  freq[elem] /= how_many\n",
        "\n",
        "print(f\"W korpusie Alicja mamy {how_many} liter.\")"
      ],
      "metadata": {
        "id": "gRxqjt3C4Njn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "766fb9d4-2d8a-4138-ee8d-052ac5837544"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']\n",
            "W korpusie Alicja mamy 107667 liter.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@markdown Sprawdźmy, jak wygląda statystyka\n",
        "\n",
        "ile = len(Vocabulary)\n",
        "r = np.arange(ile)\n",
        "szerokosc = 0.45\n",
        "\n",
        "plt.figure(figsize=(10,10))\n",
        "plt.bar(Vocabulary, freq.values(), \n",
        "        width = szerokosc, edgecolor = 'black',\n",
        "        label='Alicja')\n",
        "\n",
        "plt.title('Częstotliwości występowania liter w języku angielskim na podstawie Alicji')\n",
        "plt.xlabel('Litery')\n",
        "plt.xticks(r, Vocabulary)\n",
        "plt.ylabel('Częstotliwości / prawdopodobieństwo')\n",
        "plt.grid(linestyle='--')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "prawdopodobienstwa = list(freq.values())\n",
        "print(f\"Entropia na podstawie Alicji: {entropy(prawdopodobienstwa,base=2)} bitów/literę, \\nprzy potencjalnie maksymalnej entropii dla takiego alfabetu: {math.log2(len(prawdopodobienstwa))} bitów/literę.\")"
      ],
      "metadata": {
        "id": "A9iRv5yI5BCd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 662
        },
        "outputId": "ec8cd6c9-b3a0-4139-e722-0098b18a1fcc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Entropia na podstawie Alicji: 4.160930615023794 bitów/literę, \n",
            "przy potencjalnie maksymalnej entropii dla takiego alfabetu: 4.700439718141092 bitów/literę.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Widać, że nawet pół bita to może być dosyć dużo!"
      ],
      "metadata": {
        "id": "_E4RcTBU6FBE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Entropia jest niższa niż dla równomiernego rozkładu częstotliwości liter:\n",
        "*   Co to znaczy?\n",
        "*   Czy można jeszcze dokładniej oszacować entropię języka angielskiego?\n",
        "\n",
        "Swoją drogą, **jak takie dane można wykorzystać w kryptoanalizie**?"
      ],
      "metadata": {
        "id": "iFDhxl-GIMhb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Na ile wytworzony rozkład coś nam mówi o języku Alicji?\n",
        "\n",
        "ile = 30 #@param {type: \"slider\", min:10, max:100, step:20}\n",
        "\n",
        "liczby = list(range(len(Vocabulary)))\n",
        "custm = rv_discrete(values=(liczby, prawdopodobienstwa))\n",
        "\n",
        "probka_liczby = custm.rvs(size=ile)\n",
        "alfabet = dict(zip(liczby,Vocabulary))\n",
        "probka = [alfabet[key] for key in probka_liczby]\n",
        "\n",
        "print(''.join(probka))"
      ],
      "metadata": {
        "id": "aASLazE2HkUb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1807eaee-ef55-4136-da6a-2de556ee7833"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "IEUIEAISUPEUERDTERNLWCCTHGFATL\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Co może bardziej przypominać język? Normalnie znamy przecież kontekst (na tym też opiera się NLP z użyciem UM)..."
      ],
      "metadata": {
        "id": "TuvuHUALKGPv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Wytworzymy częstotliwości względne dla liter\n",
        "#@markdown * Prawdopodobieństwa warunkowe typu $\\Pr\\{a|b\\}$: jakie jest prawdopodobieństwo, że bo literze $b$ wystąpi litera $a$?\n",
        "#@markdown * Nie będziemy tego już robić na piechotę, wykorzystamy narzędzia do obróbki języka\n",
        "#@markdown * Tokenizacja = wydzielenie podstawowych obiektów językowych (tu akurat: liter), ważne w NLP w przypadku UM\n",
        "#@markdown * Okno przesuwne zbiera nam tzw. $n$-gramy (tutaj $n=2$ generuje bigramy, bo sprawdzamy jakie jest prawdopodobieństwo, że jedna litera wystąpi po drugiej)\n",
        "\n",
        "# Bierzemy tylko litery (tokenizacja na poziomie znaków)\n",
        "filtered_text = [token for token in text if token in Vocabulary]\n",
        "\n",
        "# Obliczamy częstotliwości względne na podstawie bigramów: zestawów po dwie kolejne litery (np. `ba`)\n",
        "cfd = ConditionalFreqDist(nltk.bigrams(filtered_text))\n",
        "\n",
        "print(\"Przykładowe bigramy:\")\n",
        "for n, bigram in enumerate(nltk.bigrams(filtered_text)):\n",
        "  if n >=0 and n<=15:\n",
        "    print(bigram)"
      ],
      "metadata": {
        "id": "znDjhGByKWEk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "607b9284-c59b-4a19-8f2f-c48634441d40"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Przykładowe bigramy:\n",
            "('A', 'L')\n",
            "('L', 'I')\n",
            "('I', 'C')\n",
            "('C', 'E')\n",
            "('E', 'S')\n",
            "('S', 'A')\n",
            "('A', 'D')\n",
            "('D', 'V')\n",
            "('V', 'E')\n",
            "('E', 'N')\n",
            "('N', 'T')\n",
            "('T', 'U')\n",
            "('U', 'R')\n",
            "('R', 'E')\n",
            "('E', 'S')\n",
            "('S', 'I')\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@markdown * To jest dużo większa statystyka niż dla pojedynczych liter!\n",
        "#@markdown * Dla pojedynczych liter był wykres (liniowy), tu jest cała tablica (można byłoby zwizualizować na wykresie 3D)\n",
        "\n",
        "print(cfd.tabulate())"
      ],
      "metadata": {
        "id": "iD9oN7h5MeGT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "95c9421b-afed-488b-9946-278005cb9606"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "     A    B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z \n",
            "A    9  251  208  477    0   93  203   48  719   15  130 1047  232 1621    6  152    3  729  964 1221   78  201  111    4  260    5 \n",
            "B   81   66    0    1  524    0    0    1  111    7    0  105    1    0  203    0    0   59   27    9  204    0    0    0   75    0 \n",
            "C  317    1   16    0  704    0    0  449   30    0  177   66    0    0  341    0    0  110    1   74  103    0    0    0    8    0 \n",
            "D  542  163   57  120  472   91   86  181  451   15    8  123   60  184  595   47   14  137  340  841  100   48  155    0  100    0 \n",
            "E 1252  240  439 1204  568  265  306  347  383   47  122  608  508 1052  367  285   98 1991 1179 1004   41  230  601  104  314   14 \n",
            "F  195   23   40    7  163  133   12   64  250    1    3   53   25   15  342   12    2   94   52  320  108    6   34    0   46    0 \n",
            "G  385   37   13   26  297   28   23  371  175    4    1   77   27   30  293   19    6  220  151  203   63   15   46    0   17    1 \n",
            "H 1276   11   18   19 3788   14    7   71  838    2    1   14   26    8  613   10    0   83   70  341   60    2   36    0   64    0 \n",
            "I   50   27  638  755  198  166  223   34    9    0  112  348  304 2038  183   21    2  215  642 1359    7   95   50    9    0   26 \n",
            "J    6    0    1    0   20    0    0    0    0    0    0    0    0    0   17    0    0    0    0    0  102    0    0    0    0    0 \n",
            "K   77    7    4    3  366    9    1   17  245    2    1   25    9  147   30    4    1    5   36  118    8    4   16    0   23    0 \n",
            "L  374   37   25  352  745  163   12   35  915    4   61  691   32    8  363   24    1   26  130  161   20   18   49    0  466    1 \n",
            "M  375   73    6    7  585   20    8   15  201    0    1    2   19   29  340   77    2    5   60   58  128    2   20    0   74    0 \n",
            "N  449   57  216 1293  581   64 1156  105  349    7  121  115   35   73  620   16    9   34  292 1052   70   25  124   17  133    0 \n",
            "O  137  122  135  147   68  659   86  174  186    1  218  216  345 1077  492  129   14  699  297  618 1570   95  596   11   47    2 \n",
            "P  166   18    5    4  287    1    0   65  157    0    1  181    3    2  199  115    0   88   42   89   70    4    8    0   17    0 \n",
            "Q    0    0    0    0    0    0    0    1    0    0    0    0    0    0    0    0    0    0    0    0  208    0    0    0    0    0 \n",
            "R  481   37   99  211 1187   75   79  153  474    6   69   95  117  112  421  102   10  100  514  467   88   23  106    3  404    0 \n",
            "S 1004   66   95   36  835   69   55  973  445    9   51  116   89  140  533  123   22   33  433  942  175   33  175    0   43    0 \n",
            "T  682  133  112   94  794   81   51 3666  823   12   23  368  117   51 1255   57   19  196  581  850  234   22  339    0  124    0 \n",
            "U   49   36  199   84  168   14  184   15   88    5   47  349   85  251   17  215    0  522  461  615    1    7   39    0    3   14 \n",
            "V   20    0    0    0  698    0    0    0   60    0    0    0    0    0   62    0    0    0    0    1    1    0    0    0    3    0 \n",
            "W  628    7   10   24  351   12    1  528  406    0    1   41   15  144  282    5    2   35   54   64    6    5   42    0   10    1 \n",
            "X   15    0   13    0   24    0    0    1   25    0    0    0    0    0    4   23    0    0    0   42    0    0    1    0    0    0 \n",
            "Y  209   62   48   67  115   43   35   58  161    9   10   59   58   31  563   86    4   52  169  235   23   10  126    0   31    0 \n",
            "Z    7    0    0    0   31    0    0    0   10    0    0   14    0    0    0    0    0    0    0    0    0    0    0    0    2   14 \n",
            "None\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "W powyższej tabeli: warunki w wierszach - czyli np. E po A występuje bardzo często, ale A po E w ogóle..."
      ],
      "metadata": {
        "id": "E2aJ5iWgi7FU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Przerabiamy na rozkład prawdopodobieństwa\n",
        "\n",
        "cpd = nltk.ConditionalProbDist(cfd, nltk.MLEProbDist)\n",
        "\n",
        "#@markdown Wypiszemy dla dwóch liter\n",
        "jedna = \"A\" #@param {type:\"string\"}\n",
        "druga = \"E\" #@param {type:\"string\"}\n",
        "\n",
        "litery = [jedna, druga]\n",
        "\n",
        "for condition in cfd.conditions():\n",
        "  if condition in litery:\n",
        "    print(f\"\\nPo {condition}:\")\n",
        "    for event in cfd[condition]:\n",
        "        probability = cpd[condition].prob(event)\n",
        "        print(f\"\\tnastępuje {event}: {probability:.4f}\")"
      ],
      "metadata": {
        "id": "15JHXm3BOzpH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d9b9c8ea-8ec8-48ab-9da2-635d29f2ebd0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Po A:\n",
            "\tnastępuje N: 0.1845\n",
            "\tnastępuje T: 0.1390\n",
            "\tnastępuje L: 0.1192\n",
            "\tnastępuje S: 0.1097\n",
            "\tnastępuje R: 0.0830\n",
            "\tnastępuje I: 0.0818\n",
            "\tnastępuje D: 0.0543\n",
            "\tnastępuje Y: 0.0296\n",
            "\tnastępuje B: 0.0286\n",
            "\tnastępuje M: 0.0264\n",
            "\tnastępuje C: 0.0237\n",
            "\tnastępuje G: 0.0231\n",
            "\tnastępuje V: 0.0229\n",
            "\tnastępuje P: 0.0173\n",
            "\tnastępuje K: 0.0148\n",
            "\tnastępuje W: 0.0126\n",
            "\tnastępuje F: 0.0106\n",
            "\tnastępuje U: 0.0089\n",
            "\tnastępuje H: 0.0055\n",
            "\tnastępuje J: 0.0017\n",
            "\tnastępuje A: 0.0010\n",
            "\tnastępuje O: 0.0007\n",
            "\tnastępuje Z: 0.0006\n",
            "\tnastępuje X: 0.0005\n",
            "\tnastępuje Q: 0.0003\n",
            "\n",
            "Po E:\n",
            "\tnastępuje R: 0.1467\n",
            "\tnastępuje A: 0.0923\n",
            "\tnastępuje D: 0.0887\n",
            "\tnastępuje S: 0.0869\n",
            "\tnastępuje N: 0.0775\n",
            "\tnastępuje T: 0.0740\n",
            "\tnastępuje L: 0.0448\n",
            "\tnastępuje W: 0.0443\n",
            "\tnastępuje E: 0.0419\n",
            "\tnastępuje M: 0.0374\n",
            "\tnastępuje C: 0.0324\n",
            "\tnastępuje I: 0.0282\n",
            "\tnastępuje O: 0.0270\n",
            "\tnastępuje H: 0.0256\n",
            "\tnastępuje Y: 0.0231\n",
            "\tnastępuje G: 0.0226\n",
            "\tnastępuje P: 0.0210\n",
            "\tnastępuje F: 0.0195\n",
            "\tnastępuje B: 0.0177\n",
            "\tnastępuje V: 0.0170\n",
            "\tnastępuje K: 0.0090\n",
            "\tnastępuje X: 0.0077\n",
            "\tnastępuje Q: 0.0072\n",
            "\tnastępuje J: 0.0035\n",
            "\tnastępuje U: 0.0030\n",
            "\tnastępuje Z: 0.0010\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Próbkujemy dla takiego rozkładu warunkowego\n",
        "\n",
        "# Długość\n",
        "ile = 100 #@param {type:\"integer\"}\n",
        "\n",
        "# Start\n",
        "start_bigram = (\"A\",\"L\")\n",
        "\n",
        "# Wygenerowany tekst\n",
        "generated_text = [start_bigram[0], start_bigram[1]]\n",
        "\n",
        "for i in range(ile):\n",
        "    # poprzednia litera\n",
        "    last = generated_text[-1]\n",
        "    # częstotliwości warunkowane ostatnią literą\n",
        "    bigram_cpd = cpd[last]\n",
        "    # losujemy z takiego prawdopodobieństwa następną literę\n",
        "    next = random.choices(list(bigram_cpd.samples()), weights=list(bigram_cpd.freqdist().values()))[0]\n",
        "    # dodajemy nową literę\n",
        "    generated_text.append(next)\n",
        "\n",
        "generated_text_str = ''.join(generated_text)\n",
        "print(generated_text_str)"
      ],
      "metadata": {
        "id": "zimkm01ic_fX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2ff93d1f-b125-491d-c083-db5bcf1e0370"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ALLYOUSHEDLINECHEDWOCANGOUHTANWASTASOOUMEWINIFSCESLYIRESENFINASAYWHIGTHIEPEQUCRLCOUREYORISHITTSTSMOATHASAMBEHGOWINELLESAITASANOENTHAINTHEENEROSOVEADBEDBBYPLILEJULEYHTTTMBLEOUERSHEXEEDANOWEYOUTHEHESOOOLSHOULEHALIKICERUMUCELENHAITANGHEDSTTYJUISYTHEDOMYITHAISHANISGINGOLSINDTHITHOPLLIGEFSAPEDBOMTHERARLINDINLATHEATTIERMAMUTOFLOALOWIKNDATLONDHICOREORECIEWOINGANICKANOULLKFOOUDSARHEQUCLYGAMAYDWHTECARTAINOUCLESTOUASHEEETTIDTHERFITRTHECEMIRUSWHEYARALEREPPEHYOUNDNETHEQUKETHILLAIFPINSHALINETEVEPAITWADHLINGSITEWENDPIPILOULTYTHEAPICEALITAYITHANSOUTHALTHEETHENCHEDTHASHEMACOUTHTHACOUCREQUTILYSHENDOUTHEDOPEFITOGWOMULITAYMALITHEAICANCONGSTHICRNORHETTTDOUREWHSWECKEYOKIGTSITLINOFONGSOMOMININDTFOINDOULLLAISTHASSALOINDINDNGHAISQUNGIKITHERALTQUNCHEREBOOWOWHEDSANLLERATHELIKISATOSTHTHERLSHEGGODITIETHIMSTHOFUNOURSHANHEWHRMWYORPLITHEWERGTAVEBUPONDOURERECEAYORTHYMAWARUNSINDSTOUSWECOFTHSMULOSCIERESONINATOMBEMETTHEWISOTYBECEYINDOUNKINTJEOOUPOUASANDDENSIOERUNINTUROGTTHTHASARYATHERIDIDHELTHARIRESOUSFYGOTLLLLLAICKESATSE\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown * A teraz jeszcze dokładniej: statystyki typu $\\Pr\\{a|b,c\\}$\n",
        "#@markdown * Okno przesuwne zbiera nam trigramy (tutaj $n=3$, bo sprawdzamy jakie jest prawdopodobieństwo, że jedna litera wystąpi po dwóch literach)\n",
        "\n",
        "# Długość\n",
        "ile = 100 #@param {type:\"integer\"}\n",
        "\n",
        "trigrams = list(nltk.trigrams(filtered_text))\n",
        "\n",
        "cfd = nltk.ConditionalFreqDist(((w1, w2), w3) for w1, w2, w3 in trigrams)\n",
        "cpd = nltk.ConditionalProbDist(cfd, nltk.MLEProbDist)\n",
        "\n",
        "start_trigram = (\"A\", \"L\", \"I\")\n",
        "generated_text = [start_trigram[0], start_trigram[1], start_trigram[2]]\n",
        "\n",
        "for i in range(ile):\n",
        "    last_two_words = (generated_text[-2], generated_text[-1])\n",
        "    trigram_cpd = cpd[last_two_words]\n",
        "    next_word = trigram_cpd.generate()\n",
        "    generated_text.append(next_word)\n",
        "\n",
        "generated_text_str = ''.join(generated_text)\n",
        "print(generated_text_str)"
      ],
      "metadata": {
        "id": "AgLIejyTeyj8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "471ff990-2a01-4566-b080-85e36c1e34d4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "ALITGOFHJUDLYCLEABOUWOLDDERSHURTINKYLOWNOSHEFONTANDHANDTHEWHEMENOTMALOVERSHERTHERPROUTWHADIFANDSAIDORGE\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Lepiej jak zachowamy spacje i inne znaki \n",
        "#@markdown Najpierw zbierzemy statystyki, czyli oszacowania:\n",
        "#@markdown * Na podstawie unigramów: $\\Pr\\{.\\}$\n",
        "#@markdown * Na podstawie unigramów: $\\Pr\\{a|.\\}$\n",
        "#@markdown * Na podstawie unigramów: $\\Pr\\{a|b.\\}$\n",
        "\n",
        "unigrams = list(\"\".join(text))\n",
        "bigrams = list(nltk.bigrams(text))\n",
        "trigrams = list(nltk.trigrams(text))\n",
        "\n",
        "freq_dist = nltk.FreqDist(unigrams)\n",
        "total_letters = len(unigrams)\n",
        "probabilities = {letter: freq / total_letters for letter, freq in freq_dist.items()}\n",
        "\n",
        "# print the top 10 most probable letters\n",
        "print(\"Dziesięć najczęstszych znaków:\")\n",
        "for letter, probability in sorted(probabilities.items(), key=lambda x: x[1], reverse=True)[:10]:\n",
        "    print(f\"{letter}: {probability:.3f}\")\n",
        "\n",
        "cfd2 = nltk.ConditionalFreqDist(bigrams)\n",
        "cpd2 = nltk.ConditionalProbDist(cfd2, nltk.MLEProbDist)\n",
        "\n",
        "cfd3 = nltk.ConditionalFreqDist(((w1, w2), w3) for w1, w2, w3 in trigrams)\n",
        "cpd3 = nltk.ConditionalProbDist(cfd3, nltk.MLEProbDist)\n",
        "\n",
        "start_digram = (\"A\", \"L\")\n",
        "start_trigram = (\"A\", \"L\", \"I\")\n",
        "\n",
        "generated_text2 = [start_trigram[0], start_trigram[1]]\n",
        "generated_text3 = [start_trigram[0], start_trigram[1], start_trigram[2]]\n",
        "\n",
        "for i in range(ile):\n",
        "    last_word = (generated_text3[-1])\n",
        "    trigram_cpd2 = cpd2[last_word]\n",
        "    next_word2 = trigram_cpd2.generate()\n",
        "    generated_text2.append(next_word2)\n",
        "\n",
        "    last_two_words = (generated_text3[-2], generated_text3[-1])\n",
        "    trigram_cpd3 = cpd3[last_two_words]\n",
        "    next_word3 = trigram_cpd3.generate()\n",
        "    generated_text3.append(next_word3)"
      ],
      "metadata": {
        "id": "CuJTmn5YfejN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8a7edf29-3703-490c-c966-c8c37e8e3abf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Dziesięć najczęstszych znaków:\n",
            " : 0.195\n",
            "E: 0.091\n",
            "T: 0.072\n",
            "A: 0.059\n",
            "O: 0.055\n",
            "I: 0.051\n",
            "H: 0.050\n",
            "N: 0.047\n",
            "S: 0.044\n",
            "R: 0.037\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "W Alicji spacja jest najczęstsza, a nie litera `E`..."
      ],
      "metadata": {
        "id": "fh66oznK985o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Obejrzymy sobie, na ile sekwencje losowe przypominają język, gdy będziemy próbkować z coraz precyzyjniejszych rozkładów\n",
        "\n",
        "# Długość\n",
        "ile = 48 #@param {type:\"integer\"}\n",
        "\n",
        "generated_text1 = random.choices(list(probabilities.keys()), weights=list(probabilities.values()), k=ile)\n",
        "print(\"=\"*50)\n",
        "print(\"Bezwarunkowo\")\n",
        "print(\"=\"*50)\n",
        "generated_text_str1 = ''.join(generated_text1)\n",
        "print(generated_text_str1)\n",
        "print(\"=\"*50)\n",
        "print(\"=\"*50)\n",
        "print()\n",
        "\n",
        "print(\"=\"*50)\n",
        "print(\"Warunek: jedna litera\")\n",
        "print(\"=\"*50)\n",
        "generated_text_str2 = ''.join(generated_text2)\n",
        "print(generated_text_str2)\n",
        "print(\"=\"*50)\n",
        "print(\"=\"*50)\n",
        "print()\n",
        "\n",
        "print(\"=\"*50)\n",
        "print(\"Warunek: dwie litery\")\n",
        "print(\"=\"*50)\n",
        "generated_text_str3 = ''.join(generated_text3)\n",
        "print(generated_text_str3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nnyuP42e-MR7",
        "outputId": "5dd63a8f-7516-4376-ea89-caefa7abd247"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "==================================================\n",
            "Bezwarunkowo\n",
            "==================================================\n",
            "TOISER`LNLDE TRL LLT WOOLFEYOF  S  KN H ASTHLUTO\n",
            "==================================================\n",
            "==================================================\n",
            "\n",
            "==================================================\n",
            "Warunek: jedna litera\n",
            "==================================================\n",
            "ALEI, L HAETIFOGTA AEM ;LOOG  INL TI:`USHTYL ,FRL TAIUHC -GI RN T TTIM:RHOTT TU  VE EN    NY'EBTAUPY  \n",
            "==================================================\n",
            "==================================================\n",
            "\n",
            "==================================================\n",
            "Warunek: dwie litery\n",
            "==================================================\n",
            "ALIED AFTER LOW SLE\n",
            "DODY CON THE GULD BUTILL YOULETCHOW THAT WAS SAID TOGS HE OF IT\n",
            "MOURT ALITY WOURE;\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Oczywiście w NLP tokenizujemy na podstawie słów, a nie liter. Proszę się zastanowić, jak ogromne statystyki musielibyśmy przechowywać, gdybyśmy przetwarzali bezpośrednio prawdopodobieństwa warunkowe!"
      ],
      "metadata": {
        "id": "v5CZwsHRdJVX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Jak się te rozkłady prawdopodobieństwa mają do entropii?\n",
        "\n",
        "Im więcej wiemy, tym mniej jesteśmy zaskoczeni! Czyli: entropia jest zrelatywizowana do naszej wiedzy nt. źródła wiadomości."
      ],
      "metadata": {
        "id": "gKW-5-nkbv7o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@markdown Policzymy trzy entropie: bezwarunkową i dwie warunkowe\n",
        "\n",
        "print(f'Entropia BEZWARUNKOWA dla pojedynczych znaków: {entropy(list(probabilities.values()),base=2)} bit/znak.')\n",
        "\n",
        "prawd_pairs = {}\n",
        "entropy2 = 0\n",
        "for condition1 in cfd2.conditions():\n",
        "    p_sum = 0\n",
        "    for event in cfd2[condition1]:\n",
        "        p = cpd2[condition1].prob(event)\n",
        "        prawd_pairs[(condition1,event)] = probabilities[condition1] * p\n",
        "        p_sum += prawd_pairs[(condition1,event)] * math.log2(p)\n",
        "    entropy2 -= p_sum\n",
        "print(f'Entropia WARUNKOWA na podstawie bigramów (warunek: pojedyncza litera): {entropy2} bit/znak.')"
      ],
      "metadata": {
        "id": "GrI139v1b-1l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c20b4844-0a70-4161-a47d-4382317daa11"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Entropia BEZWARUNKOWA dla pojedynczych znaków: 4.339002576245449 bit/znak.\n",
            "Entropia WARUNKOWA na podstawie bigramów (warunek: pojedyncza litera): 3.45133919483068 bit/znak.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "*   Już pojedynczy warunek wprowadza ogromny spadek entropii (prawie o 1 bit)! Dla rozszerzania warunków o kolejne litery ten spadek wartości nie jest już tak radykalny.\n",
        "*   Dla trigramów jeszcze mniejsza wartość entropii - można policzyć samodzielnie (byleby poprawnie). Przewidziano [bonusy do aktywności](https://upel.agh.edu.pl/mod/assign/view.php?id=112861) za ćwiczenia :)\n",
        "*   Entropia dla pojedynczych znaków jest większa niż dla pojedynczych liter (obliczona wcześniej, przy okazji wykresu częstotliwości). Dlaczego?"
      ],
      "metadata": {
        "id": "Waw7J17hEuwC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Przy okazji liczenia entropii zebraliśmy sobie też oszacowanie statystyczne prawdopodobieństw łącznych $\\Pr\\{a,b\\}$. Teraz to wykorzystamy."
      ],
      "metadata": {
        "id": "cAEDaLrPDxbC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@markdown Co myśmy tu sobie zebrali...\n",
        "\n",
        "ile_tego = 0\n",
        "sumuje_sie = 0\n",
        "\n",
        "print(\"Przykładowe prawdopodobieństwa dla bigramów: \")\n",
        "for condition1 in cfd2.conditions():\n",
        "    for event in cfd2[condition1]:\n",
        "      pr = prawd_pairs[(condition1,event)]\n",
        "      sumuje_sie += pr\n",
        "      ile_tego += 1\n",
        "      if ile_tego>138 and ile_tego<148:\n",
        "        print(f'Pr({condition1}{event}) = {pr}')\n",
        "\n",
        "print()\n",
        "print(f\"Wartości sumują się do {sumuje_sie}. Co to znaczy?\")\n",
        "print(f\"\\nJest ich w sumie: {ile_tego}. Dlaczego tyle wartości?\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oPeFgrM_EE8C",
        "outputId": "06932d83-e801-44a6-dd9e-21a745d6c78b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Przykładowe prawdopodobieństwa dla bigramów: \n",
            "Pr(IM) = 0.00149514079242462\n",
            "Pr(IR) = 0.001441261844949859\n",
            "Pr(IG) = 0.0014075875027781332\n",
            "Pr(IE) = 0.0012863598709599209\n",
            "Pr(IO) = 0.0011651322391417083\n",
            "Pr(IF) = 0.0010775789494952216\n",
            "Pr(I') = 0.0009092072386365933\n",
            "Pr(IK) = 0.0006532822381314781\n",
            "Pr(IV) = 0.00040409210606070817\n",
            "\n",
            "Wartości sumują się do 0.9999932651315666. Co to znaczy?\n",
            "\n",
            "Jest ich w sumie: 805. Dlaczego tyle wartości?\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Entropia łączna (też bezwarunkowa) dla bigramów\n",
        "#@markdown Policzyliśmy już $H(Y)$, $H(X|Y)$, zobaczymy jeszcze entropię łączną (też bezwarunkową) $H(X,Y)$\n",
        "\n",
        "entr_joint = entropy(list(prawd_pairs.values()),base=2)\n",
        "\n",
        "print(f'Entropia ŁĄCZNA dla bigramów: {entr_joint} bit/bigram. Wartość maksymalna mogłaby wynieść: {math.log2(ile_tego)}.')\n",
        "print(f'To znaczy, że gdy patrzymy na sekwencję - entropia na znak: {entr_joint/2} bit/(znak w sekwencji).')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gtbgSflm7jAv",
        "outputId": "642a7c33-acb4-4c10-8283-b2b808bedf28"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Entropia ŁĄCZNA dla bigramów: 7.79026881669023 bit/bigram. Wartość maksymalna mogłaby wynieść: 9.65284497300198.\n",
            "To znaczy, że gdy patrzymy na sekwencję - entropia na znak: 3.895134408345115 bit/(znak w sekwencji).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Można zerknąć na wartości i widać **regułę łańcuchową** dla entropii:\n",
        "\n",
        "$$H(X,Y) = H(Y) + H(X|Y) = H(X) + H(Y|X)$$\n",
        "\n",
        "Tutaj $H(X) = H(Y)$, bo $X$ oraz $Y$ oznacza to samo, czyli rozkład pojedynczych znaków. Oczywiście w wielu przypadkach (np. kanałów transmisyjnych) to są różne zmienne losowe."
      ],
      "metadata": {
        "id": "5TPZ1IjnDcfp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Dywergencja Kullbacka-Leiblera"
      ],
      "metadata": {
        "id": "rZYsK6ZUiIQL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "\n",
        "loc = 2  #@param {type: \"slider\", min:-5, max:5, step:0.5}\n",
        "scale = 5.2 #@param {type: \"slider\", min:0.1, max:10.1, step:0.1}\n",
        "liczba_punktow = 5000 #@param {type:\"integer\"}\n",
        "\n",
        "sample1 = np.random.normal(0, 1, liczba_punktow)\n",
        "sample2 = np.random.normal(loc, scale, liczba_punktow)\n",
        "\n",
        "pdf1 = gaussian_kde(sample1)\n",
        "pdf2 = gaussian_kde(sample2)\n",
        "\n",
        "x = np.linspace(-10, 10, 100)\n",
        "density1 = pdf1(x)\n",
        "density2 = pdf2(x)\n",
        "\n",
        "eps = 1e-9\n",
        "density1 += eps\n",
        "density2 += eps\n",
        "\n",
        "plt.plot(x, density1, label = 'P = N(0,1)')\n",
        "plt.plot(x, density2, label = f'Q = N({loc},{scale})')\n",
        "plt.title('Dwa rozkłady normalne')\n",
        "plt.xlabel(f'$x$')\n",
        "plt.ylabel(f'Gęstości rozkładów $f(x)$')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "kl_divergence = entropy(pk=density1, qk=density2, base=2)\n",
        "print(f\"D(P/Q) = {kl_divergence}\")"
      ],
      "metadata": {
        "id": "HCLdPMqIjqlI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 318
        },
        "outputId": "d536d2de-07f5-457c-9d7b-b7578b64a9a3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "D(P/Q) = 1.761367556648817\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Tutaj liczymy rozbieżność na podstawie estymaty z próbek. Akurat dla rozkładów normalnych można ładnie policzyć $D_{\\text{KL}}(P||Q) = f(\\mu_1,\\mu_2,\\sigma_1,\\sigma_2)$."
      ],
      "metadata": {
        "id": "djb-VLDhjBXM"
      }
    }
  ]
}