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Open Source Program Office

Open Sourcing the Wisconsin Idea

Matern Covariance

Project leader:

Chris Geoga, (geoga@wisc.edu)

Project description:

The project mentor has a library for fast evaluation of the Matern covariance function and its derivatives, including with respect to the smoothness parameter. This originally stemmed from a paper they wrote a few years ago about using autodiff to accurately differentiate the Matern function with respect to the smoothness parameter, which is not possible in closed form without using generalized confluent hypergeometric functions. But this is a problem, because as the theory around fixed-domain asymptotics for Gaussian processes indicates this parameter is quite likely the most important one to be fitting.

The original code that they wrote was in Julia, but predictably many people have indicated that they would like to use it but would only do so if it were available in R/python. With this in mind, we’ve translated and enhanced the routines to get a minimal viable product, and in order to end up with GCC-able code we’ve also developed a very ornate pipeline that differentiates the routines using Enzyme, which works on LLVM IR, and then actually compiles the LLVM IR back to gcc-able C so that it can be used by languages like R which do not permit packages to enforce the use of a specific C compiler.

Longer term, the goal is for this library to offer (1) by far the fastest Matern covariance evaluation routines, (2) derivatives with respect to all parameters that are accurate to double precision and fast, and (3) extensions involving smarter parameterizations of geometric anisotropy and other enhancements that can serve as a backbone for casual users of front-end languages like R and Python. As of now, (1) and (2) are largely done, although the mentor is continually interested to find improvements for the runtime and algorithmic strategies of evaluating the Matern function. The mentor’s ultimate ambition is to get within the cost of three exp evaluations…although we’ll have to see if that will ever happen.

An intern could contribute to this project by:

  1. Packaging code up neatly in R and python packages
  2. Developing and enhancing an automated testing suite for all three major OSes
  3. Developing a robust build process, which is complex because the Enzyme AD engine is unstable and the LLVM C backend is only an unofficially maintained target that is kept alive by some Julia developers (of all people).
  4. Micro-optimizing current code
  5. Potentially implementing new routines and numerical strategies

Intern needs:

Students who are comfortable with the C programming language and low-level code optimization and debugging would be the best fit. For performance optimization, we are talking about shaving off nanoseconds, so it would be best for students to be interested in low-level programming and optimization as well as floating point arithmetic. For testing and distribution, a good understanding of Github pipelines and automated workflows would be ideal.

Application Requirements:

  1. Review the available projects by visiting the various project pages.
  2. Interns should apply through the UW Student Jobs portal. Applicants who are not currently admitted or enrolled as a UW-Madison Student or without a UW NetID can login as well as create an account. Please note, you must apply to each project individually that you want to be considered for.
  3. Application materials submitted through the UW Student Jobs portal should include:
  4. Submit a resume, cover letter, and three references as part of your application.
  5. Interviews will be arranged for selected candidates on a rolling basis after applications close.