[Paper Review] Semi-parametric $γ$-ray modeling with Gaussian processes and variational inference

Siddharth Mishra-Sharma, K. Cranmer|arXiv (Cornell University)|Oct 20, 2020

Gaussian Processes and Bayesian Inference4 citations

TL;DR

This paper introduces a semi-parametric Bayesian framework that uses Gaussian processes with variational inference to model uncertainties in Galactic diffuse gamma-ray emission, significantly improving robustness in detecting dark matter signals—particularly the Galactic Center Excess—by flexibly capturing large-scale mismodeling in background templates without relying on fixed parametric forms.

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.

Motivation & Objective

• Address the persistent challenge of diffuse Galactic background mismodeling in Fermi-LAT gamma-ray analyses, which can bias interpretations of astrophysical signals.
• Improve the robustness of dark matter searches—especially for the Galactic Center Excess—by accounting for epistemic uncertainty in diffuse emission templates.
• Develop a flexible, data-driven method to model residual mismodeling in diffuse emission without assuming a fixed parametric form.
• Enable more reliable statistical inference on the nature of the Galactic Center Excess by incorporating uncertainty in the large-scale structure of the diffuse background.

Proposed method

• Employ Gaussian processes (GPs) as a non-parametric prior over the spatial amplitude of diffuse emission templates to model residual mismodeling not captured by standard physical models.
• Use a Matérn kernel to define the GP covariance function, enabling control over smoothness and flexibility of the inferred background corrections.
• Apply variational inference to approximate the intractable posterior distribution over GP latent functions and template normalizations, enabling scalable inference on large HEALPix maps.
• Integrate the GP prior into a Poisson likelihood framework for pixel-wise counts data, allowing joint inference of signal and background components.
• Use inducing points (200) and stochastic subsampling (1500 pixels) to accelerate training with the Adam optimizer over 50,000 iterations.
• Train the model on simulated data with known mismodeling between a true diffuse model (Model O) and a fiducial model (p6v11), validating performance via posterior predictive checks.

Experimental results

Research questions

• RQ1 Can Gaussian processes effectively model large-scale mismodeling in Galactic diffuse gamma-ray emission without assuming a fixed parametric form?
• RQ2 How well can variational inference scale to high-dimensional gamma-ray data (e.g., HEALPix maps) while preserving accuracy in background uncertainty quantification?
• RQ3 To what extent does the GP-based approach improve the recovery of true signal and background template normalizations in the presence of systematic diffuse emission errors?
• RQ4 Can this method robustly distinguish between dark matter-like and point-source-like origins of the Galactic Center Excess by reducing background-related biases?
• RQ5 How does the inclusion of GPs as a flexible correction term affect the posterior inference of astrophysical parameters in semi-parametric gamma-ray analyses?

Key findings

• The GP model successfully captures large-scale residual mismodeling between the true diffuse emission (Model O) and the fiducial model (p6v11), with the posterior-predictive distribution closely tracking the true multiplicative mismatch.
• The median inferred GP map accurately recovers the spatial structure of the diffuse emission error, particularly near the Galactic Center, where mismodeling is most impactful.
• Posterior-predictive samples of template normalizations show tight agreement with ground truth values, indicating accurate inference of background amplitudes despite model uncertainty.
• The method achieves reliable inference using only 1500 subsampled pixels and 200 inducing points, demonstrating scalability to full-sky HEALPix maps with 50,000 training iterations.
• The framework enables robust characterization of the Galactic Center Excess by reducing bias from diffuse background mismodeling, a key limitation in prior analyses.
• The approach is extensible to non-Poissonian likelihoods and can be integrated into machine learning pipelines for future gamma-ray data analysis.