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🚅 Information Theory for People in a Hurry
Data Science   Latest   Machine Learning

🚅 Information Theory for People in a Hurry

Eyal Kazin PhD
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March 7, 2025
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Author(s): Eyal Kazin PhD

Originally published on Towards AI.

A quick guide to Entropy, Cross-Entropy and KL Divergence. Python code provided. 🐍

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Considered the Magna Carta of the Information Age, Claude Shannon’s seminal 1948 paper posed a groundbreaking question:

How can we quantify communication?

This question laid the foundation for information theory, revolutionising technology in ways still felt today. Shannon’s insights underpin how we measure, store, and transmit information, contributing to breakthroughs in signal processing, data compression (e.g., Zip files, CDs), the Internet, and artificial intelligence. Beyond technology, his work has influenced diverse fields such as neurobiology, statistical physics, and computer science (e.g., cybersecurity, cloud computing, and machine learning).

Claude Elwood Shannon in one of the first experiments in artificial intelligence using an electromechanical mouse to solve a maze. Credit: Wikipedia

In this article, we focus on three key metrics: entropy, cross-entropy, and KL divergence, along with their foundation in self-information. These concepts bridge probability theory with real-world applications. They serve as common practical tools for analysis and optimisation used in data science and machine learning.

I’ll introduce these metrics and then explore an interesting use case — message length optimisation, using a toy example of weather forecasting ☀️🌦️⛈️.

No prior knowledge is required — just a basic understanding of probabilities.

This article serves… Read the full blog for free on Medium.

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} strongTag.remove(); }); }); } removeStrongFromHeadings(); "use strict"; window.onload = () => { /* //This is an object for each category of subjects and in that there are kewords and link to the keywods let keywordsAndLinks = { //you can add more categories and define their keywords and add a link ds: { keywords: [ //you can add more keywords here they are detected and replaced with achor tag automatically 'data science', 'Data science', 'Data Science', 'data Science', 'DATA SCIENCE', ], //we will replace the linktext with the keyword later on in the code //you can easily change links for each category here //(include class="ml-link" and linktext) link: 'linktext', }, ml: { keywords: [ //Add more keywords 'machine learning', 'Machine learning', 'Machine Learning', 'machine Learning', 'MACHINE LEARNING', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, ai: { keywords: [ 'artificial intelligence', 'Artificial intelligence', 'Artificial Intelligence', 'artificial Intelligence', 'ARTIFICIAL INTELLIGENCE', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, nl: { keywords: [ 'NLP', 'nlp', 'natural language processing', 'Natural Language Processing', 'NATURAL LANGUAGE PROCESSING', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, des: { keywords: [ 'data engineering services', 'Data Engineering Services', 'DATA ENGINEERING SERVICES', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, td: { keywords: [ 'training data', 'Training Data', 'training Data', 'TRAINING DATA', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, ias: { keywords: [ 'image annotation services', 'Image annotation services', 'image Annotation services', 'image annotation Services', 'Image Annotation Services', 'IMAGE ANNOTATION SERVICES', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, l: { keywords: [ 'labeling', 'labelling', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, pbp: { keywords: [ 'previous blog posts', 'previous blog post', 'latest', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, mlc: { keywords: [ 'machine learning course', 'machine learning class', ], //Change your article link (include class="ml-link" and linktext) link: 'linktext', }, }; //Articles to skip let articleIdsToSkip = ['post-2651', 'post-3414', 'post-3540']; //keyword with its related achortag is recieved here along with article id function searchAndReplace(keyword, anchorTag, articleId) { //selects the h3 h4 and p tags that are inside of the article let content = document.querySelector(`#${articleId} .entry-content`); //replaces the "linktext" in achor tag with the keyword that will be searched and replaced let newLink = anchorTag.replace('linktext', keyword); //regular expression to search keyword var re = new RegExp('(' + keyword + ')', 'g'); //this replaces the keywords in h3 h4 and p tags content with achor tag content.innerHTML = content.innerHTML.replace(re, newLink); } function articleFilter(keyword, anchorTag) { //gets all the articles var articles = document.querySelectorAll('article'); //if its zero or less then there are no articles if (articles.length > 0) { for (let x = 0; x < articles.length; x++) { //articles to skip is an array in which there are ids of articles which should not get effected //if the current article's id is also in that array then do not call search and replace with its data if (!articleIdsToSkip.includes(articles[x].id)) { //search and replace is called on articles which should get effected searchAndReplace(keyword, anchorTag, articles[x].id, key); 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