  Often in machine learning, data are collected as a combination of multiple
conditions, e.g., the voice recordings of multiple persons, each labeled with
an ID. How could we build a model that captures the latent information related
to these conditions and generalize to a new one with few data? We present a new
model called Latent Variable Multiple Output Gaussian Processes (LVMOGP) and
that allows to jointly model multiple conditions for regression and generalize
to a new condition with a few data points at test time. LVMOGP infers the
posteriors of Gaussian processes together with a latent space representing the
information about different conditions. We derive an efficient variational
inference method for LVMOGP, of which the computational complexity is as low as
sparse Gaussian processes. We show that LVMOGP significantly outperforms
related Gaussian process methods on various tasks with both synthetic and real
data.
