A spectral model for multimodal redshift estimation

We present a physically inspired model for the problem of redshift estimation. Typically, redshift estimation has been treated as a regression problem that takes as input magnitudes and maps them to a single target redshift. In this work we acknowledge the fact that observed magnitudes may actually admit multiple plausible redshifts, i.e. the distribution of redshifts explaining the observed magnitudes (or colours) is multimodal. Hence, employing one of the standard regression models, as is typically done, is insufficient for this kind of problem, as most models implement either one-to-one or many-to-one mappings. The observed multimodality of solutions is a direct consequence of (a) the variety of physical mechanisms that give rise to the observations, (b) the limited number of measurements available and (c) the presence of noise in photometric measurements. Our proposed solution consists in formulating a model from first principles capable of generating spectra. The generated spectra are integrated over filter curves to produce magnitudes which are then matched to the observed magnitudes. The resulting model naturally expresses a multimodal posterior over possible redshifts, includes measurement uncertainty (e.g. missing values) and is shown to perform favourably on a real dataset.