  We introduce a novel conditional density estimation model termed the
conditional density operator (CDO). It naturally captures multivariate,
multimodal output densities and shows performance that is competitive with
recent neural conditional density models and Gaussian processes. The proposed
model is based on a novel approach to the reconstruction of probability
densities from their kernel mean embeddings by drawing connections to
estimation of Radon-Nikodym derivatives in the reproducing kernel Hilbert space
(RKHS). We prove finite sample bounds for the estimation error in a standard
density reconstruction scenario, independent of problem dimensionality.
Interestingly, when a kernel is used that is also a probability density, the
CDO allows us to both evaluate and sample the output density efficiently. We
demonstrate the versatility and performance of the proposed model on both
synthetic and real-world data.
