Incorporating Measurement Error in Astronomical Object Classification

Abstract

Most general-purpose classification methods, such as support-vector machine (SVM) and random forest (RF), fail to account for an unusual characteristic of astronomical data: known measurement error uncertainties. In astronomical data, this information is often given in the data but discarded because popular machine learning classifiers cannot incorporate it. We propose a simulation-based approach that incorporates heteroscedastic measurement error into existing classification method to better quantify uncertainty in classification. The proposed method first simulates perturbed realizations of the data from a Bayesian posterior predictive distribution of a Gaussian measurement error model. Then, a chosen classifier is fit to each simulation. The variation across the simulations naturally reflects the uncertainty propagated from the measurement errors in both labeled and unlabeled data sets. We demonstrate the use of this approach via two numerical studies. The first is a thorough simulation study applying the proposed procedure to SVM and RF, which are well-known hard and soft classifiers, respectively. The second study is a realistic classification problem of identifying high-$z$ $(2.9\le z\le 5.1)$ quasar candidates from photometric data. The data are from merged catalogs of the Sloan Digital Sky Survey, the $Spitzer$ IRAC Equatorial Survey, and the $Spitzer$-HETDEX Exploratory Large-Area Survey. The proposed approach reveals that out of 11,847 high-$z$ quasar candidates identified by a random forest without incorporating measurement error, 3,146 are potential misclassifications with measurement error. Additionally, out of $1.85$ million objects not identified as high-$z$ quasars without measurement error, 936 can be considered new candidates with measurement error.

References in corpus (20)

• Natural Scales in Geographical Patterns
• Some Aspects of Measurement Error in Linear Regression of Astronomical Data
• Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations?
• Flexible and Scalable Methods for Quantifying Stochastic Variability in the Era of Massive Time-Domain Astronomical Data Sets
• Think Outside the Color Box: Probabilistic Target Selection and the SDSS-XDQSO Quasar Targeting Catalog
• The SDSS Coadd: 275 deg^2 of Deep SDSS Imaging on Stripe 82
• Photometric redshifts and quasar probabilities from a single, data-driven generative model
• Stability
• The Sloan Digital Sky Survey Stripe 82 Imaging Data: Depth-Optimized Co-adds Over 300 Deg^2 in Five Filters
• Robust Machine Learning Applied to Astronomical Datasets III: Probabilistic Photometric Redshifts for Galaxies and Quasars in the SDSS and GALEX
• The Spitzer-HETDEX Exploratory Large-Area Survey
• Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms
• Bayesian High-Redshift Quasar Classification from Optical and Mid-IR Photometry
• Quasar Probabilities and Redshifts from WISE mid-IR through GALEX UV Photometry
• The Clustering of High-Redshift (2.9 $\le$ z $\le$ 5.1) Quasars in SDSS Stripe 82
• SpIES: The Spitzer IRAC Equatorial Survey
• Modeling Stochastic Variability in Multi-Band Time Series Data
• How proper are Bayesian models in the astronomical literature?
• 21st Century Statistical and Computational Challenges in Astrophysics
• Robust and Accurate Inference via a Mixture of Gaussian and Student's t Errors

Cited by in corpus (1)

• Classifying Unidentified X-ray Sources in the Chandra Source Catalog Using a Multiwavelength Machine-learning Approach