Classy non-linear optimisation
Project description
PyAutoFit
PyAutoFit is a Python-based probablistic programming language that enables contemporary Bayesian inference techniques to be straightforwardly integrated into scientific modeling software. PyAutoFit allows automated transdimensional model-fitting pipelines for large data-sets to be written, by acting as an interface between Python classes and non-linear sampling packages such as PyMultiNest.
PyAutoFit specializes in advanced model-fitting problems, where highly complex models with many plausible model paramertizations are fitted. PyAutoFit breaks the model-fitting procedure into a series of linked non-linear searches, or 'phases', where the results of earlier phases initialize the fitting of more complex models in later phases.
This allows transdimensional model-fitting pipelines to be built that enable fitting of extremely complex and high dimensional models to be reduced to a series of bite-sized model fits, such that even the most complex model fitting task can be fully automated.
Python Example
We will illustrate this with an example fitting two 2D Gaussians:
We are going to fit each Gaussian with a 2D Gaussian pofile. Traditional methods would both Gaussians simultaneously, making parameter space more complex, slower to sample and increasing the risk that we fail to locate the global maxima solution. With PyAutoFit we can instead build a transdimensional model fitting pipeline which breaks the the analysis down into 3 phases:
- Fit only the left Gaussian.
- Fit only the right Gaussian, using the model of the left Gaussian from phase 1 to improve their deblending.
- Fit both Gaussians simultaneously, using the results of phase 1 & 2 to initialize where the non-linear optimizer searches parameter space.
PyAutoFit determines the components of a model by interacting with Python classes. For this example we use the SphericalGaussian class:
class SphericalGaussian(object):
def __init__(
self,
centre = (0.0, 0.0), # <- PyAutoFit recognises these constructor arguments are the model
intensity = 0.1, # <- parameters of SphericalGaussian profile.
sigma = 0.01,
):
self.centre = centre
self.intensity = intensity
self.sigma = sigma
This model, and its model parameters, are then used by PyAutoFit to build our 3 phase model-fitting pipeline:
import autofit as af
def make_pipeline():
# In phase 1, we will fit the Gaussian on the left.
phase1 = af.Phase(
phase_name="phase_1__left_gaussian",
gaussians=af.CollectionPriorModel(gaussian_0=af.profiles.SphericalGaussian),
optimizer_class=af.MultiNest,
)
# In phase 2, we will fit the Gaussian on the right, where the best-fit Gaussian resulting from phase 1
# above fits the left-hand Gaussian.
phase2 = af.Phase(
phase_name="phase_2__right_gaussian",
phase_folders=phase_folders,
gaussians=af.CollectionPriorModel(
gaussian_0=phase1.result.instance.gaussians.gaussian_0, # <- Use the Gaussian fitted in phase 1
gaussian_1=gaussian_1,
),
optimizer_class=af.MultiNest,
)
# In phase 3, we fit both Gaussians, using the results of phases 1 and 2 to initialize their model parameters.
phase3 = af.Phase(
phase_name="phase_3__both_gaussian",
phase_folders=phase_folders,
gaussians=af.CollectionPriorModel(
gaussian_0=phase1.result.model.gaussians.gaussian_0, # <- use phase 1 Gaussian results.
gaussian_1=phase2.result.model.gaussians.gaussian_1, # <- use phase 2 Gaussian results.
),
optimizer_class=af.MultiNest,
)
return toy.Pipeline(pipeline_name, phase1, phase2, phase3)
Of course, fitting two Gaussians is a fairly trivial model-fitting problem that does not require PyAutoFit. Nevertheless, the example above illustrates how one can break a model-fitting task down with PyAutoFit, an approach which is crucial for the following software packages:
- PyAutoLens - Software for fitting galaxy-galaxy strong gravitational lensing systems. In this example, a 5-phase PyAutoFit pipeline performs strong lens modeling using 10 different model components producing models with 20-40 parameters.
Yet Another Probablistic Programming Language?
There already exist many options for incorporating Bayesian inference techniques into model fitting problems, such as PyMC3 and STAN. These packages allow simple models to be quickly defined, parametrized and fitted to data.
PyAutoFit focuses on complex model-fitting tasks, where many models parameterized in different ways are fitted. This problem necessiates model-fitting pipelines like that shown in the example above. If you're problem doesn't require such complex model fitting, you probably don't need to use PyAutoFit!
Features
Advanced statistical modeling features in PyAutoFit include:
- Model Mapping - Interface with Python classes to define and fit complex models parameterized with many different model components.
- Pipelines - Write transdimensional analysis pipelines to fit complex models to large data-sets in a fully automated way.
- Non-linear Optimizers - Combine a variety of non-linear search techniques (e.g. gradient descent, nested sampling, MCMC).
- Aggregation - Model results are stored in a database format that enables quick manipulate of large sets of results for inspection and interpretation.
Future
The following features are planned for 2020:
- Generalized Linear Models - After fitting a large suite of data fit for global trends in the PyAutoFit model results.
- Hierarchical modeling - Combine fits over multiple data-sets to perform hierarchical inference.
- Time series modelling - Fit temporally varying models using fits which marginalize over time.
- Approximate Bayesian Computational - Likelihood-free modeling.
- Transdimensional Sampling - Sample non-linear parameter spaces with variable numbers of model components and parameters.
Slack
We're building a PyAutoFit community on Slack, so you should contact us on our Slack channel before getting started. Here, I will give you the latest updates on the software & discuss how best to use PyAutoFit for your science case.
Unfortunately, Slack is invitation-only, so first send me an email requesting an invite.
Depedencies
PyAutoFit requires PyMultiNest.
Installation with conda
We recommend installation using a conda environment as this circumvents a number of compatibility issues when installing PyMultiNest.
First, install conda.
Create a conda environment:
conda create -n autofit python=3.7 anaconda
Activate the conda environment:
conda activate autofit
Install multinest:
conda install -c conda-forge multinest
Install autofit:
pip install autofit
Installation with pip
Installation is also available via pip, however there are reported issues with installing PyMultiNest that can make installation difficult, see the file INSTALL.notes
$ pip install autofit
Support & Discussion
If you're having difficulty with installation, lens modeling, or just want a chat, feel free to message us on our Slack channel.
Contributing
If you have any suggestions or would like to contribute please get in touch.
Credits
Developers
Richard Hayes - Lead developer
James Nightingale - Lead developer
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