mirror of https://github.com/jlizier/jidt
357 lines
76 KiB
Plaintext
357 lines
76 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "87e17b68-7539-4539-aeab-9df6fc819f22",
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"metadata": {},
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"source": [
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"# Mutual information of written English text\n",
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"\n",
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"Author: J. Lizier, Isabelle De Backer, 2022-; based on the original Matlab tutorials.\n",
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"\n",
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"The following block aims to import all the relevant libraries to analyse data"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "55ca6967-2ca7-45e8-9858-6bb0356c2bee",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import math\n",
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"\n",
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"# Specifics required for the text processing here:\n",
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"import string\n",
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"import re"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bc5119d3-c9d3-4139-ad43-3346098ea85d",
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"metadata": {},
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"source": [
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"# Preparing your environment\n",
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"\n",
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"As per `Module_2_notebook.ipynb` etc. we need to use the functions we have defined in our previous work in other notebooks. So gather the new functions you wrote in this module into your `simpleinfotheory.py` script, and make sure it is referencable from here (you may need to change the folder referenced below) before you run the import line in the next cell:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "8df5b524-117e-4a02-989e-9647b336dcc5",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Option 3: edit simpleinfotheory.py and past your functions into that as you write them\n",
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"import sys\n",
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"sys.path.append('../../Module1-IntroToInfoTheory/PythonCode/completed/')\n",
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"import simpleinfotheory"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4ecca927-eb6b-4840-8ea5-d4ea2bf79869",
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"metadata": {},
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"source": [
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"# 6. (Optional extension) Mutual information between successive letters in written English\n",
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"\n",
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"In this extension activity, we will continue our analysis of written English extracted from the [Seinfeld](https://en.wikipedia.org/wiki/Seinfeld) scripts as begun in the previous module.\n",
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"\n",
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"1. Download the scripts from the links on Module 2 on Canvas, load into Python and preprocess as per steps 1-4 of the activity from the previous module, such that we have the characters stored in the numpy array `processedStr`:<br/>\n",
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"_Note:_ you may need to alter the filename/path to match your own --"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "0cebd6af-93fe-4377-9bdf-adfc995bcd10",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([' ', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l',\n",
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" 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y',\n",
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" 'z'], dtype='<U1')"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"filename = './Seinfeld-scripts-textOnly.txt'\n",
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"with open(filename, 'rt') as f:\n",
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" str = f.read()\n",
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"p = re.compile('[!\"#\\$%&\\'\\(\\)\\*\\+\\,-\\.\\/:;<=>\\?@\\[\\]\\\\\\^_`{\\|}~0-9]*');\n",
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"processedStr = p.sub('', str); # Remove punctuation characters and digits\n",
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"processedStr = ' '.join(processedStr.split('\\n')); # Replace newline characters with spaces\n",
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"processedStr = processedStr.lower(); # Convert all upper case into lower case\n",
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"processedStr = np.array(list(processedStr)); # Finally convert this into a numpy array so we can work with it\n",
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"np.unique(processedStr)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4e6b1195-3c3b-4570-ac49-742810f94025",
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"metadata": {},
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"source": [
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"2. How can we now compute the mutual information between one character and the character that comes next in the text? We will need to provide samples of a previous character and the next character to our `simpleinfotheory.mutualinformationempirical()` function.<br/>\n",
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" _Hint_: to select all but the last item in a numpy array `x`, you can refer to `x[:-1]`, whilst to select all but the first item in an array `x`, you can refer to `x[1:]`"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "f1225213-86e2-49f3-9ff9-dfe0f6d34876",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0.7196084319029961"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Compute the mutual information between successive characters:\n",
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"simpleinfotheory.mutualinformationempirical(processedStr[:-1],processedStr[1:])[0]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ab60c5ec-592a-4e15-97c7-280f7ce91253",
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"metadata": {},
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"source": [
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"3. Compare the mutual information that you computed above to the average entropy of each character computed as per step 5 of the activity in the previous module. Consider the following:\n",
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" 1. What proportion of our uncertainty about the next character in the written text is reduced by observing the previous character?\n",
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" 1. How much code could we save in communicating a character if our coding scheme took the previous character into account?\n",
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" 1. The mutual information computes a measure of the relationship between the consecutive characters here. You're probably familiar with using correlation to measure a relationship between variables -- could correlation be used here? We will see more about how MI and correlation are related in the coming weeks.\n",
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"4. Are there relationships between previous characters and later characters beyond those which are consecutive?<br/>\n",
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" Can you modify your call to `simpleinfotheory.mutualinformationempirical()` above to compute the mutual information between characters that are not consecutive but separated by a lag of 2 (i.e. with one character in between them)? Is there still a substantial relationship? Is this information solely contained in the earlier character or is it perhaps also included in the immediately previous character?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "7dc60b50-fc49-40a8-9d9c-9afc67e081fc",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0.3280241319399746"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Compute the mutual information between characters separated by a lag of two:\n",
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"simpleinfotheory.mutualinformationempirical(processedStr[:-2],processedStr[2:])[0]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "75e18172-0164-46e0-9be3-18970c294c30",
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"metadata": {},
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"source": [
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"5. Can you see how this relationship changes over longer lags still? Plot the mutual information as a function of lag (up to say 10). At what point would you say there is no longer a relationship? We will discuss statistical approaches to answering that in the coming weeks."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "aaf73d8c-a21a-4503-9281-b3bd8e7f670f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Compute and plot the MI as a function of lag:\n",
|
|
"maxLag = 10;\n",
|
|
"\n",
|
|
"misVsLag = np.zeros(maxLag);\n",
|
|
"\n",
|
|
"for lag in range(1,maxLag+1): # To go from 1 up to maxLag\n",
|
|
" misVsLag[lag-1] = simpleinfotheory.mutualinformationempirical(processedStr[:-lag],processedStr[lag:])[0];\n",
|
|
"\n",
|
|
"plt.scatter(range(1,maxLag+1), misVsLag, c=\"red\", marker=\"x\");\n",
|
|
"plt.xlabel('Lag')\n",
|
|
"plt.ylabel('MI (bits)');\n",
|
|
"plt.title('Average MI between characters separated by the given lag');"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7445b88c-d912-4976-9368-11478dbbcf74",
|
|
"metadata": {},
|
|
"source": [
|
|
"# 7. (Optional extension) Pointwise mutual information between successive letters in written English\n",
|
|
"\n",
|
|
"_Further challenge_ -- It would be interesting to inspect the **local or pointwise mutual information** between each possible pair of consecutive letters. (See Part 3 of the lecture)\n",
|
|
"\n",
|
|
"1. To do this, first note how `simpleinfotheory.jointentropyempirical()` returns the set of symbols and their probabilities, as well as the joint entropy value.\n",
|
|
"2. Now we will alter `simpleinfotheory.mutualinformationempirical()` to similarly retrieve and return all of the relevant probabilities for each consecutive character pair:\n",
|
|
" 1. Notice how the calls for the joint entropy, $Y$ entropy and $X$ entropy already retrieve these for us.\n",
|
|
" 2. Then alter the return statement so that all of these relevant values are returned: `return result, xySymbols, xyProbs, xSymbols, xProbs, ySymbols, yProbs` (this is already done in the solution code for `simpleinfotheory.py`).\n",
|
|
" 3. You will need to restart the kernel to reload the library. You'll also need to update the function calls above, since they're now returning a list. If you append `[0]` to them, such as `simpleinfotheory.mutualinformationempirical(...)[0]`, then this will just pick out the main `result` return variable for the above as desired.\n",
|
|
"3. Next, call `simpleinfotheory.mutualinformationempirical()` again as per step 2 of the previous exercise for lag 1, but this time storing all of these return values:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "539b82af-b94e-4ca1-9362-ba70078c30cb",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"0.7196084319029961\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Call the mutual information empirical again, this time storing all of the return values.\n",
|
|
"result, xySymbols, xyProbs, xSymbols, xProbs, ySymbols, yProbs = simpleinfotheory.mutualinformationempirical(processedStr[:-1],processedStr[1:]);\n",
|
|
"print(result)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9ec8b8b0-92ea-444b-9b02-aeb3c01ab679",
|
|
"metadata": {},
|
|
"source": [
|
|
"4. Now, we loop over all possible joint symbols and compute the pointwise mutual information -- fill in the line of the code marked with `???` to compute the pointwise MI and then run this code block:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "b3a37011-0238-47d0-85a3-b384573fa2c0",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"pointwiseMIs = np.zeros((xSymbols.size, ySymbols.size)); # Create array to store the pointwise MI values for each possible character pair\n",
|
|
"for firstCharIndex in range(xSymbols.size):\n",
|
|
" firstChar = xSymbols[firstCharIndex];\n",
|
|
" probFirst = xProbs[firstCharIndex];\n",
|
|
" for secondCharIndex in range(ySymbols.size):\n",
|
|
" secondChar = ySymbols[secondCharIndex];\n",
|
|
" probSecond = yProbs[secondCharIndex];\n",
|
|
" jointSymbolIndex = np.argwhere((xySymbols[:,0] == firstChar) & (xySymbols[:,1] == secondChar));\n",
|
|
" if (jointSymbolIndex.size == 0):\n",
|
|
" pointwiseMIs[firstCharIndex, secondCharIndex] = 0; # No occurence, so set to 0\n",
|
|
" continue;\n",
|
|
" probJoint = xyProbs[jointSymbolIndex];\n",
|
|
" # Compute the pointwise MI from probJoint, probFirst and probSecond\n",
|
|
" pointwiseMIs[firstCharIndex, secondCharIndex] = np.log2( probJoint / (probFirst * probSecond) );"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e7f91288-9d24-4736-ae88-b8f3562d09a4",
|
|
"metadata": {},
|
|
"source": [
|
|
"5. Can you plot these values using `plt.imshow()`? Run the command `plt.colorbar()` to insert a colour bar to show the scale. The plot will have the first letters along the y axis, and second letters along the x axis. You can label these using:\n",
|
|
"\n",
|
|
" <code>plt.xlabel('Second letter')\n",
|
|
" plt.xticks(ticks=range(0,27), labels=ySymbols.flatten()) # second letters - y - goes on x axis\n",
|
|
" plt.ylabel('First letter');\n",
|
|
" plt.yticks(ticks=range(0,27), labels=xSymbols.flatten()) # first letters - x - goes on y axis\n",
|
|
" cbar = plt.colorbar()\n",
|
|
" cbar.set_label('MI (bits)');\n",
|
|
" plt.title('MI between successive letters of text');</code>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "d4351b95-71de-4509-9278-6790516c007e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Make the heatmap plot:\n",
|
|
"plt.imshow( pointwiseMIs )\n",
|
|
"# Add the labels pasting in the code from above:\n",
|
|
"plt.xlabel('Second letter')\n",
|
|
"plt.xticks(ticks=range(0,27), labels=ySymbols.flatten())\n",
|
|
"plt.ylabel('First letter');\n",
|
|
"plt.yticks(ticks=range(0,27), labels=xSymbols.flatten())\n",
|
|
"cbar = plt.colorbar()\n",
|
|
"cbar.set_label('MI (bits)');\n",
|
|
"plt.title('MI between successive letters of text');"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "37b50b62-6af9-4b66-84c3-b2c180ad9d28",
|
|
"metadata": {},
|
|
"source": [
|
|
"6. Examine the values and determine whether you can identify character pairs where the second is highly predictable from the first, and where the first character is misinformative about the second. Can you explain these results?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "def04a11-19af-437a-a3d1-15a09548dc5b",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.10.12"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|