I’ve finally had a bit of time to finish up the code for the Rock-Paper-Scissors bot discussed in the previous posts; I’ve put the code in a GitHub repository here. Feel free to file issues if you would like it to be a bit more user friendly.
The bot which uses the Fourier transform on move probabilities to search for profitable patterns is named `diaconis`, after Persi Diaconis. It’s currently working just fine, but is a bit slow computationally. On startup, it generates all possible move patterns that it will investigate during the course of each game, as well as some character tables. After each play, it tests some of these patterns, and tries to determine if their predictive power is better than any of the patterns seen thus far. If so, it begins using that pattern to choose move probabilities.
This works fine as a proof-of-concept of the basic ideas. Additional improvements could be had by doing some code optimization to speed things up a bit, and keeping a list of good patterns and allowing a bit more dexterity in switching between the patterns used for prediction.
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.
I’ve recently been doing some reading on machine learning with a mind towards applying some of my prior knowledge of representation theory. The initial realization that representation theory might have some interesting applications in machine learning came from discussions with Chris Olah at the Toronto HackLab a couple months ago; you can get interesting new insights by exploring new spaces! Over winter break I’ve been reading Bishop’s ‘Pattern Recognition and Machine Learning‘ (slowly), alongside faster reads like ‘Building Machine Learning Systems with Python.‘ As I’ve read, I’ve realized that there is plenty of room for introducing group theory into machine learning in interesting ways. (Note: This is the first of a few posts on this topic.)
There’s a strong tradition of statisticians using group theory, perhaps most famously Persi Diaconis, who used representation theory of the symmetric group to find the mixing time for card shuffling. His notes ‘Group Representations in Probability and Statistics‘ are an excellent place to pick up the background material with a strong eye towards applications. Over the next few posts I’ll make a case for the use of representation theory in machine learning, emphasizing automatic factor selection and Bayesian methods.
First, an extremely brief overview of what machine learning is about, and an introduction to using a Bayesian approach to play RoShamBo, or rock paper scissors. In the second post, I’ll motivate the viewpoint of representation by exploring the Fourier transform and how to use it to beat repetitive opponents. Finally, in the third post I’ll look at how we can use representations to select factors for our Bayesian algorithm by examining likelihood functions as functions on a group.