Starkindler: An Uncertainty Aware Objective for Photometric Redshift Estimation
Raahul Singh, Ashutosh Pandey
TL;DR
Starkindler tackles photometric redshift estimation by addressing aleatoric uncertainty in observed data. It introduces a training objective that treats $z_{spec} \sim \mathcal{N}(\mu_{spec}, \sigma_{spec}^2)$ as ground truth and trains a CNN to predict $z_{pred} \sim \mathcal{N}(\mu_{pred}, \sigma_{pred}^2)$ by minimizing $KL(z_{spec} \ || \ z_{pred})$; this yields improved accuracy (lower MSE/MAE) and better calibration (lower ECE and more uniform PIT) with reduced outliers, compared to SDSS photometric redshifts and an ablation using only NLL. The ablation shows that ignoring $zErr_{spec}$ degrades performance, highlighting the regularizing effect of incorporating aleatoric uncertainty. The approach is model-agnostic and can extend to other astrophysical measurements where measurement errors are available, enabling more interpretable uncertainty estimates for large surveys.
Abstract
Photometric Redshift is critical for analyzing astronomical objects, but existing ML methods often overlook the aleatoric uncertainties inherent in observed data. We introduce Starkindler, a novel training objective that explicitly incorporates observational errors into the model's objective function, thereby directly accounting for aleatoric uncertainty. Unlike traditional probabilistic models that focus solely on epistemic uncertainty, Starkindler provides uncertainty estimates that are regularised by aleatoric uncertainty, and is designed to be more interpretable. We train a simple convolutional neural network (CNN) using data from Sloan Digital Sky Survey (SDSS) and compare against the Photometric redshift estimates provided by SDSS. We show improvements in accuracy, calibration and reduction in predicted outlier rate. We also conduct an ablation study which confirms that excluding observational errors significantly degrades model performance, underscoring the importance of accounting for aleatoric uncertainty. Our results suggest that Starkindler not only enhances predictive performance but also provides interpretable uncertainty estimates, making it a robust tool for astronomical data analysis.