https://github.com/astro-informatics/proxnest
Proximal Nested Sampling for high-dimensional Bayesian model selection
https://github.com/astro-informatics/proxnest
bayesian model-selection nested-sampling proximal-algorithms
Last synced: 4 months ago
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Proximal Nested Sampling for high-dimensional Bayesian model selection
- Host: GitHub
- URL: https://github.com/astro-informatics/proxnest
- Owner: astro-informatics
- License: gpl-3.0
- Created: 2022-05-05T12:46:23.000Z (almost 4 years ago)
- Default Branch: main
- Last Pushed: 2024-04-18T09:52:15.000Z (almost 2 years ago)
- Last Synced: 2025-09-23T01:13:18.582Z (5 months ago)
- Topics: bayesian, model-selection, nested-sampling, proximal-algorithms
- Language: Jupyter Notebook
- Homepage: https://astro-informatics.github.io/proxnest/
- Size: 15.9 MB
- Stars: 25
- Watchers: 9
- Forks: 4
- Open Issues: 2
-
Metadata Files:
- Readme: README.rst
- License: LICENSE.txt
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README
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|logo| Proximal nested sampling for high-dimensional Bayesian model selection
=================================================================================================================
.. |logo| raw:: html
``ProxNest`` is an open source, well tested and documented Python implementation of the *proximal nested sampling* framework (`Cai et al. 2022 `_) to compute the Bayesian model evidence or marginal likelihood in high-dimensional log-convex settings. Furthermore, non-smooth sparsity-promoting priors are also supported.
This is achieved by exploiting tools from proximal calculus and Moreau-Yosida regularisation (`Moreau 1962 `_) to efficiently sample from the prior subject to the hard likelihood constraint. The resulting Markov chain iterations include a gradient step, approximating (with arbitrary precision) an overdamped Langevin SDE that can scale to very high-dimensional applications.
Basic Usage
===========
The following is a straightforward example application to image denoising (Phi = I), regularised with Daubechies wavelets (DB6).
.. code-block:: Python
# Import relevant modules.
import numpy as np
import ProxNest
# Load your data and set parameters.
data = np.load()
params = params # Parameters of the prior resampling optimisation problem.
options = options # Options associated with the sampling strategy.
# Construct your forward model (phi) and wavelet operators (psi).
phi = ProxNest.operators.sensing_operators.Identity()
psi = ProxNest.operators.wavelet_operators.db_wavelets(["db6"], 2, (dim, dim))
# Define proximal operators for both your likelihood and prior.
proxH = lambda x, T : ProxNest.operators.proximal_operators.l1_projection(x, T, delta, Psi=psi)
proxB = lambda x, tau: ProxNest.optimisations.l2_ball_proj.sopt_fast_proj_B2(x, tau, params)
# Write a lambda function to evaluate your likelihood term (here a Gaussian)
LogLikeliL = lambda sol : - np.linalg.norm(y-phi.dir_op(sol), 'fro')**2/(2*sigma**2)
# Perform proximal nested sampling
BayEvi, XTrace = ProxNest.sampling.proximal_nested.ProxNestedSampling(
np.abs(phi.adj_op(data)), LogLikeliL, proxH, proxB, params, options
)
At this point you have recovered the tuple **BayEvi** and dict **Xtrace** which contain
.. code-block:: python
Live = options["samplesL"] # Number of live samples
Disc = options["samplesD"] # Number of discarded samples
# BayEvi is a tuple containing two values:
BayEvi[0] = 'Estimate of Bayesian evidence (float).'
BayEvi[1] = 'Variance of Bayesian evidence estimate (float).'
# XTrace is a dictionary containing the np.ndarrays:
XTrace['Liveset'] = 'Set of live samples (shape: Live, dim, dim).'
XTrace['LivesetL'] = 'Likelihood of live samples (shape: Live).'
XTrace['Discard'] = 'Set of discarded samples (shape: Disc, dim, dim).'
XTrace['DiscardL'] = 'Likelihood of discarded samples (shape: Disc).'
XTrace['DiscardW'] = 'Weights of discarded samples (shape: Disc).'
XTrace['DiscardPostProb'] = 'Posterior probability of discarded samples (shape: Disc)'
XTrace['DiscardPostMean'] = 'Posterior mean solution (shape: dim, dim)'
from which one can perform *e.g.* Bayesian model comparison.
Installation
============
Brief installation instructions are given below (for further details see the full installation documentation).
Quick install (PyPi)
--------------------
The ``ProxNest`` package can be installed by running
.. code-block:: bash
pip install ProxNest
Install from source (GitHub)
----------------------------
The ``ProxNest`` package can also be installed from source by running
.. code-block:: bash
git clone https://github.com/astro-informatics/proxnest
cd harmonic
and running the install script, within the root directory, with one command
.. code-block:: bash
bash build_proxnest.sh
To check the install has worked correctly run the unit tests with
.. code-block:: bash
pytest --black ProxNest/tests/
Contributors
============
`Matthew Price `_, `Xiaohao Cai `_, `Jason McEwen `_, `Marcelo Pereyra `_, and contributors.
Attribution
===========
A BibTeX entry for ``ProxNest`` is:
.. code-block::
@article{Cai:ProxNest:2021,
author = {Cai, Xiaohao and McEwen, Jason~D. and Pereyra, Marcelo},
title = {"High-dimensional Bayesian model selection by proximal nested sampling"},
journal = {ArXiv},
eprint = {arXiv:2106.03646},
year = {2021}
}
License
=======
``ProxNest`` is released under the GPL-3 license (see `LICENSE.txt `_), subject to
the non-commercial use condition (see `LICENSE_EXT.txt `_)
.. code-block::
ProxNest
Copyright (C) 2022 Matthew Price, Xiaohao Cai, Jason McEwen, Marcelo Pereyra & contributors
This program is released under the GPL-3 license (see LICENSE.txt),
subject to a non-commercial use condition (see LICENSE_EXT.txt).
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.