Photometric Redshift Estimation with Convolutional Neural Networks and Galaxy Images: A Case Study of Resolving Biases in Data-Driven Methods

Abstract

Deep Learning models have been increasingly exploited in astrophysical studies, yet such data-driven algorithms are prone to producing biased outputs detrimental for subsequent analyses. In this work, we investigate two major forms of biases, i.e., class-dependent residuals and mode collapse, in a case study of estimating photometric redshifts as a classification problem using Convolutional Neural Networks (CNNs) and galaxy images with spectroscopic redshifts. We focus on point estimates and propose a set of consecutive steps for resolving the two biases based on CNN models, involving representation learning with multi-channel outputs, balancing the training data and leveraging soft labels. The residuals can be viewed as a function of spectroscopic redshifts or photometric redshifts, and the biases with respect to these two definitions are incompatible and should be treated in a split way. We suggest that resolving biases in the spectroscopic space is a prerequisite for resolving biases in the photometric space. Experiments show that our methods possess a better capability in controlling biases compared to benchmark methods, and exhibit robustness under varying implementing and training conditions provided with high-quality data. Our methods have promises for future cosmological surveys that require a good constraint of biases, and may be applied to regression problems and other studies that make use of data-driven models. Nonetheless, the bias-variance trade-off and the demand on sufficient statistics suggest the need for developing better methodologies and optimizing data usage strategies.

29 pages, 12+11 figures, 2+3 tables; accepted in Astronomy & Astrophysics

References in corpus (20)

• zCOSMOS: A Large VLT/VIMOS redshift survey covering 0 < z < 3 in the COSMOS field
• 3D-HST WFC3-selected Photometric Catalogs in the Five CANDELS/3D-HST Fields: Photometry, Photometric Redshifts and Stellar Masses
• The VIMOS Ultra-Deep Survey: ~10,000 galaxies with spectroscopic redshifts to study galaxy assembly at early epochs 2<z<~6
• Calibrating Redshift Distributions Beyond Spectroscopic Limits with Cross-Correlations
• The Zurich Extragalactic Bayesian Redshift Analyzer (ZEBRA) and its first application: COSMOS
• Galaxy And Mass Assembly (GAMA): the G02 field, Herschel-ATLAS target selection and Data Release 3
• Photometric redshift estimation via deep learning
• Precision photometric redshift calibration for galaxy-galaxy weak lensing
• The VANDELS ESO public spectroscopic survey: final Data Release of 2087 spectra and spectroscopic measurements
• The-wiZZ: Clustering redshift estimation for everyone
• The WiggleZ Dark Energy Survey: Final Data Release and the Metallicity of UV-Luminous Galaxies
• Star formation rates and stellar masses from machine learning
• A cooperative approach among methods for photometric redshifts estimation: an application to KiDS data
• Galaxy cluster mass estimation with deep learning and hydrodynamical simulations
• Light curve classification with recurrent neural networks for GOTO: dealing with imbalanced data
• Using Deep Neural Networks to compute the mass of forming planets
• The PAU Survey: narrowband photometric redshifts using Gaussian processes
• Augmenting machine learning photometric redshifts with Gaussian mixture models
• How not to obtain the redshift distribution from probabilistic redshift estimates: Under what conditions is it not inappropriate to estimate the redshift distribution N(z) by stacking photo-z PDFs?
• Photometric Redshift Estimation with Galaxy Morphology using Self-Organizing Maps