Semi-parametric γ-ray modeling with Gaussian processes and variational inference

Siddharth Mishra-Sharma and Kyle Cranmer

Abstract

Mismodeling the uncertain, diffuse emission of Galactic origin can seriously bias the characterization of astrophysical gamma-ray data, particularly in the region of the Inner Milky Way where such emission can make up over 80% of the photon counts observed at ~GeV energies. We introduce a novel class of methods that use Gaussian processes and variational inference to build flexible background and signal models for gamma-ray analyses with the goal of enabling a more robust interpretation of the make-up of the gamma-ray sky, particularly focusing on characterizing potential signals of dark matter in the Galactic Center with data from the Fermi telescope.

Code

Dependencies

The code dependencies are given in environment.yml.

Running experiments

The inference.constructor.ModelConstructor class creates simulated Fermi data and instantiates a GPyTorch/Pyro model for GP inference. The inference.trainer.PyroSVITrainer class is used for training.

The following instantiates these classes and reproduces the experiments used for the paper:

python train.py --guide_name MVN --num_inducing 200 --poiss_only
python train.py --guide_name IAF --num_inducing 200 --poiss_only
python train.py --guide_name ConditionalIAF --num_inducing 200 --poiss_only

where the --guide_name option specifies different variational distributions that can be used for the template parameters:

• MVN: Multivariate normal guide, models template parameters as correlated Gaussians.
• IAF: Uses an inverse autoregressive flow to model template parameters.
• ConditionalIAF: Uses an inverse autoregressive flow conditioned on summary statistics of the Gaussian process draws (see paper for more information).

These variational guides are defined in models/template_param.py.

notebooks/fermi-gp-poiss.ipynb can be used to analyze the runs and also run inference interactively in a notebook. See inference/constructor.py for a list of configurable parameters.

Non-Poissonian regression

Removing the --poiss_only option runs a non-Poissonian template fit. This is untested. A stand-alone, differentiable version of the non-Poissonian likelihood can be found in models/likelihoods.py.

Citation

This code is associated with the paper:

@inproceedings{Mishra-Sharma:2020kjb,
    author = "Mishra-Sharma, Siddharth and Cranmer, Kyle",
    title = "{Semi-parametric $\gamma$-ray modeling with Gaussian processes and variational inference}",
    booktitle = "{Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020)}",
    eprint = "2010.10450",
    archivePrefix = "arXiv",
    primaryClass = "astro-ph.HE",
    month = "10",
    year = "2020"
}

The repository borrows data products and code from NPTFit (paper), and heavily relies on Pyro, GPyTorch, and PyTorch.