Monte Carlo Anti-Differentiation for Approximate Weighted Model
  Integration
  Probabilistic inference in the hybrid domain, i.e. inference over
discrete-continuous domains, requires tackling two well known #P-hard problems
1)~weighted model counting (WMC) over discrete variables and 2)~integration
over continuous variables. For both of these problems inference techniques have
been developed separately in order to manage their #P-hardness, such as
knowledge compilation for WMC and Monte Carlo (MC) methods for (approximate)
integration in the continuous domain. Weighted model integration (WMI), the
extension of WMC to the hybrid domain, has been proposed as a formalism to
study probabilistic inference over discrete and continuous variables alike.
Recently developed WMI solvers have focused on exploiting structure in WMI
problems, for which they rely on symbolic integration to find the primitive of
an integrand, i.e. to perform anti-differentiation. To combine these advances
with state-of-the-art Monte Carlo integration techniques, we introduce
\textit{Monte Carlo anti-differentiation} (MCAD), which computes MC
approximations of anti-derivatives. In our empirical evaluation we substitute
the exact symbolic integration backend in an existing WMI solver with an MCAD
backend. Our experiments show that that equipping existing WMI solvers with
MCAD yields a fast yet reliable approximate inference scheme.
