  In many real-world scenarios, it is crucial to be able to reliably and
efficiently reason under uncertainty while capturing complex relationships in
data. Probabilistic circuits (PCs), a prominent family of tractable
probabilistic models, offer a remedy to this challenge by composing simple,
tractable distributions into a high-dimensional probability distribution.
However, learning PCs on heterogeneous data is challenging and densities of
some parametric distributions are not available in closed form, limiting their
potential use. We introduce characteristic circuits (CCs), a family of
tractable probabilistic models providing a unified formalization of
distributions over heterogeneous data in the spectral domain. The one-to-one
relationship between characteristic functions and probability measures enables
us to learn high-dimensional distributions on heterogeneous data domains and
facilitates efficient probabilistic inference even when no closed-form density
function is available. We show that the structure and parameters of CCs can be
learned efficiently from the data and find that CCs outperform state-of-the-art
density estimators for heterogeneous data domains on common benchmark data
sets.
