Monte Carlo Techniques for Addressing Large Errors and Missing Data in Simulation-based Inference

TL;DR

This paper introduces a Monte Carlo method to handle missing data and out-of-distribution errors in simulation-based inference, significantly improving efficiency and applicability for large astronomical datasets.

Contribution

The authors develop a Monte Carlo technique that allows SBI to effectively manage heterogeneous data with missing observations and variable uncertainties, expanding its use in astronomy.

Findings

Out-of-distribution errors can be approximated with SBI evaluations.

Missing data can be marginalized using nearby data realizations.

Inference time increases from 1 second to 1.5 minutes per object, still faster than traditional methods.

Abstract

Upcoming astronomical surveys will observe billions of galaxies across cosmic time, providing a unique opportunity to map the many pathways of galaxy assembly to an incredibly high resolution. However, the huge amount of data also poses an immediate computational challenge: current tools for inferring parameters from the light of galaxies take $\gtrsim 10$ hours per fit. This is prohibitively expensive. Simulation-based Inference (SBI) is a promising solution. However, it requires simulated data with identical characteristics to the observed data, whereas real astronomical surveys are often highly heterogeneous, with missing observations and variable uncertainties determined by sky and telescope conditions. Here we present a Monte Carlo technique for treating out-of-distribution measurement errors and missing data using standard SBI tools. We show that out-of-distribution measurement errors can be approximated by using standard SBI evaluations, and that missing data can be marginalized over using SBI evaluations over nearby data realizations in the training set. While these techniques slow the inference process from $\sim 1$ sec to $\sim 1.5$ min per object, this is still significantly faster than standard approaches while also dramatically expanding the applicability of SBI. This expanded regime has broad implications for future applications to astronomical surveys.