From 7bfededb9542780a13f38527c8ff21e89d6c08af Mon Sep 17 00:00:00 2001 From: Neil Smith Date: Wed, 12 Feb 2014 22:24:25 +0000 Subject: [PATCH] Investigation into unknown word probabilities --- .gitignore | 3 +- challenge7.ipynb | 3 - cipher.sublime-project | 2 + unknown-word-probability-investigation.ipynb | 177 +++++++++++++++++++ 4 files changed, 181 insertions(+), 4 deletions(-) create mode 100644 cipher.sublime-project create mode 100644 unknown-word-probability-investigation.ipynb diff --git a/.gitignore b/.gitignore index 715720a..9f5e769 100644 --- a/.gitignore +++ b/.gitignore @@ -4,4 +4,5 @@ /tmp /__pycache__/* *pyc - +.ipynb* +*.sublime-workspace diff --git a/challenge7.ipynb b/challenge7.ipynb index 23723c2..d7d18f4 100644 --- a/challenge7.ipynb +++ b/challenge7.ipynb @@ -11,9 +11,6 @@ "cell_type": "code", "collapsed": false, "input": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "\n", "from cipherbreak import *\n", "with open('2013/mona-lisa-words.txt') as f:\n", " mlwords = [line.rstrip() for line in f]\n", diff --git a/cipher.sublime-project b/cipher.sublime-project new file mode 100644 index 0000000..2c63c08 --- /dev/null +++ b/cipher.sublime-project @@ -0,0 +1,2 @@ +{ +} diff --git a/unknown-word-probability-investigation.ipynb b/unknown-word-probability-investigation.ipynb new file mode 100644 index 0000000..75931f9 --- /dev/null +++ b/unknown-word-probability-investigation.ipynb @@ -0,0 +1,177 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "from math import log10\n", + "from cipherbreak import *\n", + "from language_models import *" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fractions = [1.0]\n", + "for wordlen in range(1, 20):\n", + " known_words = len([w for w in keywords if len(w) == wordlen])\n", + " possible_words = 26 ** wordlen\n", + " fractions += [known_words / possible_words]\n", + "fractions" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 9, + "text": [ + "[1.0,\n", + " 1.0,\n", + " 0.34615384615384615,\n", + " 0.05974055530268548,\n", + " 0.007654668954168271,\n", + " 0.0005913456488541394,\n", + " 3.6129588927177356e-05,\n", + " 1.8010883826943671e-06,\n", + " 7.107795165409739e-08,\n", + " 2.4355817367258945e-09,\n", + " 7.469162662303339e-11,\n", + " 1.979378237044537e-12,\n", + " 4.875878520286003e-14,\n", + " 1.1095648437193016e-15,\n", + " 2.199659830168053e-17,\n", + " 4.185399254019551e-19,\n", + " 6.83349209784038e-21,\n", + " 1.199477188056649e-22,\n", + " 2.0013901045062867e-24,\n", + " 1.5656245928341226e-26]" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(fractions)\n", + "plt.ylabel(\"Probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot([log10(f) for f in fractions])\n", + "plt.plot([log10(f) for f in fractions], 'bo')\n", + "plt.ylabel(\"Log probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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lRZs2bZg2bRr33nuv3UPeTuskRKQot3eRHT8+nIiITkyZAv/8J/zrX9C6tdEp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\n7dmwYQP33nsvJpOJOnXqkJm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+ "text": [ + "" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot([log10(f) for f in fractions], 'bo')\n", + "plt.plot([i for i in range(2,20)], [-(i-2) for i in range(2,20)], 'g-')\n", + "plt.ylabel(\"Log probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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8TuMusI6OjorprytXrjRaQERE5iA2dijc3ObXO/a8SWCoSBGJg0umiYiUqC1O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\n/w+H/CoI41pxawAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot([log10(f) for f in fractions], 'bo')\n", + "plt.plot([i for i in range(2,20)], [-(i-2) for i in range(2,20)], 'g-')\n", + "plt.plot([i for i in range(2,20)], [-(i-3)*1.5 for i in range(2,20)], 'r-')\n", + "plt.ylabel(\"Log probability of word\")\n", + "plt.xlabel(\"Word length\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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gxjuJzz77DOHh4eWGm3x9fbFgwYL6irES3kk0HKU1CavrI7AF85GPZvjUqive/cq/Tntt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\nSRARkVJMEkREpBSTBBERKcU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