Title: STACCATO: A Novel Solution to Supernova Photometric Classification with Biased Training Sets,
Abstract: We present a new solution to the problem of classifying Type Ia supernovae
from their light curves alone given a spectroscopically confirmed but biased
training set, circumventing the need to obtain an observationally expensive
unbiased training set. We use Gaussian processes (GPs) to model the
supernovae's (SN) light curves, and demonstrate that the choice of covariance
function has only a small influence on the GPs ability to accurately classify
SNe. We extend and improve the approach of Richards et al (2012} -- a diffusion
map combined with a random forest classifier -- to deal specifically with the
case of biassed training sets. We propose a novel method, called STACCATO
(SynThetically Augmented Light Curve ClassificATiOn') that synthetically
augments a biased training set by generating additional training data from the
fitted GPs. Key to the success of the method is the partitioning of the
observations into subgroups based on their propensity score of being included
in the training set. Using simulated light curve data, we show that STACCATO
increases performance, as measured by the area under the Receiver Operating
Characteristic curve (AUC), from 0.93 to 0.96, close to the AUC of 0.977
obtained using the 'gold standard' of an unbiased training set and
significantly improving on the previous best result of 0.88. STACCATO also
increases the true positive rate for SNIa classification by up to a factor of
50 for high-redshift/low brightness SNe.