## 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.

## Thoughts on Machine Learning, Representation Theory, and RoShamBo – Part I

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.

## Know Your Sensor

Recently I’ve been playing with building a regression model for the brightness of images produced with the Raspberry Pi’s camera board. Essentially, I want to quickly figure out – hopefully from a single image – what shutter speed and ISO to choose to get an image of a given brightness.

This is a pretty standard regression problem: We some data, extract some information from it, and use that information to make a prediction. To get a better handle on the algorithms involved, I wrote my own code to perform the regression, using NumPy for fast linear algebra operations. You always learn something from re-inventing the wheel, after all.

## Pi-Lapse 3: Toronto Skyline

I’ve done quite a bit to improve my Raspberry Pi-based timelapser.  I have a pretty good system together now, thanks in part to recent firmware updates to the Pi which allow me to directly control the shutter speed and ISO of the camera sensor instead of relying on auto-exposure settings.  The auto-exposure is pretty unreliable from one shot to the next: the camera makes a different decision each time it snaps a picture, which leads to quite a lot of flicker.  Previously, I was dealing with this flicker by manipulating the images in post-production, but I’ve now written some code to get the camera to try to maintain a constant image brightness across a long shoot.

The code now consists of a ‘timelapser’ class, which keeps track of its current shutterspeed and ISO (SS/ISO henceforth), and the brightness of the last few images taken.  It then adjusts SS/ISO to try to get the image brightness to 100.  By keeping track of the last few images, it is a bit less susceptible to being upset by one strange image (like, say, if I put my hand over the lens for one shot, producing a black image), or more standard movement within the frame.  On the other hand, it takes a while longer to settle down to the ‘right’ SS/ISO.  So it’s currently set up with an initialization step, where it finds a good SS/ISO pretty quickly, and then transitions to actually taking pictures.  The result is very little flicker as the timelapse goes on, and a pretty constant level of image brightness when light levels gradually change: like when we watch dawn or dusk.  (If you’re interested in playing around with the code, I’ve set up a github repository here.)

As an example, this is a video that we shot over about three days on my friends Ketan and Ananya’s balcony.  They have a great view over Toronto, from the CN Tower to Honest Ed’s.

## Pi-Lapse 2: Wychwood Barns Farmer’s Market

Almost immediately after my first foray with the Raspberry Pi timelapse I was contacted by Cookie Roscoe, who coordinates a weekly farmer’s market for The Stop.  The Stop is a community food center here in Toronto, providing lots of programming and emergency food access for lower-income people.  My partner, Elizabeth, worked with them for about three years, so I was super happy to try doing a time-lapse of their market.

Here’s the results!  Lots of technical stuff about what went into the video after the break!

## Pi-Lapse Test Footage

My recent DIY electronics project has been putting together a Raspberry Pi-based camera.  The Pi foundation sells a camera board which plugs into the Pi; it’s sold as ‘a bit better than the average camera in a mobile phone.’ But the Pi’s default Raspbian Linux installation comes with a couple programs for controlling the camera, and lets you take still pictures and videos easily.

In the interest of using the camera for something you can’t usually do with a store-bought digital camera, I wrote a short python script which takes a photo assigns it a file name based on the date and time taken.  It then does some sampling of the picture, and only keeps pictures which aren’t ‘too dark.’  And then cron runs the photo script once every five minutes.  In other words, the Pi is set up for long-form time-lapse photography.  The resulting pictures are then easy to compile into a movie.

## Two Weeks in Paris

Back for a day in Nairobi after visiting Paris for FPSAC 2013 and Sage-Days 49.  On the whole, it was a really productive visit; I met a number of my primary goals.  On the mathematics front, Kenya has been extremely isolating: One of the big goals for the conference, then, was to connect to some new things to work on and figure out what’s been happening in the algebraic combinatorics world in the last year.  It was exciting to actually work on math with people: when I arrived in Maseno, it turned out that no new graduate students had come into pure maths in some time, which meant there was no real outlet for doing math with other people.  So it’s been kind of a lonely year: I did a lot of work on education, and did some interesting community building around computer science with LakeHub, but often felt like my big area of expertise really wasn’t terribly helpful in Kenya.  The institutions weren’t really ready to make use of what I was bringing, since there wasn’t time or space for people to do research.  I obviously found lots of great stuff to work on anyway, but it felt a bit funny that I was so unable to engage people on the maths.

## Tips on Running a Headless Raspberry Pi

I was recently helping out a friend with a headless Raspberry Pi setup, and thought it would be helpful to consolidate a few useful bits here. From here, you can set up all kinds of cool projects using the GPIO pins, set up a headless web server, or anything else you can think of. For my part, when I hurt my ankle a few months ago, I hooked the Pi into a hard-to-get-to stereo system and logged in remotely from the other side of the room to play music… I also used a headless setup to run the really long compile for the Sage computer algebra system a few months ago.

## Hashes with Salt

(These are notes adapted from a presentation I gave at the LakeHub workshop this week.  They owe a lot of debt to this article, which inspired the talk.  If you already know that you should just use bcrypt or something similar, and why, you can just skip to the ‘conclusions’ section.)

So let’s suppose you’ve just made a hot new website from which you’ll make a million dollars a year.  You get to the point of creating a database for all of your users who will be logging in and doing things like buying airplanes, so you put together a database table.  Maybe it looks something like this: