Liesel: A Probabilistic Programming Framework

Liesel is a probabilistic programming framework with a focus on semi-parametric regression. It includes:

• Liesel, a library to express statistical models as Probabilistic Graphical Models (PGMs). Through the PGM representation, the user can build and update models in a natural way.
• Goose, a library to build custom MCMC algorithms with several parameter blocks and MCMC kernels such as the No U-Turn Sampler (NUTS), the Iteratively Weighted Least Squares (IWLS) sampler, or different Gibbs samplers. Goose also takes care of the MCMC bookkeeping and the chain post-processing.
• RLiesel, an R interface for Liesel which assists the user with the configuration of semi-parametric regression models such as Generalized Additive Models for Location, Scale and Shape (GAMLSS) with different response distributions, spline-based smooth terms and shrinkage priors.

The name “Liesel” is an homage to the Gänseliesel fountain, landmark of Liesel’s birth city Göttingen.

Resources

• 📰 Paper on arXiv
• 👧🦢💻 Liesel & Goose repo
• 👧🦢📖 Liesel & Goose API docs
• ®️💻 RLiesel repo
• 📖 Tutorials

Usage

The following example shows how to build a simple i.i.d. normal model with Liesel. We set up two parameters and one observed variable, and combine them in a model.

import jax.numpy as jnp
import tensorflow_probability.substrates.jax.distributions as tfd
import liesel.model as lsl

loc = lsl.param(0.0, name="loc")
scale = lsl.param(1.0, name="scale")

y = lsl.obs(
    value=jnp.array([1.314, 0.861, -1.813, 0.587, -1.408]),
    distribution=lsl.Dist(tfd.Normal, loc=loc, scale=scale),
    name="y",
)

model = lsl.Model([loc, scale, y])

The model allows us to evaluate the log-probability through a property, which is updated automatically if the value of a node is modified.

model.log_prob

Array(-8.635652, dtype=float32)

model.vars["loc"].value = -0.5
model.log_prob

Array(-9.031153, dtype=float32)

We can estimate the mean parameter with Goose and a NUTS sampler. Goose’s workhorse to run an MCMC algorithm is the Engine, which can be constructed with the EngineBuilder. The builder allows us to assign different MCMC kernels to one or more parameters. We also need to specify the model, the initial values, and the sampling duration, before we can run the sampler.

import liesel.goose as gs

builder = gs.EngineBuilder(seed=42, num_chains=4)

builder.add_kernel(gs.NUTSKernel(["loc"]))
builder.set_model(gs.LieselInterface(model))
builder.set_initial_values(model.state)

builder.set_duration(warmup_duration=1000, posterior_duration=1000)

engine = builder.build()

liesel.goose.builder - WARNING - No jitter functions provided. The initial values won't be jittered
liesel.goose.engine - INFO - Initializing kernels...
liesel.goose.engine - INFO - Done

engine.sample_all_epochs()

liesel.goose.engine - INFO - Starting epoch: FAST_ADAPTATION, 75 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 2, 1, 2, 0 / 75 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 25 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 1, 1, 1 / 25 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 50 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 1, 1, 1 / 50 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 100 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 2, 2, 1 / 100 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 200 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 4, 1, 1 / 200 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: SLOW_ADAPTATION, 500 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 2, 1, 1, 2 / 500 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Starting epoch: FAST_ADAPTATION, 50 transitions, 25 jitted together
liesel.goose.engine - WARNING - Errors per chain for kernel_00: 1, 1, 2, 2 / 50 transitions
liesel.goose.engine - INFO - Finished epoch
liesel.goose.engine - INFO - Finished warmup
liesel.goose.engine - INFO - Starting epoch: POSTERIOR, 1000 transitions, 25 jitted together
liesel.goose.engine - INFO - Finished epoch

Finally, we can print a summary table and view some diagnostic plots.

results = engine.get_results()
gs.Summary(results)

Parameter summary:

		kernel	mean	sd	q_0.05	q_0.5	q_0.95	sample_size	ess_bulk	ess_tail	rhat
parameter	index
loc	()	kernel_00	-0.083	0.445	-0.810	-0.091	0.652	4000	1459.234	1874.643	1.002

Error summary:

				count	relative
kernel	error_code	error_msg	phase
kernel_00	1	divergent transition	warmup	38	0.009
			posterior	0	0.000

gs.plot_param(results, param="loc")

Installation

Liesel requires Python ≥ 3.10. Create and activate a virtual environment, and install the latest release from PyPI:

pip install liesel

You can also install the development version from GitHub:

git clone https://github.com/liesel-devs/liesel.git
cd liesel
pip install .
# or `pip install -e .[dev]` for an editable install including the dev utils

Liesel depends on JAX and jaxlib. As of now, there are no official jaxlib wheels for Windows. If you are on Windows, the JAX developers recommend using the Windows Subsystem for Linux. Alternatively, you can build jaxlib from source or try the unofficial jaxlib wheels from https://github.com/cloudhan/jax-windows-builder.

If you are using the lsl.plot_model() function, installing pygraphviz will greatly improve the layout of the model graphs. Make sure you have the Graphviz development headers on your system and run:

pip install pygraphviz

Again, the installation is a bit more challenging on Windows, but there are instructions on the pygraphviz website.

Development

Please run

1. pre-commit run -a before committing your work,
2. make sure the tests don’t fail with pytest --run-mcmc, and
3. make sure the examples in your docstrings are up-to-date with pytest --doctest-modules liesel.

Acknowledgements

Liesel is being developed by Paul Wiemann, Hannes Riebl, Johannes Brachem and Gianmarco Callegher with support from Thomas Kneib. Important contributions were made by Joel Beck and Alex Afanasev. We are grateful to the German Research Foundation (DFG) for funding the development through grant KN 922/11-1.