Exploiting Non-Linear Structure in Astronomical Data for Improved Statistical Inference

TL;DR

This paper discusses how spectral kernel methods, especially diffusion maps, can transform complex astronomical data into simpler forms, improving statistical inference for tasks like redshift estimation and supernova classification.

Contribution

It introduces the application of spectral connectivity analysis to astronomical data, highlighting its potential to enhance data interpretation and inference accuracy.

Findings

Spectral methods reveal underlying data geometry effectively.

Applications include photometric redshift estimation and supernova classification.

Challenges and future directions in computational and statistical aspects are discussed.

Abstract

Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and make accurate inferences, it is crucial to transform the data into a simpler, reduced form. Spectral kernel methods are non-linear data transformation methods that efficiently reveal the underlying geometry of observable data. Here we focus on one particular technique: diffusion maps or more generally spectral connectivity analysis (SCA). We give examples of applications in astronomy; e.g., photometric redshift estimation, prototype selection for estimation of star formation history, and supernova light curve classification. We outline some computational and statistical challenges that remain, and we discuss some promising future directions for astronomy and data mining.