Roshambo Part III – Representation Theory

In the last two posts, we’ve looked at using machine learning for playing iterated Roshambo.  Specifically, we saw how to use Bayes’ theorem to try to detect and exploit patterns, and then saw how Fourier transforms can give us a concrete measurement of the randomness (and non-randomness) in our opponent’s play.  Today’s post is about how we can use representation theory to improve our chances of finding interesting patterns.

Niels Henrik Abel, for whom 'Abelian groups' are named.
Niels Henrik Abel, for whom ‘Abelian groups’ are named.  These are groups where xy=yx for any x, y.

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Roshambo Part II – Fourier Analysis

In the last post, we looked at using an algorithm suggested by Bayes’ Theorem to learn patterns in an opponent’s play and exploit them.  The game we’re playing is iterated rock-paper-scissors, with 1000 rounds of play per game.  The opponent’s moves are a string of choices, ‘r’, ‘p’, or ‘s’, and if we can predict what they will play, we’ll be able to beat them.  In trying to discover patterns automatically we’ll gain some general knowledge about detecting patterns in streams of characters, which has interesting applications ranging from biology (imagine ‘GATC’ instead of ‘rps’) to cryptography.

Fourier analysis is helpful in a wide variety of domains, ranging from music to image encoding.  A great example suggested by ‘Building Machine Learning Algorithms with Python‘ is classifying pieces of music by genre.  If we’re given a wave-form of a piece of music, automatically detecting its genre is difficult.  But applying the Fourier transform breaks the music up into its component frequencies, which turn out to be quite useful in determining whether a song is (say) classical or metal.

This goat recognizes and apparently enjoys metal.  Possibly using a furrier transform...
This goat recognizes and apparently enjoys metal. Possibly using a furrier transform… (sorry.)

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