In this lecture, we review the concept of entropy from physics and introduce information-theoretic connections to the increase in entropy and the erasure of latent information. We use that to motivate why maximum entropy probability distributions are the "least biased" choices given a set of constraints. We give a few examples of maximum entropy distributions and take a little time to introduce Maximum Entropy (MaxEnt) methods in machine learning and data science that have been successful in Natural Language Processing (NLP) as well as many other fields, from archeology to ecology. Equipped with maximum entropy, we introduce the Boltzmann distribution as a key tool in the implementation of Simulated Annealing, and we highlight connections between the Boltzmann distribution and "softmax" (as well as "softmin") from Machine Learning/AI. We will conclude our introduction of Simulated Annealing in the next lecture.
Whiteboard notes for this lecture can be found at:
https://www.dropbox.com/scl/fi/dv7gei6rbb0yltqekmhrb/IEE598-Lecture5B-2025-03-20-From_Maximum_Entropy_MaxEnt_Methods_Toward_Optimization_by_Simulated_Annealing-Notes.pdf?rlkey=jaifjaxazwn3u0efui0lthlky&dl=0
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