Estimating Bayesian Posteriors for Galaxy Morphological Parameters in Hyper Suprime-Cam Data using Machine Learning

Galaxy morphology is connected to various fundamental properties of a galaxy and its environment. Thus, studying the morphology of large samples of galaxies can be a crucial clue to understanding galaxy formation and evolution. In the past few years, although machine learning has been increasingly used to determine the morphology of galaxies, most previous works have provided only broad morphological classifications and required large amounts of pre-classified training data.

We have developed Galaxy Morphology Posterior Estimation Network (GaMPEN), a machine learning framework that can estimate the Bayesian posteriors for a galaxy’s bulge-to-total light ratio, effective radius, and flux. To predict posteriors, GaMPEN uses the Monte Carlo Dropout technique and incorporates the full covariance matrix in its loss function. The latter also allows GaMPEN to incorporate structured relationships between the output parameters into its predictions. We have demonstrated that GaMPEN’s predicted posteriors are well-calibrated and accurate. GaMPEN also contains a Spatial Transformer Network (STN) that automatically crops input galaxy frames to an optimal size before determining their morphology. The STN trains along with the rest of the framework, with no additional supervision, and will be crucial in applying GaMPEN to new survey data with no radius measurements.

We have used GaMPEN to predict morphological parameters of ~1 million z < 0.75 galaxies in the Hyper Suprime-Cam (HSC) Wide field, while using minimal real training data. We achieved this by first training GaMPEN on realistic simulations of HSC galaxies and then using transfer learning on a small amount of real data. Testing shows that GaMPEN predictions become less precise for especially small or faint galaxies, where the algorithm correctly predicts correspondingly larger uncertainties. We demonstrate that by qualitative transformation of the predicted values in regions where GaMPEN’s residuals are higher, we can achieve accuracies of >95%. GaMPEN is the first machine learning framework for determining joint posterior distributions of multiple morphological parameters and is also the first application of an STN in astronomy.