WALNUTS

WALNUTS is a Markov chain Monte Carlo (MCMC) sampler that locally adapts step size for the No-U-Turn Sampler (NUTS). WALNUTS is a near-acronym for "within-oribt adaptive step-length no-U-turn sampler."

This repository contains 3 projects, which are outlined below:

1. WALNUTSpy: Flexible and highly instrumented sampler coded in Python; used for all of the experiments in the paper.

2. walnuts package: Python implementation directly following the (inefficient) pseudocode.

3. walnuts_cpp: Performant C++ implementation.

1. Original WALNUTSpy

The original implementation is in WALNUTSpy. This version includes the implicit midpoint integrator as well as the leapfrog integrator and was used for all of the experiments in the paper.

walnuts/
├── WALNUTSpy/
│   ├── adaptiveIntegrators.py 
│   ├── constants.py 
│   ├── example.py 
│   ├── mainGaussTransient.py 
│   ├── plotGaussTransient.py 
│   ├── targetDistr.py 
│   ├── MCMCutils.py 
│   ├── P2quantile.py
│   ├── WALNUTS.py 

example.py provides an example of the usage of this sampler. The file adaptiveIntegrators.py contain several different adaptive integrators, and also fixedLeapFrog() which turns the sampler into a regular NUTS sampler.

2. walnuts reference Python implementation

The implementation in the walnuts package is a reference implementation that follows the pseudocode in the paper.

walnuts/
├── pyproject.toml
├── walnuts/
│   ├── __init__.py
│   ├── walnuts.py 
│   ├── walnuts_stan.py 
├── test/
│   ├── targets.py 
│   ├── test.py 

Running the tests

To run the tests, execute the test.py script.

$ cd walnuts
$ python3 test/test.py

The tests appear as a sequence of calls at the bottom of test.py and some of them may be commented out for efficiency.

3. walnuts_cpp: Performant C++ implementation

See the README for walnuts_cpp

References

This is the paper on which the sampler is based.

• Nawaf Bou-Rabee, Bob Carpenter, Tore Selland Kleppe, and Sifan Liu. (to appear). WALNUTS: The Within-Orbit Adaptive Step-Length No-U-Turn Sampler.