🎲🎲 Quantifying Dependence — A Data Scientist’s Intro To Information Theory — Part 4/5: Mutual Information Fundamentals

Author(s): Eyal Kazin PhD

Originally published on Towards AI.

Gain an intuition into two-variable statistics as a prelude to understanding Mutual Information. Python code included. 🐍Generated using ChatGPT

Mutual Information is the amount of “Aha!” you get about one thing by learning another

This is the fourth article in an introductory series on information quantification — an essential framework for data scientists. Learning to measure information unlocks powerful tools for improving statistical analyses and refining decision criteria in machine learning.

In this article and the next we discuss the popular metric mutual information — which expresses how much knowing one variable reduces the uncertainty in another.

Or in other words:

How much information is obtained about random variable A by observing random variable B?

As throughout the series, to build a solid foundation, in this article we focus on understanding the fundamentals of two (or more) variable statistics such as the joint probability distribution and conditional probabilities. We will then relate to information theory via the building block of mutual information: point mutual information (PMI), which is regarded as “one of the most important concepts in Natural Language Processing”¹ (NLP).

To make things concrete and fun we’ll explore these concepts using a simple toy examples of NLP 🔠, a game of craps — where we roll pairs of dice 🎲🎲, and co-occurrence matrices in a market basket analysis 🧺.

With a solid grasp… Read the full blog for free on Medium.

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Published via Towards AI