Standardizing Type Ia Supernova Absolute Magnitudes Using Gaussian
  Process Data Regression
  We present a novel class of models for Type Ia supernova time-evolving
spectral energy distributions (SED) and absolute magnitudes: they are each
modeled as stochastic functions described by Gaussian processes. The values of
the SED and absolute magnitudes are defined through well-defined regression
prescriptions, so that data directly inform the models. As a proof of concept,
we implement a model for synthetic photometry built from the spectrophotometric
time series from the Nearby Supernova Factory. Absolute magnitudes at peak $B$
brightness are calibrated to 0.13 mag in the $g$-band and to as low as 0.09 mag
in the $z=0.25$ blueshifted $i$-band, where the dispersion includes
contributions from measurement uncertainties and peculiar velocities. The
methodology can be applied to spectrophotometric time series of supernovae that
span a range of redshifts to simultaneously standardize supernovae together
with fitting cosmological parameters.
