Derek Jones from The Shape of Code
I was at the Man AHL Hackathon this weekend. The theme was improving the Python Data Science ecosystem. Around 15, or so, project titles had been distributed around the tables in the Man AHL cafeteria and the lead person for each project gave a brief presentation. Stable laws in SciPy sounded interesting to me and their room location included comfy seating (avoiding a numb bum is an under appreciated aspect of choosing a hackathon team and wooden bench seating is not numbing after a while).
Team Stable laws consisted of Andrea, Rishabh, Toby and yours truly. Our aim was to implement the Stable distribution as a Python module, to be included in the next release of SciPy (the availability had been announced a while back and there has been one attempt at an implementation {which seems to contain a few mistakes}).
We were well-fed and watered by Man AHL, including fancy cream buns and late night sushi.
A probability distribution is stable if the result of linear combinations of the distribution has the same distribution; the Gaussian, or Normal, distribution is the most well-known stable distribution and the central limit theorem leads many to think, that is that.
Two other, named, stable distributions are the Cauchy distribution and most interestingly (from my perspective this weekend) the Lévy distribution. Both distributions have very fat tails; the mean and variance of the Cauchy distribution is undefined (i.e., the values jump around as the sample size increases, never converging to a fixed value), while they are both infinite for the Lévy distribution.
Analytic expressions exist for various characteristics of the Stable distribution (e.g., probability distribution function), with the Gaussian, Cauchy and Lévy distributions as special cases. While solutions for implementing these expressions have been proposed, care is required; the expressions are ill-behaved in different ways over some intervals of their parameter values.
Andrea has spent several years studying the Stable distribution analytically and was keen to create an implementation. My approach for complicated stuff is to find an existing implementation and adopt it. While everybody else worked their way through the copious papers that Andrea had brought along, I searched for existing implementations.
I found several implementations, but they all suffered from using approaches that delivered discontinuities and poor accuracies over some range of parameter values.
Eventually I got lucky and found a paper by Royuela-del-Val, Simmross-Wattenberg and Alberola-López, which described their implementation in C: Libstable (licensed under the GPL, perfect for SciPy); they also provided lots of replication material from their evaluation. An R package was available, but no Python support.
No other implementations were found. Team Stable laws decided to create a new implementation in Python and to create a Python module to interface to the C code in libstable (the bit I got to do). Two implementations would allow performance and accuracy to be compared (accuracy checks really need three implementations to get some idea of which might be incorrect, when output differs).
One small fix was needed to build libstable under OS X (change Makefile to link against .so library, rather than .a) and a different fix was needed to install the R package under OS X (R patch; Windows and generic Unix were fine).
Python’s ctypes module looked after loading the C shared library I built, along with converting the NumPy arrays. My PyStable module will not win any Python beauty contest, it is a means of supporting the comparison of multiple implementations.
Some progress was made towards creating a new implementation, more than 24 hours is obviously needed (libstable contains over 4,000 lines of code). I had my own problems with an exception being raised in calls to stable_pdf; libstable used the GNU Scientific Library and I tracked the problem down to a call into GSL, but did not get any further.
We all worked overnight, my first 24-hour hack in a very long time (I got about 4-hours sleep).
After Sunday lunch around 10 teams presented and after a quick deliberation, Team Stable laws were announced as the winners; yea!
Hopefully, over the coming weeks a usable implementation will come into being.